The document discusses the Fundamental Theorem of Calculus and provides announcements for an introductory calculus class. It lists the midterm exam results and upcoming exam and movie day. It also provides the dates and times for problem sessions and the instructor's office hours. The outline indicates that the previous class discussed the Second Fundamental Theorem of Calculus.
This document discusses the history and applications of integration. It provides an overview of how integration was developed over time by mathematicians like Archimedes, Gauss, Leibniz, and Newton. It also outlines real-world uses of integration in engineering projects like designing the PETRONAS Towers and Sydney Opera House. The document then explains numerical integration methods like the Trapezoidal Rule, Simpson's Rule, and their variations. It provides formulas and examples of how to apply these rules to approximate definite integrals.
Integration is used in physics to determine rates of change and distances given velocities. Numerical integration is required when the antiderivative is unknown. It involves approximating the definite integral of a function as the area under its curve between bounds. The Trapezoidal Rule approximates this area using straight lines between points, while Simpson's Rule uses quadratic or cubic functions, achieving greater accuracy with fewer points. Both methods involve dividing the area into strips and summing their widths multiplied by the function values at strip points.
This document discusses numerical integration techniques. It begins by explaining the need for numerical integration when exact integrals cannot be evaluated. It then introduces the trapezoidal rule, which approximates the area under a curve as a trapezoid. The document shows how dividing the interval into more subintervals improves accuracy. Simpson's rule is also covered, which uses a quadratic interpolation between three points. Examples are provided to demonstrate applying these numerical integration techniques.
This document discusses numerical integration and its applications. It introduces various numerical integration methods like the trapezoidal rule and Simpson's rule. The trapezoidal rule approximates the curve using straight lines between points to calculate the area under the curve. Simpson's rule further improves upon this by approximating the curve with a quadratic or cubic function between points. The document explains the formulas for the trapezoidal rule, Simpson's 1/3 rule, and Simpson's 3/8 rule.
- Simpson's rule estimates the area under a curve by dividing it into equal width strips and fitting quadratic curves to points in each strip.
- The number of strips must be even and the number of ordinates is always one more than the number of strips.
- The formula for Simpson's rule involves summing terms with coefficients that alternate between 4/3, 1, 4/3, etc. depending on the number of strips.
Gaussian Quadrature Formulas, which are simple and will help learners learn about Gauss's One, Two and Three Point Formulas, I have also included sums so that learning can be easy and the method can be understood.
This document contains announcements and an outline for a calculus class. It announces that the midterm is finished with average score of 43 and standard deviation of 6. It also announces the date for Midterm III and lists the instructor's office hours. The outline previews that the class will cover evaluating definite integrals with examples and the concept of total change, and will introduce indefinite integrals with examples.
The document discusses the Fundamental Theorem of Calculus and provides announcements for an introductory calculus class. It lists the midterm exam results and upcoming exam and movie day. It also provides the dates and times for problem sessions and the instructor's office hours. The outline indicates that the previous class discussed the Second Fundamental Theorem of Calculus.
This document discusses the history and applications of integration. It provides an overview of how integration was developed over time by mathematicians like Archimedes, Gauss, Leibniz, and Newton. It also outlines real-world uses of integration in engineering projects like designing the PETRONAS Towers and Sydney Opera House. The document then explains numerical integration methods like the Trapezoidal Rule, Simpson's Rule, and their variations. It provides formulas and examples of how to apply these rules to approximate definite integrals.
Integration is used in physics to determine rates of change and distances given velocities. Numerical integration is required when the antiderivative is unknown. It involves approximating the definite integral of a function as the area under its curve between bounds. The Trapezoidal Rule approximates this area using straight lines between points, while Simpson's Rule uses quadratic or cubic functions, achieving greater accuracy with fewer points. Both methods involve dividing the area into strips and summing their widths multiplied by the function values at strip points.
This document discusses numerical integration techniques. It begins by explaining the need for numerical integration when exact integrals cannot be evaluated. It then introduces the trapezoidal rule, which approximates the area under a curve as a trapezoid. The document shows how dividing the interval into more subintervals improves accuracy. Simpson's rule is also covered, which uses a quadratic interpolation between three points. Examples are provided to demonstrate applying these numerical integration techniques.
This document discusses numerical integration and its applications. It introduces various numerical integration methods like the trapezoidal rule and Simpson's rule. The trapezoidal rule approximates the curve using straight lines between points to calculate the area under the curve. Simpson's rule further improves upon this by approximating the curve with a quadratic or cubic function between points. The document explains the formulas for the trapezoidal rule, Simpson's 1/3 rule, and Simpson's 3/8 rule.
- Simpson's rule estimates the area under a curve by dividing it into equal width strips and fitting quadratic curves to points in each strip.
- The number of strips must be even and the number of ordinates is always one more than the number of strips.
- The formula for Simpson's rule involves summing terms with coefficients that alternate between 4/3, 1, 4/3, etc. depending on the number of strips.
Gaussian Quadrature Formulas, which are simple and will help learners learn about Gauss's One, Two and Three Point Formulas, I have also included sums so that learning can be easy and the method can be understood.
This document contains announcements and an outline for a calculus class. It announces that the midterm is finished with average score of 43 and standard deviation of 6. It also announces the date for Midterm III and lists the instructor's office hours. The outline previews that the class will cover evaluating definite integrals with examples and the concept of total change, and will introduce indefinite integrals with examples.
This document provides an outline for a lecture on surface area. It lists the topics that will be covered, including calculating the area of rectangles, parallelograms, and curved surfaces by dividing them into smaller shapes and taking a limit. It also notes the instructor's office hours and problem session times.
The document announces that the midterm exam is on Wednesday April 30th, that Friday May 2nd is movie day, lists times for problem sessions on Sunday and Thursday at 7pm in room SC 310, and office hours on Tuesday and Wednesday from 2-4pm in room SC 323. It also tentatively lists the final exam date as May 23rd at 9:15am.
This document outlines the goals, topics, grading structure, and contact information for a discrete mathematics course taught by Professor Matthew Leingang in the spring of 2009. The course will cover set theory, algorithms, number theory, probability, recurrence, graph theory, and more. Grades are based on homework, midterms, quizzes, and a final exam. Students are encouraged to ask questions, and the professor and TAs are available to help.
The document announces upcoming problem sessions on Sundays and Thursdays at 7pm in room SC 310, as well as office hours on Tuesdays and Wednesdays from 2-4pm in room SC 323. It also notes that Midterm II will take place on April 11th in class and will cover sections 4.3 through 4.8. The document outlines that it will cover antiderivatives and the Mean Value Theorem, and will include tabulating antiderivatives for power functions and combinations.
The general area problem needs some kind of infinite process, whether an infinite series or a limit of finite sums. Once we define the definite integral, we examine its properties.
This document provides an outline for a lecture on Newton's Method for finding the zeros of functions or the roots of equations. It includes announcements about upcoming problem sessions, office hours, and an upcoming midterm exam. The outline also lists topics to be covered such as an introduction to Newton's Method, how it works graphically and symbolically, applications for finding zeros and roots, and potential flaws in the method like lack of convergence or convergence to incorrect values.
You knew this was coming. From double integrals over plane regions we move onward to triple integrals over solid regions. The visualization is a little harder, but the calculus not that much.
Lesson 15: Linear Approximation and DifferentialsMatthew Leingang
The tangent line to a graph at a point is the best possible linear approximation that agrees at that point. We can use it for estimation and error control.
Inquiry-Based Learning Opportunities for Secondary Teachers and StudentsMatthew Leingang
The Harvard ALM in Mathematics for Teaching in Extension degree is described, along with two inquiry-based learning courses taught in that program. Also covered is the Harvard Secondary School Program and an IBL course taught in it.
The gradient of a function is the collection of its partial derivatives, and is a vector field always perpendicular to the level curves of the function.
Lesson 22: Applications to Business and EconomicsMatthew Leingang
Calculus and economics have an interesting interplay. The laws of economics can be expressed in terms of calculus, and find extreme points can be a lucrative operation!
Thomas Simpson published Simpson's Rule in 1743, which uses parabolas instead of straight lines to better approximate the area under a curve. Simpson's Rule requires an even number of intervals or ordinates and is more accurate than the Trapezium Rule. Two examples are provided where Simpson's Rule is used with either five ordinates or four intervals to estimate the value of integrals.
This document provides information about a final review session for a Math 21a course, including announcements about additional review sessions and details on the final exam. It outlines the topics to be covered in Part I of the review session, which will focus on partial derivatives and related concepts from chapter 11 on functions of several variables. These include the definition of partial derivatives, Clairaut's theorem, tangent planes, linear approximations, the chain rule, and implicit differentiation.
This document outlines a lecture on Stokes' Theorem. It includes announcements about the final exam, office hours, and problem sessions. The lecture will cover Stokes' Theorem, including its statement and proof. The previous lecture covered surface and flux integrals. The next lecture will cover the Divergence Theorem. Worksheets will also be provided.
The document announces that the midterm exam for the calculus class will cover sections 5.1 through 5.6 on integration by parts. It also lists the date for the midterm, an upcoming movie day, the tentative date for the final exam, times for problem sessions, and the professor's office hours.
This document provides an introduction to functions and their representations. It defines what a function is and gives examples of functions expressed through formulas, numerically, graphically and verbally. It also covers properties of functions including monotonicity, symmetry, even and odd functions. Key examples are used throughout to illustrate concepts.
Lesson 21: Indeterminate forms and L'Hôpital's RuleMatthew Leingang
This document is the outline for a calculus lecture on indeterminate forms and L'Hopital's rule. It lists announcements about problem sessions, office hours, and an upcoming midterm exam. The outline then states that the lecture will cover indeterminate forms and L'Hopital's rule, specifically how to apply the rule to indeterminate products, differences, and limits involving infinity over infinity or zero over zero forms.
This document provides information on numerical integration techniques, specifically the Trapezoidal rule and Simpson's rule. It begins with an overview of integration and the basis of the Trapezoidal rule in approximating the integrand as a linear polynomial. It then discusses the derivation and application of the Trapezoidal rule, as well as extending it to multiple segments to improve accuracy. Simpson's rule is introduced as approximating the integrand as a quadratic polynomial. The document gives examples applying single- and multi-segment Trapezoidal and Simpson's rules. It concludes with an introduction to the Romberg rule as an extrapolation method to further increase the accuracy of numerical integration estimates.
This document discusses Gaussian quadrature, a method for numerical integration. It begins by comparing Gaussian quadrature to Newton-Cotes formulae, noting that Gaussian quadrature selects both weights and locations of integration points to exactly integrate higher order polynomials. The document then provides examples of 2-point and 3-point Gaussian quadrature on the interval [-1,1], showing how to determine the points and weights to integrate polynomials up to a certain order exactly. It also discusses extending Gaussian quadrature to other intervals via a coordinate transformation, and provides an example integration problem.
This document provides guidance on developing effective lesson plans for calculus instructors. It recommends starting by defining specific learning objectives and assessments. Examples should be chosen carefully to illustrate concepts and engage students at a variety of levels. The lesson plan should include an introductory problem, definitions, theorems, examples, and group work. Timing for each section should be estimated. After teaching, the lesson can be improved by analyzing what was effective and what needs adjustment for the next time. Advanced preparation is key to looking prepared and ensuring students learn.
Streamlining assessment, feedback, and archival with auto-multiple-choiceMatthew Leingang
Auto-multiple-choice (AMC) is an open-source optical mark recognition software package built with Perl, LaTeX, XML, and sqlite. I use it for all my in-class quizzes and exams. Unique papers are created for each student, fixed-response items are scored automatically, and free-response problems, after manual scoring, have marks recorded in the same process. In the first part of the talk I will discuss AMC’s many features and why I feel it’s ideal for a mathematics course. My contributions to the AMC workflow include some scripts designed to automate the process of returning scored papers
back to students electronically. AMC provides an email gateway, but I have written programs to return graded papers via the DAV protocol to student’s dropboxes on our (Sakai) learning management systems. I will also show how graded papers can be archived, with appropriate metadata tags, into an Evernote notebook.
This document provides an outline for a lecture on surface area. It lists the topics that will be covered, including calculating the area of rectangles, parallelograms, and curved surfaces by dividing them into smaller shapes and taking a limit. It also notes the instructor's office hours and problem session times.
The document announces that the midterm exam is on Wednesday April 30th, that Friday May 2nd is movie day, lists times for problem sessions on Sunday and Thursday at 7pm in room SC 310, and office hours on Tuesday and Wednesday from 2-4pm in room SC 323. It also tentatively lists the final exam date as May 23rd at 9:15am.
This document outlines the goals, topics, grading structure, and contact information for a discrete mathematics course taught by Professor Matthew Leingang in the spring of 2009. The course will cover set theory, algorithms, number theory, probability, recurrence, graph theory, and more. Grades are based on homework, midterms, quizzes, and a final exam. Students are encouraged to ask questions, and the professor and TAs are available to help.
The document announces upcoming problem sessions on Sundays and Thursdays at 7pm in room SC 310, as well as office hours on Tuesdays and Wednesdays from 2-4pm in room SC 323. It also notes that Midterm II will take place on April 11th in class and will cover sections 4.3 through 4.8. The document outlines that it will cover antiderivatives and the Mean Value Theorem, and will include tabulating antiderivatives for power functions and combinations.
The general area problem needs some kind of infinite process, whether an infinite series or a limit of finite sums. Once we define the definite integral, we examine its properties.
This document provides an outline for a lecture on Newton's Method for finding the zeros of functions or the roots of equations. It includes announcements about upcoming problem sessions, office hours, and an upcoming midterm exam. The outline also lists topics to be covered such as an introduction to Newton's Method, how it works graphically and symbolically, applications for finding zeros and roots, and potential flaws in the method like lack of convergence or convergence to incorrect values.
You knew this was coming. From double integrals over plane regions we move onward to triple integrals over solid regions. The visualization is a little harder, but the calculus not that much.
Lesson 15: Linear Approximation and DifferentialsMatthew Leingang
The tangent line to a graph at a point is the best possible linear approximation that agrees at that point. We can use it for estimation and error control.
Inquiry-Based Learning Opportunities for Secondary Teachers and StudentsMatthew Leingang
The Harvard ALM in Mathematics for Teaching in Extension degree is described, along with two inquiry-based learning courses taught in that program. Also covered is the Harvard Secondary School Program and an IBL course taught in it.
The gradient of a function is the collection of its partial derivatives, and is a vector field always perpendicular to the level curves of the function.
Lesson 22: Applications to Business and EconomicsMatthew Leingang
Calculus and economics have an interesting interplay. The laws of economics can be expressed in terms of calculus, and find extreme points can be a lucrative operation!
Thomas Simpson published Simpson's Rule in 1743, which uses parabolas instead of straight lines to better approximate the area under a curve. Simpson's Rule requires an even number of intervals or ordinates and is more accurate than the Trapezium Rule. Two examples are provided where Simpson's Rule is used with either five ordinates or four intervals to estimate the value of integrals.
This document provides information about a final review session for a Math 21a course, including announcements about additional review sessions and details on the final exam. It outlines the topics to be covered in Part I of the review session, which will focus on partial derivatives and related concepts from chapter 11 on functions of several variables. These include the definition of partial derivatives, Clairaut's theorem, tangent planes, linear approximations, the chain rule, and implicit differentiation.
This document outlines a lecture on Stokes' Theorem. It includes announcements about the final exam, office hours, and problem sessions. The lecture will cover Stokes' Theorem, including its statement and proof. The previous lecture covered surface and flux integrals. The next lecture will cover the Divergence Theorem. Worksheets will also be provided.
The document announces that the midterm exam for the calculus class will cover sections 5.1 through 5.6 on integration by parts. It also lists the date for the midterm, an upcoming movie day, the tentative date for the final exam, times for problem sessions, and the professor's office hours.
This document provides an introduction to functions and their representations. It defines what a function is and gives examples of functions expressed through formulas, numerically, graphically and verbally. It also covers properties of functions including monotonicity, symmetry, even and odd functions. Key examples are used throughout to illustrate concepts.
Lesson 21: Indeterminate forms and L'Hôpital's RuleMatthew Leingang
This document is the outline for a calculus lecture on indeterminate forms and L'Hopital's rule. It lists announcements about problem sessions, office hours, and an upcoming midterm exam. The outline then states that the lecture will cover indeterminate forms and L'Hopital's rule, specifically how to apply the rule to indeterminate products, differences, and limits involving infinity over infinity or zero over zero forms.
This document provides information on numerical integration techniques, specifically the Trapezoidal rule and Simpson's rule. It begins with an overview of integration and the basis of the Trapezoidal rule in approximating the integrand as a linear polynomial. It then discusses the derivation and application of the Trapezoidal rule, as well as extending it to multiple segments to improve accuracy. Simpson's rule is introduced as approximating the integrand as a quadratic polynomial. The document gives examples applying single- and multi-segment Trapezoidal and Simpson's rules. It concludes with an introduction to the Romberg rule as an extrapolation method to further increase the accuracy of numerical integration estimates.
This document discusses Gaussian quadrature, a method for numerical integration. It begins by comparing Gaussian quadrature to Newton-Cotes formulae, noting that Gaussian quadrature selects both weights and locations of integration points to exactly integrate higher order polynomials. The document then provides examples of 2-point and 3-point Gaussian quadrature on the interval [-1,1], showing how to determine the points and weights to integrate polynomials up to a certain order exactly. It also discusses extending Gaussian quadrature to other intervals via a coordinate transformation, and provides an example integration problem.
This document provides guidance on developing effective lesson plans for calculus instructors. It recommends starting by defining specific learning objectives and assessments. Examples should be chosen carefully to illustrate concepts and engage students at a variety of levels. The lesson plan should include an introductory problem, definitions, theorems, examples, and group work. Timing for each section should be estimated. After teaching, the lesson can be improved by analyzing what was effective and what needs adjustment for the next time. Advanced preparation is key to looking prepared and ensuring students learn.
Streamlining assessment, feedback, and archival with auto-multiple-choiceMatthew Leingang
Auto-multiple-choice (AMC) is an open-source optical mark recognition software package built with Perl, LaTeX, XML, and sqlite. I use it for all my in-class quizzes and exams. Unique papers are created for each student, fixed-response items are scored automatically, and free-response problems, after manual scoring, have marks recorded in the same process. In the first part of the talk I will discuss AMC’s many features and why I feel it’s ideal for a mathematics course. My contributions to the AMC workflow include some scripts designed to automate the process of returning scored papers
back to students electronically. AMC provides an email gateway, but I have written programs to return graded papers via the DAV protocol to student’s dropboxes on our (Sakai) learning management systems. I will also show how graded papers can be archived, with appropriate metadata tags, into an Evernote notebook.
This document discusses electronic grading of paper assessments using PDF forms. Key points include:
- Various tools for creating fillable PDF forms using LaTeX packages or desktop software.
- Methods for stamping completed forms onto scanned documents including using pdftk or overlaying in TikZ.
- Options for grading on tablets or desktops including GoodReader, PDFExpert, Adobe Acrobat.
- Extracting data from completed forms can be done in Adobe Acrobat or via command line with pdftk.
Integration by substitution is the chain rule in reverse.
NOTE: the final location is section specific. Section 1 (morning) is in SILV 703, Section 11 (afternoon) is in CANT 200
Lesson 26: The Fundamental Theorem of Calculus (slides)Matthew Leingang
g(x) represents the area under the curve of f(t) between 0 and x.
.
x
What can you say about g? 2 4 6 8 10f
The First Fundamental Theorem of Calculus
Theorem (First Fundamental Theorem of Calculus)
Let f be a con nuous func on on [a, b]. Define the func on F on [a, b] by
∫ x
F(x) = f(t) dt
a
Then F is con nuous on [a, b] and differentiable on (a, b) and for all x in (a, b),
F′(x
Lesson 26: The Fundamental Theorem of Calculus (slides)Matthew Leingang
The document discusses the Fundamental Theorem of Calculus, which has two parts. The first part states that if a function f is continuous on an interval, then the derivative of the integral of f is equal to f. This is proven using Riemann sums. The second part relates the integral of a function f to the integral of its derivative F'. Examples are provided to illustrate how the area under a curve relates to these concepts.
Lesson 27: Integration by Substitution (handout)Matthew Leingang
This document contains lecture notes on integration by substitution from a Calculus I class. It introduces the technique of substitution for both indefinite and definite integrals. For indefinite integrals, the substitution rule is presented, along with examples of using substitutions to evaluate integrals involving polynomials, trigonometric, exponential, and other functions. For definite integrals, the substitution rule is extended and examples are worked through both with and without first finding the indefinite integral. The document emphasizes that substitution often simplifies integrals and makes them easier to evaluate.
Lesson 26: The Fundamental Theorem of Calculus (handout)Matthew Leingang
1) The document discusses lecture notes on Section 5.4: The Fundamental Theorem of Calculus from a Calculus I course. 2) It covers stating and explaining the Fundamental Theorems of Calculus and using the first fundamental theorem to find derivatives of functions defined by integrals. 3) The lecture outlines the first fundamental theorem, which relates differentiation and integration, and gives examples of applying it.
This document contains notes from a calculus class lecture on evaluating definite integrals. It discusses using the evaluation theorem to evaluate definite integrals, writing derivatives as indefinite integrals, and interpreting definite integrals as the net change of a function over an interval. The document also contains examples of evaluating definite integrals, properties of integrals, and an outline of the key topics covered.
This document contains lecture notes from a Calculus I class covering Section 5.3 on evaluating definite integrals. The notes discuss using the Evaluation Theorem to calculate definite integrals, writing derivatives as indefinite integrals, and interpreting definite integrals as the net change of a function over an interval. Examples are provided to demonstrate evaluating definite integrals using the midpoint rule approximation. Properties of integrals such as additivity and the relationship between definite and indefinite integrals are also outlined.
Lesson 24: Areas and Distances, The Definite Integral (handout)Matthew Leingang
We can define the area of a curved region by a process similar to that by which we determined the slope of a curve: approximation by what we know and a limit.
Lesson 24: Areas and Distances, The Definite Integral (slides)Matthew Leingang
We can define the area of a curved region by a process similar to that by which we determined the slope of a curve: approximation by what we know and a limit.
At times it is useful to consider a function whose derivative is a given function. We look at the general idea of reversing the differentiation process and its applications to rectilinear motion.
At times it is useful to consider a function whose derivative is a given function. We look at the general idea of reversing the differentiation process and its applications to rectilinear motion.
This document contains lecture notes from a Calculus I class discussing optimization problems. It begins with announcements about upcoming exams and courses the professor is teaching. It then presents an example problem about finding the rectangle of a fixed perimeter with the maximum area. The solution uses calculus techniques like taking the derivative to find the critical points and determine that the optimal rectangle is a square. The notes discuss strategies for solving optimization problems and summarize the key steps to take.
Uncountably many problems in life and nature can be expressed in terms of an optimization principle. We look at the process and find a few good examples.
The document discusses curve sketching of functions by analyzing their derivatives. It provides:
1) A checklist for graphing a function which involves finding where the function is positive/negative/zero, its monotonicity from the first derivative, and concavity from the second derivative.
2) An example of graphing the cubic function f(x) = 2x^3 - 3x^2 - 12x through analyzing its derivatives.
3) Explanations of the increasing/decreasing test and concavity test to determine monotonicity and concavity from a function's derivatives.
The document contains lecture notes on curve sketching from a Calculus I class. It discusses using the first and second derivative tests to determine properties of a function like monotonicity, concavity, maxima, minima, and points of inflection in order to sketch the graph of the function. It then provides an example of using these tests to sketch the graph of the cubic function f(x) = 2x^3 - 3x^2 - 12x.
Lesson 20: Derivatives and the Shapes of Curves (slides)Matthew Leingang
This document contains lecture notes on derivatives and the shapes of curves from a Calculus I class taught by Professor Matthew Leingang at New York University. The notes cover using derivatives to determine the intervals where a function is increasing or decreasing, classifying critical points as maxima or minima, using the second derivative to determine concavity, and applying the first and second derivative tests. Examples are provided to illustrate finding intervals of monotonicity for various functions.
Lesson 20: Derivatives and the Shapes of Curves (handout)Matthew Leingang
This document contains lecture notes on calculus from a Calculus I course. It covers determining the monotonicity of functions using the first derivative test. Key points include using the sign of the derivative to determine if a function is increasing or decreasing over an interval, and using the first derivative test to classify critical points as local maxima, minima, or neither. Examples are provided to demonstrate finding intervals of monotonicity for various functions and applying the first derivative test.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
1. Section 5.7
Numerical Integration
Math 1a
Introduction to Calculus
April 25, 2008
Announcements
Midterm III is Wednesday 4/30 in class (covers §4.9–5.6)
◮
Friday 5/2 is Movie Day!
◮
Final (tentative) 5/23 9:15am
◮
Problem Sessions Sunday, Thursday, 7pm, SC 310
◮
◮ . . . . . .
2. Announcements
Midterm III is Wednesday 4/30 in class (covers §4.9–5.6)
◮
Friday 5/2 is Movie Day!
◮
Final (tentative) 5/23 9:15am
◮
Problem Sessions Sunday, Thursday, 7pm, SC 310
◮
Office hours Tues, Weds, 2–4pm SC 323
◮
. . . . . .