The 21st Century Educator - students as partners in teaching and learning Simon Bates
The document discusses using technology and student engagement to improve 21st century education. It provides an example of a case study where students created an online question repository to more deeply engage with formative assessment. This student-generated question bank grew substantially over time and analysis found it improved learning outcomes correlated with students' final exam scores. The document also discusses ensuring high-quality student-generated questions and explanations through scaffolding and rubrics.
A genetic algorithm for a university weekly courses timetabling problemMotasem Smadi
This document presents a genetic algorithm for solving a university weekly course timetabling problem. The timetabling problem involves allocating courses, teachers, rooms and time slots while satisfying constraints. The authors propose a sector-based genetic algorithm that represents timetables as chromosomes. Preliminary experimental results show the algorithm is promising for generating timetables that satisfy constraints. The algorithm uses genetic operators like crossover and mutation to evolve timetable solutions over multiple generations.
Systemic Risk Modeling - André Lucas, April 16 2014SYRTO Project
This document discusses challenges in modeling systemic risk and presents a new class of time series models for systemic risk modeling. It introduces a factor copula model that uses a multivariate skewed-t density with time-varying parameters to assess joint and conditional measures of financial sector risk. The model uses a conditional law of large numbers to efficiently compute risk measures without simulation for high-dimensional, non-Gaussian data. It also defines measures to analyze systemic influence and connectedness within the financial system.
Classes without Dependencies - UseR 2018Sam Clifford
Presented by Sam Clifford at the 2018 UseR conference, Brisbane, Australia. The talk describes the design of SEB113 - Quantitative Methods in Science, a first year statistics/mathematics unit in the Bachelor of Science at Queensland University of Technology. The unit uses RStudio and the tidyverse packages to give students the skills to do meaningful data manipulation and analysis without relying on prior knowledge of advanced mathematics.
An alternative learning experience in transition level mathematicsDann Mallet
QUT Mathematical Sciences Seminar series, November 1 2013
Traditionally at QUT, mathematics and statistics are taught using a face-to-face lecture/tutorial model involving large lecture classes for around 1/2 to 3/4 of the time and smaller group tutorials for the remainder of the time. This is also one of the main models for teaching at other campus-based institutions. Recently, in response to (learning) technology advances and changes in the ways learners seek education, QUT has made a significant commitment to a “Digital Transformation” project across the university. In this seminar I will present a technical overview, with some demonstrations, of a pilot project that seeks to investigate how digital transformation might work in a QUT mathematics or statistics subject. In particular, I will discuss the use of tablet PC technology and specialist software to produce video learning packages. This approach has been trialled in a transition level mathematics unit this semester. I will also cover integration of these learning packages with QUTs Learning Management System “Blackboard”. This seminar is a technical preview to another talk I will give early in the new year that will look at the impact of the altered learning experience on student outcomes, feedback and the unit itself.
S1 - Process product optimization using design experiments and response surfa...CAChemE
An intensive practical course mainly for PhD-students on the use of designs of experiments (DOE) and response surface methodology (RSM) for optimization problems. The course covers relevant background, nomenclature and general theory of DOE and RSM modelling for factorial and optimisation designs in addition to practical exercises in Matlab. Due to time limitations, the course concentrates on linear and quadratic models on the k≤3 design dimension. This course is an ideal starting point for every experimental engineering wanting to work effectively, extract maximal information and predict the future behaviour of their system.
Mikko Mäkelä (DSc, Tech) is a postdoctoral fellow at the Swedish University of Agricultural Sciences in Umeå, Sweden and is currently visiting the Department of Chemical Engineering at the University of Alicante. He is working in close cooperation with Paul Geladi, Professor of Chemometrics, and using DOE and RSM for process optimization mainly for the valorization of industrial wastes in laboratory and pilot scales.”
The document provides guidance on solving physics problems using a general 5-step strategy and the KUDOS method for word problems. It begins with an overview of the learning objectives which are to learn a general problem-solving technique, how to solve word problems, how to prepare for exams, and tips for taking exams. Examples then demonstrate applying the 5-step general strategy and the KUDOS (Known, Unknown, Definitions, Output, Substantiate) method to solve sample physics problems step-by-step. The strategies provide a systematic approach to breaking down problems and connecting known information to unknowns through definitions and equations.
The 21st Century Educator - students as partners in teaching and learning Simon Bates
The document discusses using technology and student engagement to improve 21st century education. It provides an example of a case study where students created an online question repository to more deeply engage with formative assessment. This student-generated question bank grew substantially over time and analysis found it improved learning outcomes correlated with students' final exam scores. The document also discusses ensuring high-quality student-generated questions and explanations through scaffolding and rubrics.
A genetic algorithm for a university weekly courses timetabling problemMotasem Smadi
This document presents a genetic algorithm for solving a university weekly course timetabling problem. The timetabling problem involves allocating courses, teachers, rooms and time slots while satisfying constraints. The authors propose a sector-based genetic algorithm that represents timetables as chromosomes. Preliminary experimental results show the algorithm is promising for generating timetables that satisfy constraints. The algorithm uses genetic operators like crossover and mutation to evolve timetable solutions over multiple generations.
Systemic Risk Modeling - André Lucas, April 16 2014SYRTO Project
This document discusses challenges in modeling systemic risk and presents a new class of time series models for systemic risk modeling. It introduces a factor copula model that uses a multivariate skewed-t density with time-varying parameters to assess joint and conditional measures of financial sector risk. The model uses a conditional law of large numbers to efficiently compute risk measures without simulation for high-dimensional, non-Gaussian data. It also defines measures to analyze systemic influence and connectedness within the financial system.
Classes without Dependencies - UseR 2018Sam Clifford
Presented by Sam Clifford at the 2018 UseR conference, Brisbane, Australia. The talk describes the design of SEB113 - Quantitative Methods in Science, a first year statistics/mathematics unit in the Bachelor of Science at Queensland University of Technology. The unit uses RStudio and the tidyverse packages to give students the skills to do meaningful data manipulation and analysis without relying on prior knowledge of advanced mathematics.
An alternative learning experience in transition level mathematicsDann Mallet
QUT Mathematical Sciences Seminar series, November 1 2013
Traditionally at QUT, mathematics and statistics are taught using a face-to-face lecture/tutorial model involving large lecture classes for around 1/2 to 3/4 of the time and smaller group tutorials for the remainder of the time. This is also one of the main models for teaching at other campus-based institutions. Recently, in response to (learning) technology advances and changes in the ways learners seek education, QUT has made a significant commitment to a “Digital Transformation” project across the university. In this seminar I will present a technical overview, with some demonstrations, of a pilot project that seeks to investigate how digital transformation might work in a QUT mathematics or statistics subject. In particular, I will discuss the use of tablet PC technology and specialist software to produce video learning packages. This approach has been trialled in a transition level mathematics unit this semester. I will also cover integration of these learning packages with QUTs Learning Management System “Blackboard”. This seminar is a technical preview to another talk I will give early in the new year that will look at the impact of the altered learning experience on student outcomes, feedback and the unit itself.
S1 - Process product optimization using design experiments and response surfa...CAChemE
An intensive practical course mainly for PhD-students on the use of designs of experiments (DOE) and response surface methodology (RSM) for optimization problems. The course covers relevant background, nomenclature and general theory of DOE and RSM modelling for factorial and optimisation designs in addition to practical exercises in Matlab. Due to time limitations, the course concentrates on linear and quadratic models on the k≤3 design dimension. This course is an ideal starting point for every experimental engineering wanting to work effectively, extract maximal information and predict the future behaviour of their system.
Mikko Mäkelä (DSc, Tech) is a postdoctoral fellow at the Swedish University of Agricultural Sciences in Umeå, Sweden and is currently visiting the Department of Chemical Engineering at the University of Alicante. He is working in close cooperation with Paul Geladi, Professor of Chemometrics, and using DOE and RSM for process optimization mainly for the valorization of industrial wastes in laboratory and pilot scales.”
The document provides guidance on solving physics problems using a general 5-step strategy and the KUDOS method for word problems. It begins with an overview of the learning objectives which are to learn a general problem-solving technique, how to solve word problems, how to prepare for exams, and tips for taking exams. Examples then demonstrate applying the 5-step general strategy and the KUDOS (Known, Unknown, Definitions, Output, Substantiate) method to solve sample physics problems step-by-step. The strategies provide a systematic approach to breaking down problems and connecting known information to unknowns through definitions and equations.
The document provides guidance on solving physics problems using a general 5-step strategy and the KUDOS method for word problems. It begins with an overview of the learning objectives which are to learn a general problem-solving technique, how to solve word problems, how to prepare for exams, and tips for taking exams. Examples then demonstrate applying the 5-step general strategy and the KUDOS (Known, Unknown, Definitions, Output, Substantiate) method to sample physics word problems.
The document summarizes the Afterschool quantitative aptitude and PGPSE social entrepreneurship program. It provides details about the flexible and practical curriculum aimed at developing social entrepreneurs. The program is available fully online or in person with locations opening in major cities. It focuses on case studies, workshops, and developing entrepreneurship skills through projects and mentorship.
The document provides study material for mathematics for class 10 students of Kendriya Vidyalaya Sangathan. It was prepared by the Patna regional office in accordance with instructions from KVS headquarters. The study material aims to help students understand concepts well and meet quality expectations. It was prepared under the guidance of the Deputy Commissioner with contributions from teachers of KV No. 2 Gaya.
Criteria
Achievement Level
Level 1
Level 2
Level 3
Level 4
Level 5
Depth of Reflection
(50 points)
0 - 29
Response does not consider the theories, concepts, and/or strategies. Viewpoints and interpretations are unclear.
30 - 34
Response reflects a lack of consideration or personalization of the theories, concepts, and/or strategies. Viewpoints and interpretations may be missing, inappropriate, and/or unsupported.
35 - 39
Response reflects minimal consideration and personalization of the theories, concepts, and/or strategies presented. Viewpoints and interpretations may be unsupported or supported with flawed arguments.
40 - 44
Response reflects some consideration and personalization of the theories, concepts, and/or strategies presented. Most viewpoints and interpretations are supported; some may be fairly insightful.
45 - 50
Response reflects in-depth consideration and personalization of the theories, concepts, and/or strategies presented. Viewpoints and interpretations are insightful and supported.
Writing Mechanics
(10 points)
0 - 5
Writing lacks clarity and conciseness. Serious problems with sentence structure and grammar. Numerous major or minor errors in punctuation and/or spelling.
6 - 6
Writing lacks clarity or conciseness. Minor problems with sentence structure and some grammatical errors. Several minor errors in punctuation and/or spelling.
7 - 7
Writing is somewhat clear and concise. Sentence structure and grammar are adequate and mostly correct. Few minor errors in punctuation and/or spelling.
8 - 8
Writing is mostly clear and concise. Sentence structure and grammar are strong and mostly correct. Few minor errors in punctuation and/or spelling.
9 - 10
Writing is clear and concise. Sentence structure and grammar are excellent. Correct use of punctuation. No spelling errors.
Components
(15 points)
0 - 8
The response veers off topic and fails to address the components.
9 - 10
The response does a poor job of addressing the following major components or does not address them: • accurate accounts of the topic area, • critical analysis of the topic area, and • scholarly or professional application of the topic area.
11 - 11
The response addresses some but excludes one or more of the major components: • accurate accounts of the topic area, • critical analysis of the topic area, and • scholarly or professional application of the topic area.
12 - 13
The response addresses most of the major components, but one component is incomplete or insufficient: • accurate accounts of the topic area, • critical analysis of the topic area, and • scholarly or professional application of the topic area.
14 - 15
The response includes all of the major components: • accurate accounts of the topic area, • critical analysis of the topic area, and • scholarly or professional application of the topic area.
Identification of Future Learning Opportunities
(25 points)
0 - 14
Response does not identify any future learning opportunities.
15 - 17
Response demonstrates ...
CC282 Decision trees Lecture 2 slides for CC282 Machine ...butest
This document provides an overview of decision trees and their use in machine learning. It discusses key concepts like concept learning, hypothesis space, inductive learning, and overfitting. It also describes how decision trees work, including how they are constructed using a top-down approach to select the attribute that yields the highest information gain at each step, and how rules can be extracted from fully grown decision trees.
1. The document discusses the Finite Difference Time Domain (FDTD) method for computational electromagnetics (CEM). FDTD solves Maxwell's equations by approximating the derivatives with central finite differences and marching the solution in both space and time.
2. It provides the 1D update equations for the electric and magnetic fields in the FDTD method. The fields are discretized and interleaved in both space and time.
3. The update equations are expressed in terms of the electric and magnetic fields at previous time steps to march the solution forward in time. This allows the fields to be solved for numerically via a computer program.
This document is the first page of a physics exam from the University of Cambridge. It provides instructions to candidates regarding writing their information on the exam, using appropriate materials, and answering all questions. It includes a list of relevant physics formulas, constants, and units that may be used for reference. The exam consists of 15 printed pages and 1 blank page.
This document discusses the steps to solve an engineering problem numerically. It begins with an example of a bascule bridge trunnion getting stuck during assembly due to insufficient contraction from cooling. Better models are developed to estimate the contraction using numerical integration and the solution is to cool it further with liquid nitrogen. The document then outlines various numerical methods like nonlinear equations, differentiation, interpolation, regression, integration, and ODE solving that can be applied to engineering problems.
1. For each of the following code segments, use OpenMP pragmas.docxdurantheseldine
1. For each of the following code segments, use OpenMP pragmas to make the loop parallel, or
explain why the code segment is not suitable for parallel execution.
a. for (i = 0; i < (int) sqrt(x); i++) {
a[i] = i + 12;
if (i < 10) b[i] = a[i];
}
b. flag = 0;
for (i = 0; (i < n) \& (!flag); i++) {
a[i] = 2.8 * i;
if (a[i] < b[i]) flag = 1;
}
c. for (i = 0; i < n; i++) {
a[i] = fun(i);
}
d. for (i = 0; i < n; i++) {
a[i] = fun(i);
if (a[i] < b[i]) b[i] = a[i];
}
e. for (i = 0; i < n; i++) {
a[i] = fun(i);
if (a[i] < b[i]) break;
}
f. product = 0;
for (i = 0; i < n; i++) {
product += a[i] * b[i];
}
g. for (i = j; i < 3 * j; i++) {
a[i] = a[i] + a[i-j];
}
h. for (i = j; i < n; i++) {
a[i] = c * a[i-j];
}
2. Suppose a parallel program completes execution on 32 processors in 348 seconds, and it has
been found that this program spends 21 seconds in initialization and cleanup on one processor, and for
the remaining time all 32 processors are active. What is the scaled speedup of this parallel program?
3. Suppose a parallel program executing on 20 processors spends 98% of its time inside parallel
code. What is the scaled speedup of this parallel program?
4. The table below shows the speedups observed for six different parallel programs A, B, C, D,
E, F as the number of processors is increased from 1 through 8.
Processors Speedup
A B C D E F
1 1.00 1.00 1.00 1.00 1.00 1.00
2 1.60 1.92 1.92 1.96 1.74 1.94
3 2.00 2.73 2.78 2.88 2.30 2.82
4 2.29 3.39 3.57 3.67 2.74 3.65
5 2.50 3.91 4.31 4.46 3.09 4.42
6 2.67 4.29 5.00 5.22 3.38 5.15
7 2.80 4.55 5.65 5.93 3.62 5.84
8 2.91 4.71 6.25 6.25 3.81 6.50
Using the Karp-Flatt metric as the basis, choose the statement that best describes the expected speedup
for each program with 16 processors.
I. The speedup achieved on 16 processors will probably be at least 40% higher than the speedup
achieved on eight processors.
II. The speedup achieved on 16 processors will probably be less than 40% higher than the speedup
achieved on eight processors, due to the increase in overhead as processors are added.
III. The speedup achieved on 16 processors will probably be less than 40% higher than the speedup
achieved on eight processors, due to the large serial component of the computation.
5. Let n ≥ f(p) denote the isoefficiency relation of a parallel system and let M(n) denote the
amount of memory required to store a problem of size n. Use the scalability function to rank the
parallel systems shown below from the most scalable to the least scalable:
a. f(p) = Cp, M(n) = n2.
b. f(p) = C√p, M(n) = n2.
c. f(p) = C√plog p, M(n) = n2.
d. f(p) = Cplog p, M(n) = n2.
e. f(p) = Cp, M(n) = n.
f. f(p) = Cp√p, M(n) = n.
g. f(p) = Cp2√p, M(n) = n.
6. Suppose a problem of size 100,000 can be solved in 15 hours on a computer today. Assuming
that the execution time is solely determined by the CPU speed, d.
This document provides an overview of key concepts from the first chapter of a physics textbook. It introduces why physics is studied, important terminology in physics, use of mathematics in physics, scientific notation and significant figures, units and dimensional analysis, problem-solving techniques, and graphing. Examples are provided for many topics to illustrate physics concepts and calculations involving units, proportions, percentages, and graphing patient temperature data.
Establishing meta-learning metrics when programming Mindstorms EV3 robotsMichael Vallance
Presentation at LTEC 2016 in Hagen, Germany. July 2016.
Abstract. Recently, wider issues of social relationships, contexts, feelings and personal goals have been recognized as impacting upon learning. Moreover, as the Higher Education paradigm appears to be shifting towards students as consumers, there is added pressure on academics to ensure students evaluate and subsequently ‘make sense’ of their educational experiences. This has been termed ‘meta-learning’ but there has been little research on meta-learning compared to the more recognized cognitive science term of metacognition. The paper describes a project in a Japanese university where meta-learning was promoted among first-year Systems Information Science students learning to program LEGO Mindstorms EV3 robots. Students were engaged in a collaborative, creative cycle termed TKF (Tsukutte つくって- Create)/ Katatte かたって- Share)/ Furikaeru ふりかえる- Reflect) to build and program robots to solve systematic problems. This paper will demonstrate that learners actively engaged in iteratively challenging robot-mediated interactive tasks can develop generic, declarative and epistemic competencies, with a consequential development of meta-learning.
This document discusses using a geodesic dome model to simulate economic growth and GDP changes. It describes how structural analysis techniques like the stiffness method used for geodesic domes can be applied to economic problems. Temperature loads on the dome are analogous to economic inputs like investment, spending, and entrepreneurship that cause the GDP to expand. The paper provides equations to calculate strains and stresses on members of the geodesic dome under different economic conditions, representing how the entire economy adjusts to changes. It aims to demonstrate how structural engineering techniques can help economists model and solve economic issues.
This document discusses using a geodesic dome model to simulate economic growth and GDP changes. It describes how structural analysis techniques like the stiffness method used for geodesic domes can be applied to economic problems. Temperature loads on the dome are analogous to increases in economic factors like investment, spending, and entrepreneurship that cause GDP to expand. The paper provides equations to calculate strains, stresses, compatibility, and energy changes in the dome from these "temperature loads" to model their economic effects. It aims to demonstrate how a geodesic dome structure can be used to solve problems studied by econophysics.
The document provides an agenda for a class that includes warm-up exercises solving for variables in equations, reviewing formulas, and class work. Warm-up problems involve solving equations for unknown variables. Formulas covered include perimeter and area of squares, triangles, and the distance and temperature conversion formulas. Class work assignments are listed from problems 2 to 8 on both sides of the paper.
This document outlines the first session of a Calculus Applied to Physics 1 course. It introduces the instructor and expectations for the course. The session aims to teach students about the scientific method and dimensional analysis through exponent algebra. Key concepts covered include the scientific method, dimensional analysis, exponent laws, and example dimensional analysis problems. Students are expected to understand these foundations and be able to perform dimensional analyses by the end of the session.
From Telsa to TESTA: meanderings in chemistry education researchKatherine Haxton
This document summarizes Dr. Katherine Haxton's work developing diagnostic tests to assess student understanding of chemistry concepts. It discusses developing tests to identify alternative conceptions, analyzing student responses, and using insights to improve teaching. Tests were administered to first and second year students in areas like spectroscopy, NMR, and reaction mechanisms. Student confidence levels and prior knowledge were also assessed. Response analysis revealed common errors to target in teaching. The process involves iterative development and refinement of the tests based on data and focus groups. The goal is to better understand student thinking and inform course improvements.
This document summarizes a presentation on using an enclosure method to detect inclusions for the p-Laplace equation from boundary measurements. It introduces Calderon's problem for the p-Laplace equation and discusses prior work. A main idea is to use special oscillating solutions that focus energy on one side of a half-space and define an indicator function based on boundary measurements. It is shown that the indicator function grows exponentially if the inclusion intersects the half-space and decays exponentially if it is outside, allowing recovery of the inclusion's convex hull. Details of the upper and lower bound proofs are provided.
The document discusses assignment problems and their applications. It provides examples of assignment problems involving assigning workers to jobs or tasks. The goal is typically to minimize costs or maximize satisfaction. The document then summarizes a research article that uses a genetic algorithm to solve the specific problem of optimally assigning teachers to courses while considering various constraints.
The document provides a summary of Khan Academy work completed over the weekend, including time spent and subjects covered. It then lists topics covered in today's Khan Academy session, including: warm-up exercises; solving equations for variables; formulas like perimeter and area of shapes, temperature conversions, and absolute value equations; and class work problems.
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
The document provides guidance on solving physics problems using a general 5-step strategy and the KUDOS method for word problems. It begins with an overview of the learning objectives which are to learn a general problem-solving technique, how to solve word problems, how to prepare for exams, and tips for taking exams. Examples then demonstrate applying the 5-step general strategy and the KUDOS (Known, Unknown, Definitions, Output, Substantiate) method to sample physics word problems.
The document summarizes the Afterschool quantitative aptitude and PGPSE social entrepreneurship program. It provides details about the flexible and practical curriculum aimed at developing social entrepreneurs. The program is available fully online or in person with locations opening in major cities. It focuses on case studies, workshops, and developing entrepreneurship skills through projects and mentorship.
The document provides study material for mathematics for class 10 students of Kendriya Vidyalaya Sangathan. It was prepared by the Patna regional office in accordance with instructions from KVS headquarters. The study material aims to help students understand concepts well and meet quality expectations. It was prepared under the guidance of the Deputy Commissioner with contributions from teachers of KV No. 2 Gaya.
Criteria
Achievement Level
Level 1
Level 2
Level 3
Level 4
Level 5
Depth of Reflection
(50 points)
0 - 29
Response does not consider the theories, concepts, and/or strategies. Viewpoints and interpretations are unclear.
30 - 34
Response reflects a lack of consideration or personalization of the theories, concepts, and/or strategies. Viewpoints and interpretations may be missing, inappropriate, and/or unsupported.
35 - 39
Response reflects minimal consideration and personalization of the theories, concepts, and/or strategies presented. Viewpoints and interpretations may be unsupported or supported with flawed arguments.
40 - 44
Response reflects some consideration and personalization of the theories, concepts, and/or strategies presented. Most viewpoints and interpretations are supported; some may be fairly insightful.
45 - 50
Response reflects in-depth consideration and personalization of the theories, concepts, and/or strategies presented. Viewpoints and interpretations are insightful and supported.
Writing Mechanics
(10 points)
0 - 5
Writing lacks clarity and conciseness. Serious problems with sentence structure and grammar. Numerous major or minor errors in punctuation and/or spelling.
6 - 6
Writing lacks clarity or conciseness. Minor problems with sentence structure and some grammatical errors. Several minor errors in punctuation and/or spelling.
7 - 7
Writing is somewhat clear and concise. Sentence structure and grammar are adequate and mostly correct. Few minor errors in punctuation and/or spelling.
8 - 8
Writing is mostly clear and concise. Sentence structure and grammar are strong and mostly correct. Few minor errors in punctuation and/or spelling.
9 - 10
Writing is clear and concise. Sentence structure and grammar are excellent. Correct use of punctuation. No spelling errors.
Components
(15 points)
0 - 8
The response veers off topic and fails to address the components.
9 - 10
The response does a poor job of addressing the following major components or does not address them: • accurate accounts of the topic area, • critical analysis of the topic area, and • scholarly or professional application of the topic area.
11 - 11
The response addresses some but excludes one or more of the major components: • accurate accounts of the topic area, • critical analysis of the topic area, and • scholarly or professional application of the topic area.
12 - 13
The response addresses most of the major components, but one component is incomplete or insufficient: • accurate accounts of the topic area, • critical analysis of the topic area, and • scholarly or professional application of the topic area.
14 - 15
The response includes all of the major components: • accurate accounts of the topic area, • critical analysis of the topic area, and • scholarly or professional application of the topic area.
Identification of Future Learning Opportunities
(25 points)
0 - 14
Response does not identify any future learning opportunities.
15 - 17
Response demonstrates ...
CC282 Decision trees Lecture 2 slides for CC282 Machine ...butest
This document provides an overview of decision trees and their use in machine learning. It discusses key concepts like concept learning, hypothesis space, inductive learning, and overfitting. It also describes how decision trees work, including how they are constructed using a top-down approach to select the attribute that yields the highest information gain at each step, and how rules can be extracted from fully grown decision trees.
1. The document discusses the Finite Difference Time Domain (FDTD) method for computational electromagnetics (CEM). FDTD solves Maxwell's equations by approximating the derivatives with central finite differences and marching the solution in both space and time.
2. It provides the 1D update equations for the electric and magnetic fields in the FDTD method. The fields are discretized and interleaved in both space and time.
3. The update equations are expressed in terms of the electric and magnetic fields at previous time steps to march the solution forward in time. This allows the fields to be solved for numerically via a computer program.
This document is the first page of a physics exam from the University of Cambridge. It provides instructions to candidates regarding writing their information on the exam, using appropriate materials, and answering all questions. It includes a list of relevant physics formulas, constants, and units that may be used for reference. The exam consists of 15 printed pages and 1 blank page.
This document discusses the steps to solve an engineering problem numerically. It begins with an example of a bascule bridge trunnion getting stuck during assembly due to insufficient contraction from cooling. Better models are developed to estimate the contraction using numerical integration and the solution is to cool it further with liquid nitrogen. The document then outlines various numerical methods like nonlinear equations, differentiation, interpolation, regression, integration, and ODE solving that can be applied to engineering problems.
1. For each of the following code segments, use OpenMP pragmas.docxdurantheseldine
1. For each of the following code segments, use OpenMP pragmas to make the loop parallel, or
explain why the code segment is not suitable for parallel execution.
a. for (i = 0; i < (int) sqrt(x); i++) {
a[i] = i + 12;
if (i < 10) b[i] = a[i];
}
b. flag = 0;
for (i = 0; (i < n) \& (!flag); i++) {
a[i] = 2.8 * i;
if (a[i] < b[i]) flag = 1;
}
c. for (i = 0; i < n; i++) {
a[i] = fun(i);
}
d. for (i = 0; i < n; i++) {
a[i] = fun(i);
if (a[i] < b[i]) b[i] = a[i];
}
e. for (i = 0; i < n; i++) {
a[i] = fun(i);
if (a[i] < b[i]) break;
}
f. product = 0;
for (i = 0; i < n; i++) {
product += a[i] * b[i];
}
g. for (i = j; i < 3 * j; i++) {
a[i] = a[i] + a[i-j];
}
h. for (i = j; i < n; i++) {
a[i] = c * a[i-j];
}
2. Suppose a parallel program completes execution on 32 processors in 348 seconds, and it has
been found that this program spends 21 seconds in initialization and cleanup on one processor, and for
the remaining time all 32 processors are active. What is the scaled speedup of this parallel program?
3. Suppose a parallel program executing on 20 processors spends 98% of its time inside parallel
code. What is the scaled speedup of this parallel program?
4. The table below shows the speedups observed for six different parallel programs A, B, C, D,
E, F as the number of processors is increased from 1 through 8.
Processors Speedup
A B C D E F
1 1.00 1.00 1.00 1.00 1.00 1.00
2 1.60 1.92 1.92 1.96 1.74 1.94
3 2.00 2.73 2.78 2.88 2.30 2.82
4 2.29 3.39 3.57 3.67 2.74 3.65
5 2.50 3.91 4.31 4.46 3.09 4.42
6 2.67 4.29 5.00 5.22 3.38 5.15
7 2.80 4.55 5.65 5.93 3.62 5.84
8 2.91 4.71 6.25 6.25 3.81 6.50
Using the Karp-Flatt metric as the basis, choose the statement that best describes the expected speedup
for each program with 16 processors.
I. The speedup achieved on 16 processors will probably be at least 40% higher than the speedup
achieved on eight processors.
II. The speedup achieved on 16 processors will probably be less than 40% higher than the speedup
achieved on eight processors, due to the increase in overhead as processors are added.
III. The speedup achieved on 16 processors will probably be less than 40% higher than the speedup
achieved on eight processors, due to the large serial component of the computation.
5. Let n ≥ f(p) denote the isoefficiency relation of a parallel system and let M(n) denote the
amount of memory required to store a problem of size n. Use the scalability function to rank the
parallel systems shown below from the most scalable to the least scalable:
a. f(p) = Cp, M(n) = n2.
b. f(p) = C√p, M(n) = n2.
c. f(p) = C√plog p, M(n) = n2.
d. f(p) = Cplog p, M(n) = n2.
e. f(p) = Cp, M(n) = n.
f. f(p) = Cp√p, M(n) = n.
g. f(p) = Cp2√p, M(n) = n.
6. Suppose a problem of size 100,000 can be solved in 15 hours on a computer today. Assuming
that the execution time is solely determined by the CPU speed, d.
This document provides an overview of key concepts from the first chapter of a physics textbook. It introduces why physics is studied, important terminology in physics, use of mathematics in physics, scientific notation and significant figures, units and dimensional analysis, problem-solving techniques, and graphing. Examples are provided for many topics to illustrate physics concepts and calculations involving units, proportions, percentages, and graphing patient temperature data.
Establishing meta-learning metrics when programming Mindstorms EV3 robotsMichael Vallance
Presentation at LTEC 2016 in Hagen, Germany. July 2016.
Abstract. Recently, wider issues of social relationships, contexts, feelings and personal goals have been recognized as impacting upon learning. Moreover, as the Higher Education paradigm appears to be shifting towards students as consumers, there is added pressure on academics to ensure students evaluate and subsequently ‘make sense’ of their educational experiences. This has been termed ‘meta-learning’ but there has been little research on meta-learning compared to the more recognized cognitive science term of metacognition. The paper describes a project in a Japanese university where meta-learning was promoted among first-year Systems Information Science students learning to program LEGO Mindstorms EV3 robots. Students were engaged in a collaborative, creative cycle termed TKF (Tsukutte つくって- Create)/ Katatte かたって- Share)/ Furikaeru ふりかえる- Reflect) to build and program robots to solve systematic problems. This paper will demonstrate that learners actively engaged in iteratively challenging robot-mediated interactive tasks can develop generic, declarative and epistemic competencies, with a consequential development of meta-learning.
This document discusses using a geodesic dome model to simulate economic growth and GDP changes. It describes how structural analysis techniques like the stiffness method used for geodesic domes can be applied to economic problems. Temperature loads on the dome are analogous to economic inputs like investment, spending, and entrepreneurship that cause the GDP to expand. The paper provides equations to calculate strains and stresses on members of the geodesic dome under different economic conditions, representing how the entire economy adjusts to changes. It aims to demonstrate how structural engineering techniques can help economists model and solve economic issues.
This document discusses using a geodesic dome model to simulate economic growth and GDP changes. It describes how structural analysis techniques like the stiffness method used for geodesic domes can be applied to economic problems. Temperature loads on the dome are analogous to increases in economic factors like investment, spending, and entrepreneurship that cause GDP to expand. The paper provides equations to calculate strains, stresses, compatibility, and energy changes in the dome from these "temperature loads" to model their economic effects. It aims to demonstrate how a geodesic dome structure can be used to solve problems studied by econophysics.
The document provides an agenda for a class that includes warm-up exercises solving for variables in equations, reviewing formulas, and class work. Warm-up problems involve solving equations for unknown variables. Formulas covered include perimeter and area of squares, triangles, and the distance and temperature conversion formulas. Class work assignments are listed from problems 2 to 8 on both sides of the paper.
This document outlines the first session of a Calculus Applied to Physics 1 course. It introduces the instructor and expectations for the course. The session aims to teach students about the scientific method and dimensional analysis through exponent algebra. Key concepts covered include the scientific method, dimensional analysis, exponent laws, and example dimensional analysis problems. Students are expected to understand these foundations and be able to perform dimensional analyses by the end of the session.
From Telsa to TESTA: meanderings in chemistry education researchKatherine Haxton
This document summarizes Dr. Katherine Haxton's work developing diagnostic tests to assess student understanding of chemistry concepts. It discusses developing tests to identify alternative conceptions, analyzing student responses, and using insights to improve teaching. Tests were administered to first and second year students in areas like spectroscopy, NMR, and reaction mechanisms. Student confidence levels and prior knowledge were also assessed. Response analysis revealed common errors to target in teaching. The process involves iterative development and refinement of the tests based on data and focus groups. The goal is to better understand student thinking and inform course improvements.
This document summarizes a presentation on using an enclosure method to detect inclusions for the p-Laplace equation from boundary measurements. It introduces Calderon's problem for the p-Laplace equation and discusses prior work. A main idea is to use special oscillating solutions that focus energy on one side of a half-space and define an indicator function based on boundary measurements. It is shown that the indicator function grows exponentially if the inclusion intersects the half-space and decays exponentially if it is outside, allowing recovery of the inclusion's convex hull. Details of the upper and lower bound proofs are provided.
The document discusses assignment problems and their applications. It provides examples of assignment problems involving assigning workers to jobs or tasks. The goal is typically to minimize costs or maximize satisfaction. The document then summarizes a research article that uses a genetic algorithm to solve the specific problem of optimally assigning teachers to courses while considering various constraints.
The document provides a summary of Khan Academy work completed over the weekend, including time spent and subjects covered. It then lists topics covered in today's Khan Academy session, including: warm-up exercises; solving equations for variables; formulas like perimeter and area of shapes, temperature conversions, and absolute value equations; and class work problems.
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
ESA/ACT Science Coffee: Diego Blas - Gravitational wave detection with orbita...Advanced-Concepts-Team
Presentation in the Science Coffee of the Advanced Concepts Team of the European Space Agency on the 07.06.2024.
Speaker: Diego Blas (IFAE/ICREA)
Title: Gravitational wave detection with orbital motion of Moon and artificial
Abstract:
In this talk I will describe some recent ideas to find gravitational waves from supermassive black holes or of primordial origin by studying their secular effect on the orbital motion of the Moon or satellites that are laser ranged.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
Immersive Learning That Works: Research Grounding and Paths ForwardLeonel Morgado
We will metaverse into the essence of immersive learning, into its three dimensions and conceptual models. This approach encompasses elements from teaching methodologies to social involvement, through organizational concerns and technologies. Challenging the perception of learning as knowledge transfer, we introduce a 'Uses, Practices & Strategies' model operationalized by the 'Immersive Learning Brain' and ‘Immersion Cube’ frameworks. This approach offers a comprehensive guide through the intricacies of immersive educational experiences and spotlighting research frontiers, along the immersion dimensions of system, narrative, and agency. Our discourse extends to stakeholders beyond the academic sphere, addressing the interests of technologists, instructional designers, and policymakers. We span various contexts, from formal education to organizational transformation to the new horizon of an AI-pervasive society. This keynote aims to unite the iLRN community in a collaborative journey towards a future where immersive learning research and practice coalesce, paving the way for innovative educational research and practice landscapes.
The technology uses reclaimed CO₂ as the dyeing medium in a closed loop process. When pressurized, CO₂ becomes supercritical (SC-CO₂). In this state CO₂ has a very high solvent power, allowing the dye to dissolve easily.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
4. 6 new courses
Core Course :
1.Quantum Chemistry-II [CC-5-11-TH ; PHYS CHEM-4 , Sem-5]
2.Numerical Analysis [CC-5-11-TH ; PHYS CHEM-4 , Sem-5]
3.Practical : Based on Numerical Analysis [CC-5-11-P, Sem-5]
4. SEC 1 – MATHEMATICS AND STATISTICS FOR CHEMISTS; Sem-3
5. DSE-A2: APPLICATIONS OF COMPUTERS IN CHEMISTRY; Sem-5
6. DSE-A2-Practical: APPLICATIONS OF COMPUTERS IN CHEMISTRY; Sem-5
Expectation from PCTF: On
Introduction: What/why/how?
Outline (brief)
Detailed Content (with handouts?)
Exercises/Problems (with Hints/solutions?)
Q-A [Objective (SCQ, MCQ) + others
Emphasis/effective delivery
Effective References
Anything Else…?
You all are welcome
to
contribute
From either side…
5. Workshop [24/05/2018, Gokhale College]
Debasish, Kingshuk, Chaitali, Sukanya, …On
From Teacher Centric Student Centric. ?. !. …
Or, a deep rooted one!!!
Syllabus: content &
its distribution
Assessment /
ExamTeaching/covering the syllabus
CBCS and PCTF
New Topics ?
Objectives?
Objective?
“the goals of teaching and learning science include
knowledge (cognition), emotion and motivation.”
6. Objective Soft Skills Values/
Ethics
Teaching
Team work
Communication
Leadership
Time Management
Human Values
Professional Ethics
< 10% of sanctioned posts
Innovation/
Entrepreneurship
Display Skills/Talents
Employment/ self
Employment
Higher Studies
Link with society &
Industry
To The VC of all Universities
24/05/2018; Target Year: 2022
UGC Quality Mandate
Believe: Only Degrees do not make us qualified to be Teachers.
7. Induction
Program
ICT based Exam
Reforms
RC/OP
Concept/
Application
On Duty
To The VC of all Universities
24/05/2018; Target Year: 2022
UGC Quality Mandate [Initiative]
Research
Power point
On-Line (Net)
Critical
Thinking
100 % of them are Oriented about
the latest and emerging trends
The Pedagogies that translate their knowledge to he students.
Don’t believe: “Great teachers are Born, not made”
8. Teaching: The Middle Way
Formal lecture facilitation
“Inspiration >> information.”
Education= Teaching +Fostering
Mutual Growth,
Fostering Each Other
Shared Commitment
Classroom Level:
Originality, Creativity, Awareness
Human Education:
Capable of
Value CreatingBenefit
Co-living toward Personally and Socially beneficial Ends.
Oneness with the Teacher
Dialogic Process
Two components of Education
And Learning
Happy?relative Relative
Outward/
Material
QuestMiddle way/
combined
BeautyGood
9. Eugene Wigner’s two minutes Nobel speech
1963, (Nobel in Physics): Theory of atomic nucleus and elementary particles; through
the discovery and application of fundamental symmetry principles. [Google search]
He taught me…
Science begins with and consists in assimilating the coherence in a body
of phenomena and creating concepts to express these regularities in a
natural way. It is this method of science rather than the concepts
themselves (such as energy) which should be applied to (other fields of)
learning.
A student remembers his Teacher: Michael Polanyi-Wigner
How to Learn rather than learning the Topics only
“Education is what remains long after the lesson-content we were
taught has been forgotten”
Daisaku Ikeda, Educator
10. CBCS and PCTF
More syllabus-Load in Lesser Time
OSAG in stead of spoon feeding/ rote learning
Be Smart along with Chalk & Talk
Trust and Rely on, have confidence in your students
Thermodynamics
as a Model
Open
Show
Awaken
Guide
11. A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
A few fundamentals
First and second law on the same footings
Joule and Joule-Thomson: On the same footings
Show
2. Be picturesque, be Graphical
statements of second law;
Third law: dS versus S
3. Revisit the concepts
Ek Dozen Satyi-Mithye (T/F) Gappo
Awaken
4. Effective Learning: Concept map rather
than concepts only
5. Problems rather than Exercise
Understanding conventions, assumptions and
approximations
One single problem is enough!
6. Fun in finding/discovering Pattern
P Club vs. V Club:
Thermodynamics is reduced by 50%
Fun with Transformation: The Maths behind the P-
V rivalry!
7. Learning: An Interactive, Joyful
experience
Playing through Quiz, SCQ, and MCQ.
Postscript
Assessment, Timeline, What Next, References
Open Guide
12. A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
A few fundamentals
First and second law on the same
footings
Joule and Joule-Thomson: On the
same footings
2. Be picturesque, be Graphical
statements of second law;
Third law: dS versus S
3. Revisit the concepts
Ek Dozen Satyi-Mithye (T/F) Gappo
4. Effective Learning: Concept map rather than
concepts only
5. Problems rather than Exercise
Understanding conventions, assumptions and approximations
One single problem is enough!
6. Fun in finding/discovering Pattern
P Club vs. V Club:
Thermodynamics is reduced by 50%
Fun with Transformation: The Maths behind the P-V rivalry!
7. Learning: An Interactive, Joyful experience
Playing through Quiz, SCQ, and MCQ.
13. Physical &
Chemical
Processes
developing models to describe physical and
chemical processes;
David Ball in his textbook Physical Chemistry
Success= thinking about a system macroscopically, at the
molecular level, and mathematically.
The First Day in a CBCS-Physical Chemistry Class
Its Relevance,
Its uniqueness,
Its Beauty/attraction
Challenge:
how to engage students in Learning endeavors?
What do they need to be successful?
Macroscopic Molecular-Level Mathematical
Pressure Point mass, PV=RT
volume less
Liquification inter mol Lennard-Jones
of gas, TC etc forces van der Waals
Preparation Attractive/repulsive μJT = (∂T/∂P)H
of liq Nitrogen intermolecular forces
14. Subscripts are important
(∂z/∂x) = (∂z/∂y) .(∂y/∂x)
(∂z/∂x)= [1/(∂y/∂z)] [1/(∂x/∂y)
(∂z/∂x) (∂y/∂z) (∂x/∂y) = 1 (∂x/∂y) (∂y/∂z) (∂z/∂x) = 1 ;
but Euler cyclic/chain relation is (∂x/∂y) (∂y/∂z) (∂z/∂x) = −1
In fact. for, z = f (x,y),
The relation is (∂x/∂y)z (∂y/∂z)x(∂z/∂x)y = -1
R R R
For ideal gas
(∂U/∂V)T = (∂H/∂P)T = 0
(∂U/∂P)T = (∂U/∂V)T (∂V/∂P)T
(∂H/∂V)T = (∂H/∂P)T (∂P/∂V)T
(∂U/∂P)T = (∂H/∂V)T = 0
1 = -1
2 = 0 ?
15. More fundamentally,
Mala Badal…
z = f (x,y): Is dz exact differential? Is Z state function?
Prescription: (∂2z/∂y∂x) = (∂2z/∂x∂y) … (A)
Fundamentally: dz = M(x,y) dx + N(x,y) dy
If (∂M/∂y)x = (∂N/∂x)y Then dz is exact. Is it equivalent to (A)?
dz = M(x,y) dx + N(x,y) dy
dz = (∂z/∂x)y dx + (∂z/∂y)T dy
(∂M/∂y)x = (∂N/∂x)y (∂2z/∂y∂x) = (∂2z/∂x∂y) …(A)
For Volume, V: (∂2V/∂P∂T) = (∂2V/∂T∂P);
What about Work= -pdV?
dV = (∂V/∂P)T dP + (∂V/∂T)P dT
(∂2V/∂P∂T) = (∂2V/∂T∂P)= -R/P2
dV = (-RT/P2) dP + (R/P) dT
-pdV = (RT/P) dP + (-R) dT
(∂M/∂y)x = R/P but
(∂N/∂x)y = 0
So, w=-pdV is not exact.
16. Joule coefficient (μJ)
Extensive or Intensive?
μJ = (-1/CV) (∂U/∂V)T
(∂U/∂V)T ratio of two extensive intensive;
CV not independent of size μJ is not intensive;
CV 2CV, μJ (1/2) μJ ;
μJ is not additive;
so not extensive either.
So, μJ is neither intensive, nor extensive.
Mass dependent? P = n R T /V; P =f(m) or P = (1/3)m n c2, P=f(m) ?
Additivity or size-dependence:
Z = Zi, for all i (intensive); or Z = ∑i Zi (extensive). Size Dependent?
YESNO
Intensive
Keq , ∏
YESNO
Additive
Neither/Nor
μJ
Extensive
V U H
17. Entropy
Definition, origin, significance
• dS =qrev/T why rev? what for irreversible?
S is not defined but dS
• Carnot cycle; §q/T =0
• dU = dq – PdV
CVdT = dq – RT dV/V [rev., trouble in integration]
CVdT/T = dq/T - RdV/V [No trouble]
• S Randomness or disorder-ness? Subjective!
How comes from qrev/T?
• qrev /T justifies Clausius statement.
• S= kB ln W
18. On the same footing
Joule experiment
The Cause: ∆V
The Effect: ∆T
The Constant: U
Effect/Cause : ΔT/ ΔV
The coefficient: μJ = (∂T/∂V)U
Expression: =-(1/CV) (∂U/∂V)T
For ideal gas: μJ =0; ΔT = 0
Observation
Status: Wrong
Joule-Thomson
∆ P
∆T
H
ΔT/ΔP
μJT =(∂T/∂P)H
=-(1/CP) (∂H/∂P)T
μJT =0; ΔT = 0
Right
μJT = - (V/CP)[ CV μJ к - P к + 1]
Levine, Prob. 2.35, Page-75
19. Each of q, w, ΔU and ΔH is positive, zero or
negative?
Joule experiment
q = 0 ; adiabatic
w = 0; Pex =0, w=-P dV
ΔU = q + w = 0
ΔH = ΔU + Δ(PV)
= nR ΔT
=0 [ΔT = 0 as μJ =0]
Joule-Thomson experiment
q = 0 ; adiabatic
ΔH = 0
as μJT =0 for a perfect gas,
So, ΔT = 0 ,
hence ΔU = CV ΔT = 0
w = ΔU – q = 0 – 0
w = 0
20. 1st and 2nd Law on same footings
1st law [Phalo kaRi makho tel]
• Conservation
• possibility
• Introduces U
• dU = q + w
• ∆U =0, isolated system
• PMM-I not possible.
• PMM-I: keeps on doing work
without any supply of energy.
2nd law [a natural Tax]
• Spontaneity/direction
• Feasibility
• Introduces S
• ds=qrev /T
• ∆S ≥ 0, isolated system.
• PMM-II not possible
• PMM-II: Which can draw energy
and do work but does not
require a sink.
21. 1st and 2nd Law on same footings
1st law [Phalo kaRi makho tel]
• Carnot engine, ∆U =0
-w= qnet = qh – qc ;
Silence: qc =0?, -w = qh
Silence broken: 2nd law
-w ≠ qh ; complete
conversion of heat into
work is not possible.
2nd law [a natural Tax]
• Carnot engine:
-w/qh = (Th – Tc)/Th ; Th > Tc
Silence: Tc =0? –w=qh
Silence broken: Third Law
Tc ≠ 0; Absolute zero is not
possible.
22. A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
A few fundamentals
First and second law on the same footings
Joule and Joule-Thomson: On the same footings
2. Be picturesque, be Graphical
statements of second law;
Third law: dS versus S
3. Revisit the concepts
Ek Dozen Satyi-Mithye (T/F) Gappo
4. Effective Learning: Concept map rather
than concepts only
5. Problems rather than Exercise
Understanding conventions, assumptions and
approximations
One single problem is enough!
6. Fun in finding/discovering Pattern
P Club vs. V Club:
Thermodynamics is reduced by 50%
Fun with Transformation: The Maths behind the P-V
rivalry!
7. Learning: An Interactive, Joyful
experience
Playing through Quiz, SCQ, and MCQ.
23. No Sink: qC = 0 or TH = TC
Kelvin statement
qC=0
-w=qH
qH
-w/qH = (TH – TC)/TH ; for TC=TH , -w = 0, No work.
Kelvin: No cyclic process is possible in which heat is taken
from a hot source and converted completely into work”.
24. Let us keep a sink at TC < TH but effectively qC =0
Th
Tc
qC
qC qH
qC
-w=qH – qC
-w= qH – qC
Unfortunately, C is not possible: The Clausius statement.
“ heat does not pass from a body at low temperature
to one at high temperature without any change elsewhere”.
qH – qC
C N P
If Kelvin= 2nd Law then is Clausius=third Law?
No! They are Equivalent.
25. Why an anti-Clausius device does not exist?
Equivalence with Entropy statement
Th
Tc
q
ΔSc = - q/Tc
ΔSh = + q/Th
ΔSdevice = 0 [cyclic]
ΔSsurr = ΔSc + ΔSh
ΔSuniv = - q/Tc + q/Th
= q(Tc – Th)/(TcTh)
< 0 [Th > Tc]
But, ΔSuniv ≥ 0 [2nd law]
So the device violates the 2nd law.
26. The Third Law?
S is defined!
• No new state function like U (1st) and S (2nd), or exact differential
like dU and dS
• No new PMM-impossibility ; Only refers to T(0th)and S (2nd )
Unattainability of T=0
LtT0 S = 0 [only after statistical interpretation].
• dS = kB dln W S = kB ln W? by integration?
• S = kB ln W + S0 S0 = 0? Third Law is there.
• LtT0 ΔS =0; LtT0 S=0,;
LtT0 S = LtT0 (kB ln W) + S0
0 (3rd law) = kB ln 1 + S0 = 0 + S0
or, S0 = 0; therefore S = kB lnW
27. A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
A few fundamentals
First and second law on the same footings
Joule and Joule-Thomson: On the same footings
2. Be picturesque, be Graphical
statements of second law;
Third law: dS versus S
3. Revisit the concepts
Ek Dozen Satyi-Mithye (T/F)
Gappo
4. Effective Learning: Concept map rather
than concepts only
5. Problems rather than Exercise
Understanding conventions, assumptions and
approximations
One single problem is enough!
6. Fun in finding/discovering Pattern
P Club vs. V Club:
Thermodynamics is reduced by 50%
Fun with Transformation: The Maths behind the P-V
rivalry!
7. Learning: An Interactive, Joyful
experience
Playing through Quiz, SCQ, and MCQ.
28. Ek Dozen Satyi-Mithye Gappo
1. Isothermal ΔT = Tf – Ti = 0?
ΔT = 0 isothermal?
2. U remains constant in every isothermal process in a
closed system. T/F?
False. Only for perfect gas U=f(T, only).
Isothermal pressure change, average intermolecular
distance and hence its contribution to U through
intermolecular interaction will change.
True
False
29. Ek Dozen Satyi-Mithye Gappo
3. 1∫2 (1/V)dV = ln(V2 – V1 ) or (lnV2)/(lnV1)?
Both False. Its ln(V2/V1)
4. 1∫2 T dT = (1/2)(T2 – T1)2
False. Its (1/2)(T2
2 – T1
2 )
5. ΔU is a state function.
False. ΔU is the change in a state function.
6. For a closed system at rest in the absence of external fields, U
= q + w.
Its ΔU = q + w
30. Ek Dozen Satyi-Mithye Gappo
7. PV = k1 and V/T = k2
So, PV . V/T = k1 k2 = k
Or, PV2 /T = k; is it not PV/T = k?
8. A perfect gas [Cv,m ≠f(T) & = 3 R] expands adiabatically into vacuum
to double its initial volume.
Banga: T2/T1 = (V/2V)ϒ-1 = (V/2V)R/3R or T2 = T1/21/3 .
Bangla: ΔU =q+w =0+0 =0 and ΔU= Cv ΔT=0, so, T2 =T1
Who is correct?
T2 = T1 is correct. [since irreversible].
PV=c and PVγ =c
How both refer to
Ideal Gas?
Reversible
in which
step?
31. Ek Dozen Satyi-Mithye Gappo
9. Enthalpy (H) is called Heat Content. Why? Why
misleading?
ΔH = qp
Mislead to think that q is a state function.
10. Δq or Δw; should we write?
q and w are not state functions.
Not change of heat of a system but heat transfer in a
process?
Not work of a system but work involved in a process.
32. Ek Dozen Satyi-Mithye Gappo
11. ΔH = qp for a constant-pressure process. if P is not
constant throughout but Pinitial = Pfinal. Is ΔH=q here?
No. For example, in a cyclic process, ΔH = 0 but q
need not be zero, since q is not a state function.
12. ΔS > 0 [2nd law] and (dU)S,V > 0 or (dH)S,P > 0
[Clausius inequality]; both are criteria for
spontaneity. Don’t they contradict each other?
No. S of what? Of universe [2nd law] and of system in
Clausius inequality.
33. A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
A few fundamentals
First and second law on the same footings
Joule and Joule-Thomson: On the same
footings
2. Be picturesque, be Graphical
statements of second law;
Third law: dS versus S
3. Revisit the concepts
Ek Dozen Satyi-Mithye (T/F) Gappo
4. Effective Learning:
Concept map rather than
concepts only
5. Problems rather than Exercise
Understanding conventions, assumptions
and approximations
One single problem is enough!
6. Fun in finding/discovering
Pattern
P Club vs. V Club:
Thermodynamics is reduced by 50%
Fun with Transformation: The Maths behind
the P-V rivalry!
7. Learning: An Interactive, Joyful
experience
Playing through Quiz, SCQ, and MCQ.
34. Thermodynamic
Equation of State
What is
it?
Derivation Applying Reverse Journey
Joules Law
Ideal gas
Exact
Differential
State function
1st/2nd
Laws
Maxwell
Relations
Three Gases
PV=RT
P(V-b)=RT
V d W gas
Ideal Gas Real Gas
U &H= f(T,only)
Ideal=Perfect?
(∂CV /∂V)T
(∂CP /∂P)T
(∂H/∂P)T is better
internal pressure:a/V2
Molecular insight, IMF
Atomicity & CV
CUQ-2018: other properties
Pattern
Entropy Meter?
WHY?
Equation of state
Thermodynamic
CONCEPT MAP: An Example,
Integrated & coherent cognition, interconnected, deeper insight,
Making sense, Learning how to learn
Statistical
Partition function
35. S p
TV
(+)
U=f(S,V)
dU=TdS-PdV
(∂P/∂S)V
= - (∂T/∂V)S
H=f(S,P)
dH=TdS + VdP
(∂S/∂V)T = (∂P/∂T)V
G=f(P,T)
dG=VdP-SdT
(∂S/∂P)T = - (∂V/∂T)P
A=f(V,T)
dA=-PdV – SdT
(∂S/∂V)T = (∂P/∂T)V
(−)
dz = M(x,y) dx + N(x,y) dy
Samrajnee from some
answerscript
36. Relation between μJT and μJ
A Good Exercise on mathematical relations
Levine, unsolved Prob. 2.35, Page-75
μJT = - (V/CP)[ CV μJ к - P к + 1]
μJ = (∂T/∂V)U = -(1/CV) (∂U/∂V)T ; (∂U/∂V)T = -CV μJ
μJT = (∂T/∂P)H = -(1/CP) (∂H/∂P)T ; (∂H/∂P)T = -CP μJT
H = U + PV
(∂H/∂P)T = (∂U/∂P)T + P(∂V/∂P)T + V
= (∂U/∂V)T (∂V/∂P)T – PV к + V
-CP μJT = [-CV μJ] [-V к ] – PV к + V
= V [CV μJ к – P к + 1]
μJT = - (V/CP)[ CV μJ к - P к + 1]
37. A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
A few fundamentals
First and second law on the same footings
Joule and Joule-Thomson: On the same footings
2. Be picturesque, be Graphical
statements of second law;
Third law: dS versus S
3. Revisit the concepts
Ek Dozen Satyi-Mithye (T/F) Gappo
4. Effective Learning: Concept map rather
than concepts only
5. Problems rather than Exercise
Understanding conventions,
assumptions and
approximations
One single problem is enough!
6. Fun in finding/discovering Pattern
P Club vs. V Club:
Thermodynamics is reduced by 50%
Fun with Transformation: The Maths behind the P-V
rivalry!
7. Learning: An Interactive, Joyful
experience
Playing through Quiz, SCQ, and MCQ.
38. Understanding Physical Chemistry = understanding
conventions, assumptions and approximations
A problem on liquid water: as simple as water:
Water (liq) is vaporized at 1000 C and 1.013 bar. The heat of
vaporization is 40.69 kJ mol-1 . Find the values in kJ mol-1 of (a)
w, (b) q, (c) ΔU, and (d) ΔH.
Assumption
water vapor is ideal,
Volume of liq water is negligible.
W=-PΔV ̴ -P(Vvap) = RT -3.10
q= heat of vaporization 40.69
ΔU= q+w 37.59
ΔH= ΔU + Δ(PV) = ΔU+ P ΔV = ΔU +RT 40.69 = ΔHvap
39. Understanding Physical Chemistry =
understanding
conventions, assumptions and approximations
Consider a n-particle, 2-level system. Evaluate W1:1 and
Wtotal. Compare the results. Comment.
W= n!/Пi ni! W1:1 = (n/2)! / (n/2)!2
ln W1:1 = n ln2 = ln Wtotal
Its good! But too good to be true!
Why?
N w
1 2 (H T)
2 4 (HH, HT, TH, TT)
3 8 ( HHH
HHT HTH THH
TTH THT HTT
TTT)
N ?
40. So much from a single equation
RT ln KP = - ΔG0 (T) or, KP = Exp[- ΔG0 /RT]
ΔG0 mol-1 ? per mole of equation/reaction
KP is
Dimensionless
≠ f(P)
= f(stoichiometry)
= f(standard state)
Dimensional Analysis
[any coefficient= effect/cause
CP – CV = T V αm / βn
α = (1/V) (∂V/∂T)P
; β = (-1/V) (∂V/∂P)T
41. One single problem is enough!
[four in one, in fact]
1 mole ideal gas at T1 and P1 expands (or compresses) to P2 . Calculate q, w, ∆U,
∆H, ∆S.
To start with: w=-pexdV; ∆U = CV ∆T; ∆H=CP ∆T (ideal); ∆U=q+w ∆S=qrev /T
. Process? .
Iso, rev. Iso, irrev. Adia, rev. Adia, irrev.
T2 =T1 ; ∆T =0= ∆U= ∆H q=0, w= ∆U;
∆U=q+w; q=-w, only w! w or ∆U, hence T2 needed.
rev w= irrev rev T2= irrev
-RTln(P1/P2) -P2 (V2–V1) TPR/Cp=c w= ∆U
= -RT(1-P2/P1) gives T2 -P2(V2– V1)=CV∆T
T2=[CV +(P2/P1)R](T1/CP )
∆S=qrev /T ∆S≠qirrev /T but final
states are same; (T1,P2) ∆S=qrev /T , which T? T1 or T2?
So, ∆S=qrev /T= Rln(P1/P2) in both the cases. = 0 ∆S=CV ln(T2/T1)+Rln(P1/P2)
42. All four problems in a single frame
• Isothermal (a) reversible, (b) irreversible
• Adiabatic (c) reversible, (d) irreversible
• One mole of a perfect gas at 300 K and 106 Pa expands to 105 Pa.
Calculate w, q, ΔU, and ΔH for each process. [cV = 1.5R]
V2 T2 -W q ΔU ΔH
(a) 10V1 T1 RT ln(P1/P2) -w 0 0
(b) 10V1 T1 P2(V2-V1) -w 0 0
=RT[1-P2/P1]
(c) 3.98V1 T1(P2/P1)R/Cp -ΔU 0 CVΔT CPΔT
(d) 6.40V1 T1[CV+(P2/P1)R]/Cp - ΔU 0 CVΔT CPΔT
43. All four problems in a single frame
• Isothermal (a) reversible, (b) irreversible
• Adiabatic (c) reversible, (d) irreversible
• One mole of a perfect gas at 300 K and 106 Pa expands to 105 Pa.
Calculate w, q, ΔU, and ΔH for each process. [cV = 1.5R]
• T1 =300K, P1=106 Pa, V1,
V2 T2 -W q ΔU ΔH
(a) 10V1 T1 5744.0 5744.0 0 0
(b) 10V1 T1 2245.0 2245.0 0 0
(c) 3.98V1 119.4 2252.0 0 -2252 -3753
(d) 6.40V1 192.0 1347.0 0 -1347 -2245
T in K; energy in J
44. A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
A few fundamentals
First and second law on the same footings
Joule and Joule-Thomson: On the same footings
2. Be picturesque, be Graphical
statements of second law;
Third law: dS versus S
3. Revisit the concepts
Ek Dozen Satyi-Mithye (T/F) Gappo
4. Effective Learning: Concept map rather
than concepts only
5. Problems rather than Exercise
Understanding conventions, assumptions and
approximations
One single problem is enough!
6. Fun in finding/discovering
Pattern
P Club vs. V Club:
Thermodynamics is reduced by
50%
Fun with Transformation: The
Maths behind the P-V rivalry!
7. Learning: An Interactive, Joyful
experience
Playing through Quiz, SCQ, and MCQ.
45. Your Club vs. Our Club: P vs. V
Thermodynamics is reduced to/by 50%
• dU = q – PdV (first law)
• dUV = qV
• q behaves like a state function,
at V.
• What about q at P?
• P and V rivalry starts!
• qP = d(?)
• Let, X= U+ PV
• dX = dU+ PdV + VdP
• = q + VdP
X = H = U + PV (enthalpy)
[energy, state fun, extensive]
dH= dU + PdV + V dP
= q + V dP
q = dH - VdP, and
q = dU + PdV
Both are first law?
dXP = qP
47. P-V rivalry continues …
• A = U – T S
• dA = -PdV - SdT
• dAV,T ≤ 0
• dUS,V ≥ 0
• μj = (∂A/∂ni)V,T,nj
• = (∂U/∂ni)V,S,nj
• Helmholtz
• Van’t Hoff isochore
• KC
• (∂S/∂V)T = (∂P/∂T)V
• G = H – T S
• dG = VdP – S dT
• dGP,T ≤ 0 [most useful]
• dHS,P ≥ 0
• μj = (∂G/∂ni)P,T,nj
• = (∂H/∂ni)P,S,nj
• Gibbs
• Van’t Hoff isobar
• KP
• (∂S/∂P)T = - (∂V/∂T)P
48. Fun with Transformation:
The Maths behind the P-V rivalry!
• f= f(x,y) df = p dx + q dy
Lets play: Evaluate df – d(qy)
df–d(qy) = pdx +qdy –qdy –ydq
d(f – qy) = p dx – y dq
dX = p dx – y dq;
where, X = f – qy and X= f(x,q);
So, we got
f(x,y) X(x,q) and df dX
Similarly
• f= f(x,y) df = p dx + q dy
Lets play: Evaluate df – d(px)
df–d(px)= pdx +qdy–pdx– xdp
d(f – px) = q dy – x dp
dY = q dy – x dp;
where, Y = f – px and Y = (p,y);
So, we got
f(x,y) Y(p,y) and df dY
Can we think of yet another
transformation
f(x,y) Z(p,q) and df dZ?
49. Fun with Transformation:
The Maths behind the P-V rivalry!
• f = f(x,y) df = p dx + q dy
• X = f(x,q) = f – qy ;
• Y = f(p,y) = f – px;
• Z = f(p,q) = f – px –qy
• df = p dx + q dy
• dX = p dx – y dq
• dY = – x dp + q dy ;
• dZ = -x dp- y dq
• From 1st & 2nd laws
• dU = T dS – P dV
• d f = p dx + q dy
f = U; x=S, y=V, p=T, q=-P
therefore
f = U(S,V); dU = T dS – P dV
• X = U – (-P)V
• = U + PV
• Y = U – TS
• Z = U-TS-(-P)V = H – TS;
dH = T dS –Vd(-P)
=TdS+VdP
dA = -SdT – PdV
dG = VdP - SdT
50. A Probable Seven Point Outline
1. Structuring, Classifying, Integrating
A few fundamentals
First and second law on the same footings
Joule and Joule-Thomson: On the same
footings
2. Be picturesque, be Graphical
statements of second law;
Third law: dS versus S
3. Revisit the concepts
Ek Dozen Satyi-Mithye (T/F) Gappo
4. Effective Learning: Concept map
rather than concepts only
5. Problems rather than Exercise
Understanding conventions, assumptions
and approximations
One single problem is enough!
6. Fun in finding/discovering
Pattern
P Club vs. V Club:
Thermodynamics is reduced by 50%
Fun with Transformation: The Maths behind
the P-V rivalry!
7. Learning: An Interactive,
Joyful experience
Playing through Quiz, SCQ,
and MCQ.
Please participate
51. A few Interesting References
The Journal of Chemical Education (JCE) Articles
1. Teaching and Learning Problem Solving in Science, 58,51-55, 1981
2. Teaching Thermodynamics of Ideal Solutions: An Entropy Based Approach,
91, 74-83, 2014
3. Two Kinds of Conceptual Problems in Chemistry Teaching, 84, 172-174,
2007
4. The Chemical Adventures of Sherlock Holmes, 77, 471-474, 2000
5. Making Chemistry Learning More Meaningful, 69, 464-467, 1992
6. Introductory Students, Conceptual Understanding, and Algorithmic
Success, 75, 809-810, 1998
7. Logic, History, and the Chemistry Textbook, 75, 679-687, 1998
8. Conceptual Questions and Challenge Problems, 75, 1502-1503, 1998
9. Conceiving of Concept Maps to Foster Meaningful Learning, 81, 1303-
1308, 2004
10. Teaching Thermodynamics and Kinetics Using P-V Diagrams, 91, 74-83,
2014
52. A few more …
1. What The Best College Teachers Do, Ken Bain, Hervard University Press.
2. 53 Interesting Things To Do In Your Lectures, A. Haynes, K. Haynes, P&H,
UK.
3. Learning How to Learn, Joseph D. Novak, Cambridge University Press.
1. From Learning To Understanding: A Journey Explored Through Dialogues:
Conversation with Sanjib Bagchi, Subir Bhattacharyya and Rana Sen;
Communique, 6, No.1, 29-36, 2012
2. Value Creating Education: A Philosophical Inspiration, Communique, 10,
No.1, 35-42, 2017
3. Meaningful Learning in Science Classes: A Value Creating Inspiration,
International Conference on Soka Education, August 9-11, 2018, DePaul
University, Chicago, USA.
53. SKILL ENHANCEMENT COURSES SEC-A [SEMESTER 3]
SEC 1 – Mathematics and Statistics for Chemists (Credits: 2 Lectures: 30)
1.Functions, limits, derivative, physical significance, basic rules of differentiation,
maxima and minima, applications in chemistry, Error function, Gamma function, exact
and inexact differential, Taylor and McLaurin series, Fourier series and Fourier
Transform, Laplace transform, partial differentiation, rules of integration, definite and
indefinite integrals. (08 Lectures)
2.Differential equations: Separation of variables, homogeneous, exact, linear equations,
equations of second order, series solution method. (04 Lectures)
3. Probability : Permutations, combinations and theory of probability (03 Lectures)
4.Vectors, matrices and determinants: Vectors, dot, cross and triple products,
introduction to matrix algebra, addition and multiplication of matrices, inverse, adjoint
and transpose of matrices, unit and diagonal matrices. (04 Lectures )
5. Qualitative and quantitative aspects of analysis: Sampling, evaluation of analytical data,
errors, accuracy and precision, methods of their expression, normal law of distribution if
indeterminate errors, statistical test of data; F, Q and t test, rejection of data, and confidence
intervals. (03 Lectures)
6. Analysis and Presentation of Data: Descriptive statistics. Choosing and using
statistical tests. Chemometrics. Analysis of variance (ANOVA), Correlation and
regression, fitting of linear equations, simple linear cases, weighted linear case, analysis
of residuals, general polynomial fitting, linearizing transformations, exponential
function fit. Basic aspects of multiple linear regression analysis. (08 Lectures)
54. CEMA-CC-5-11-TH : (Credits: Theory-04, Practicals-02) PHYS CHEM – 4; Sem-5
Quantum Chemistri-II
Setting up of Schrödinger equation for many-electron atoms (He, Li)Need for
approximation methods. Statement of variation theorem and application to simple
systems(particle-ina-box, harmonic oscillator, hydrogen atom).
LCAO :Born-Oppenheimer approximation. Covalent bonding, valence bond and
molecular orbital approaches, LCAO-MO treatment of H2+; Bonding and antibonding
orbitals; Qualitative extension to H2; Comparison of LCAO-MO and VB treatments of
H2 and their limitations.( only wavefunctions, detailed solutionnot required) and their
limitations.
Numerical Analysis (10 Lectures)
Roots of Equation:Numerical methods for finding the roots of equations: Quadratic
Formula, Iterative Methods (e.g., Newton Raphson Method).
Least-Squares Fitting.Numerical Differentiation.Numerical Integration( Trapezoidal
and Simpson's Rule)
CEMA-CC-5-11-P
Computer programs(Using FORTRAN or C or C ++) based on numerical methods :
Programming 1: Roots of equations: (e.g. volume of van der Waals gas and
comparison with ideal gas, pH of a weak acid)
Programming 2: Numerical differentiation (e.g., change in pressure for small change
in volume of a van der Waals gas, Potentiometric titrations)
Programming 3: Numerical integration (e.g. entropy/ enthalpy change from heat
capacity data), probability distributions (gas kinetic theory) and mean values
55. DSE-A-2: APPLICATIONS OF COMPUTERS IN CHEMISTRY (Credits: Theory-04, Practicals-02)
Theory: 60 Lectures
• Computer Programming Basics (FORTRAN): (Lectures: 20)
Elements of FORTRAN Language. FORTRAN Keywords and commands, Logical and
Relational Operators, iteration, Array variables, Matrix addition and multiplication. Function and
Subroutine.
• Introduction to Spreadsheet Software(MS Excel): (Lectures 25)
Creating a Spreadsheet, entering and formatting information, basic functions and
formulae, creating charts, tables and graphs. Incorporating tables and graphs into word
processing documents, simple calculations.
Solution of simultaneous equations(for eg: in chemical Equilibrium problems) using Excel
SOLVER Functions. Use of Excel Goal Seek function.
Numerical Modelling : Simulation of pH metric titration curves, Excel functions
LINEST and Least Squares. Numerical Curve Fitting, Regression, Numerical Differentiation and
Integration
Statistical Analysis: (Lectures: 15)
Gaussian Distribution and Errors in Measurement and their effect on data sets.
Descriptive Statistics using Excel, Statistical Significance Testing, the T test and the F
test.
56. PRACTICALS DSE-A-2: APPLICATIONS OF COMPUTERS IN CHEMISTRY (45 Lectures)
( At least 10 experiments are to be performed.)
1. Plotting of Graphs using a spreadsheet. ( Planck's Distribution Law, Maxwell
Boltzmann Distribution Curves as a function of temperature and molecular weight)
2. Determination of vapour pressure from Van der Waals Equation of State.
3. Determination of rate constant from Concentration-time data using LINEST function.
4. Determination of Molar Extinction Coefficient from Absorbent's data using
LINEST function.
5. Determination of concentration simultaneously using Excel SOLVER Function.(For
eg: Determination of [OH-], [Mg2+] and [H3O+] from Ksp and Kw data of Mg(OH)2.)
6. Simultaneous Solution of Chemical Equilibrium Problems to determine the
equilibrium compositions from the Equilibrium Constant data at a given Pressure and
Temperature.
7. Determination of Molar Enthalpy of Vaporization using Linear and Non Linear Least
squares fit.
8. Calculation and Plotting of a Precipitation Titration Curve with MS Excel.
9. Acid-Base Titration Curve using Excel Goal Seek Function.
10. Plotting of First and Second Derivative Curve for pH metric and Potentiometric
titrations .
11. Use of spreadsheet to solve the 1D Schrodinger Equation(Numerov Method).
12. Michaelis-Menten Kinetics for Enzyme Catalysis using Linear and Non - Linear
Regression