This document outlines the proposed syllabus for the third and fourth semesters of the M.Sc. Mathematics program under the Choice Based Credit System. The third semester includes core courses in Complex Analysis, Functional Analysis, Mathematical Methods, and a core elective course that can be selected from options like Fluid Dynamics, General Relativity, and Graph Theory. It also includes a foundation course that can be selected from options in different fields. Similarly, the fourth semester outlines core courses in Dynamical Systems, Partial Differential Equations, Integral Equations, and a core elective course that can be selected from options like Fluid Dynamics, Cosmology and Combinatorics, along with a foundation course. Detailed course contents are provided
This document outlines the proposed syllabus for a Master of Science in Mathematics program to be implemented in the 2020-21 academic year. It includes 10 core courses to be taken over two semesters. The courses cover topics in group theory, ring theory, real analysis, topology, linear algebra, field theory, measure theory, advanced topology, classical mechanics, and students can choose one core elective course from options like numerical analysis, differential equations, calculus of variations, number theory, fuzzy mathematics, and others. For each course, the document lists the course code, credit hours, and a brief description of the topics to be covered in 4 units. Required textbooks and reference materials are also provided for each course.
This document contains the syllabus for the third semester of a four year Bachelor of Engineering degree in Mechanical Engineering.
It outlines 6 courses: Mathematics III, Mechanics of Materials, Fluid Power I, Engineering Thermodynamics, Manufacturing Processes I, and Workshop Practice.
The Mathematics III course covers topics like ordinary differential equations, Laplace transforms, partial differential equations, statistics, complex analysis, and numerical analysis.
The Mechanics of Materials course covers topics like mechanical properties of materials, stresses and strains, bending theory, torsion, principal stresses and deflection of beams.
The Fluid Power I course covers fluid statics, kinematics and dynamics of fluid flow, dimensional analysis, motion
The document outlines the syllabus for a Probability Theory and Stochastic Process course. It includes:
1. The course objectives which are to understand fundamentals of probability, random variables, stochastic processes, and their applications in electronic engineering.
2. The course outcomes which are to understand different random variables and their distributions, bi-variate distributions, stochastic processes in the temporal and frequency domains.
3. The syllabus which is divided into 5 units covering probability, random variables, operations on random variables, stochastic processes in the temporal and spectral characteristics domains.
The document provides the course structure and syllabus for the B.Tech Mechanical Engineering program at Jawaharlal Nehru Technological University Hyderabad for the R18 admitted batch.
It outlines the courses in the II year I semester which includes courses on Probability and Statistics, Mechanics of Solids, Material Science and Metallurgy, Production Technology, Thermodynamics, and their corresponding labs. It also provides the course code, title, credits and brief course objectives for some of the major courses like Mechanics of Solids and Material Science.
The document provides an introduction to calculus concepts including:
- Sets can represent collections of objects and are denoted using curly brackets. There are five regular solids that follow the Euler formula relating the number of faces, vertices and edges of each solid.
- The preface outlines the main purposes and organization of the two-volume calculus text, which includes fundamental concepts, applications, proofs, and multiple approaches.
- Volume I contains 5 chapters covering sets, functions, graphs, limits, differential calculus, integral calculus, sequences, summations, and applications of calculus.
This document outlines the course contents for Engineering Mathematics III, Electromagnetic Theory, Digital Electronics, and Electronic Circuits.
The Engineering Mathematics III course covers complex variables, error approximations, difference operators, interpolation methods, numerical integration and differentiation, ordinary differential equations, probability, and hypothesis testing.
The Electromagnetic Theory course covers vector calculus, static electric and magnetic fields, time-varying fields, Maxwell's equations, plane waves, reflection and refraction, and potentials.
The Digital Electronics course covers number systems, Boolean algebra, logic gates, combination circuits, multivibrators, flip-flops, shift registers, counters, semiconductor memories, and logic families.
The Electronic Circuits course covers
This document provides information on the Department of Mechanical Engineering at Manav Rachna University. It includes the course details for the first semester of the B.Tech program in Mechanical Engineering, including the subject codes, names, nature (hard/soft), type (core/elective), credit hours, and contact hours for each subject. The core subjects include Chemistry, Mathematics-I, Engineering Mechanics, Basics of Electrical & Electronics Engineering, and Thermodynamics. It also lists the textbooks recommended for each subject.
The document outlines the syllabus for the Engineering Mathematics - I course, covering topics in differential and integral calculus, vector calculus, differential equations, and linear algebra. It includes 8 units of study with topics such as derivatives, indeterminate forms, partial differentiation, and vector identities. The syllabus also provides details on textbook and reference materials for the course.
This document outlines the proposed syllabus for a Master of Science in Mathematics program to be implemented in the 2020-21 academic year. It includes 10 core courses to be taken over two semesters. The courses cover topics in group theory, ring theory, real analysis, topology, linear algebra, field theory, measure theory, advanced topology, classical mechanics, and students can choose one core elective course from options like numerical analysis, differential equations, calculus of variations, number theory, fuzzy mathematics, and others. For each course, the document lists the course code, credit hours, and a brief description of the topics to be covered in 4 units. Required textbooks and reference materials are also provided for each course.
This document contains the syllabus for the third semester of a four year Bachelor of Engineering degree in Mechanical Engineering.
It outlines 6 courses: Mathematics III, Mechanics of Materials, Fluid Power I, Engineering Thermodynamics, Manufacturing Processes I, and Workshop Practice.
The Mathematics III course covers topics like ordinary differential equations, Laplace transforms, partial differential equations, statistics, complex analysis, and numerical analysis.
The Mechanics of Materials course covers topics like mechanical properties of materials, stresses and strains, bending theory, torsion, principal stresses and deflection of beams.
The Fluid Power I course covers fluid statics, kinematics and dynamics of fluid flow, dimensional analysis, motion
The document outlines the syllabus for a Probability Theory and Stochastic Process course. It includes:
1. The course objectives which are to understand fundamentals of probability, random variables, stochastic processes, and their applications in electronic engineering.
2. The course outcomes which are to understand different random variables and their distributions, bi-variate distributions, stochastic processes in the temporal and frequency domains.
3. The syllabus which is divided into 5 units covering probability, random variables, operations on random variables, stochastic processes in the temporal and spectral characteristics domains.
The document provides the course structure and syllabus for the B.Tech Mechanical Engineering program at Jawaharlal Nehru Technological University Hyderabad for the R18 admitted batch.
It outlines the courses in the II year I semester which includes courses on Probability and Statistics, Mechanics of Solids, Material Science and Metallurgy, Production Technology, Thermodynamics, and their corresponding labs. It also provides the course code, title, credits and brief course objectives for some of the major courses like Mechanics of Solids and Material Science.
The document provides an introduction to calculus concepts including:
- Sets can represent collections of objects and are denoted using curly brackets. There are five regular solids that follow the Euler formula relating the number of faces, vertices and edges of each solid.
- The preface outlines the main purposes and organization of the two-volume calculus text, which includes fundamental concepts, applications, proofs, and multiple approaches.
- Volume I contains 5 chapters covering sets, functions, graphs, limits, differential calculus, integral calculus, sequences, summations, and applications of calculus.
This document outlines the course contents for Engineering Mathematics III, Electromagnetic Theory, Digital Electronics, and Electronic Circuits.
The Engineering Mathematics III course covers complex variables, error approximations, difference operators, interpolation methods, numerical integration and differentiation, ordinary differential equations, probability, and hypothesis testing.
The Electromagnetic Theory course covers vector calculus, static electric and magnetic fields, time-varying fields, Maxwell's equations, plane waves, reflection and refraction, and potentials.
The Digital Electronics course covers number systems, Boolean algebra, logic gates, combination circuits, multivibrators, flip-flops, shift registers, counters, semiconductor memories, and logic families.
The Electronic Circuits course covers
This document provides information on the Department of Mechanical Engineering at Manav Rachna University. It includes the course details for the first semester of the B.Tech program in Mechanical Engineering, including the subject codes, names, nature (hard/soft), type (core/elective), credit hours, and contact hours for each subject. The core subjects include Chemistry, Mathematics-I, Engineering Mechanics, Basics of Electrical & Electronics Engineering, and Thermodynamics. It also lists the textbooks recommended for each subject.
The document outlines the syllabus for the Engineering Mathematics - I course, covering topics in differential and integral calculus, vector calculus, differential equations, and linear algebra. It includes 8 units of study with topics such as derivatives, indeterminate forms, partial differentiation, and vector identities. The syllabus also provides details on textbook and reference materials for the course.
This document contains the syllabus for the third semester of the B.E. degree in Electrical and Electronics Engineering at Anna University, Chennai. It lists the theory and practical courses offered in the semester. The theory courses include Transforms and Partial Differential Equations, Digital Logic Circuits, Electromagnetic Theory, Environmental Science and Engineering, and Electronic Devices and Circuits. The practical courses include Electronics Laboratory and Linear and Digital Integrated Circuits Laboratory. It then provides detailed course objectives and content outlines for some of the theory courses, including Transforms and Partial Differential Equations, Digital Logic Circuits, and Electromagnetic Theory. Recommended textbooks are also listed for some courses.
The document discusses the syllabus and exam details for AIEEE 2012. It provides information on the types of questions on the exam papers, dates for the online and offline exams, and syllabus details for mathematics, physics, and chemistry. Specifically, it outlines the topics covered in each subject, including units on algebra, calculus, mechanics, thermodynamics, electromagnetism, and modern physics. It also specifies the exam timing and duration for the two papers.
This document outlines the course requirements for a pre-PhD program in mathematics. It includes 1) a required 5-credit research methodology course covering skills like LaTeX, mathematical software, and reviewing papers; 2) an optional 5-credit participation in an advanced training mathematics school; and 3) a variety of 5-credit optional courses in areas like differential equations, Fourier analysis, complex analysis, and more. Students must complete 20 total credits, including the required methodology course, 10 credits from two other optional courses, and an additional 5-credit reading course with their research guide.
The document provides the syllabus for the 2013 EAMCET engineering entrance exam in the state of Andhra Pradesh, India. It outlines the syllabus for the mathematics and physics portions of the exam.
The mathematics syllabus covers topics in algebra, trigonometry, vector algebra, probability, and calculus. The physics syllabus covers 20 topics including measurements and units, mechanics, properties of matter, heat and thermodynamics, waves, optics, electricity and magnetism.
The syllabus is designed to be at the level of the intermediate course curriculum introduced by the state board of education for academic years 2011-2013. It indicates the scope of topics that will be included in the exam but is not
This document provides information about a course on molecular symmetry, group theory, and applications taught by Claire Vallance. It introduces some key concepts that will be covered in the course, including classifying molecular symmetry using point groups, and using group theory to understand molecular properties, bonding, vibrations, and spectroscopy. The document recommends textbooks for further reading and lists some useful websites for tutorials and interactive examples related to symmetry and group theory. It also includes an outline of topics that will be covered in the course lectures.
This document outlines the syllabus for a Strength of Materials course taught at Visvesvaraya Technological University. The course is a 3rd semester undergraduate class in Civil Engineering. It covers 5 modules: simple stresses and strains, compound stresses, shear force and bending moment in beams, torsion in circular shafts, and bending and shear stresses in beams. The course aims to teach students how to evaluate the strength of structural elements and materials. It will cover internal forces, failure concepts, torsion analysis, and beam design. Assessment includes class participation, exams, and a focus on applying concepts to solve engineering problems.
This document outlines the syllabus for the course MA3355 Random Processes and Linear Algebra taught in the third semester of the second year of the MREC/ECE program at Anna University, Chennai as per their 2021 regulations. The course covers five units: (1) probability and random variables, (2) two-dimensional random variables, (3) random processes, (4) vector spaces, and (5) linear transformations and inner product spaces. It includes topics such as probability distributions, random processes, vector spaces, linear transformations, and orthogonalization. The document also lists the textbooks and references for the course.
This document outlines the course outcomes and content for a 4-credit course on Topics in Probability. The course covers key concepts in probability including probability measures, random variables, distribution functions, expectation of random variables, convergence of random variables, independence, and characteristic functions. It is divided into 4 units that cover: probability measures and random variables, mathematical expectation and inequalities, modes of convergence, and independence and characteristic functions.
Advanced Linear Algebra (Third Edition) By Steven RomanLisa Cain
This document provides information about the Graduate Texts in Mathematics series published by Springer Science+Business Media, LLC. It lists 75 books in the series along with their authors and topics. It also provides the names of the editorial board members for the series, Steven Axler and Kenneth Ribet.
DA entrance exam is one of the highly anticipated and aspired examinations in India which offers the aspirants a large number of government job opportunities.
Competiton gurukul Coaching for NDA recruitment . Competition gurukul institute is the best coaching center for NDA in delhi India. NDA carry out selection and enrolment of Army , Navy, Air Force Officers . The National Defence Academy (NDA) admits students to the Army, Navy and Air Force wings through an entrance examination held twice a year, generally in the months of April and September. This examination is conducted by the Union Public Service Commission
Competition gurukul is a fine and promising institute for NDA coaching and our selection 75%. It provides all necessary resources of coaching for cracking NDA exam with marvelous ranking. The quality of coaching that competition gurukul provides is unique in various ways:
The syllabus is covered in specified duration with larger focus on concept development, knowledge building, through trick fusion frequent practice of formulas, facts and figures.
Wisely revised and highly graded study material.
Interactive, practical and sound approach conducted in classroom by highly qualified knowledge and dynamic professional teachers and experts.
Regular test and assessment as well as marks record keeping and maintenance system.
Time to time notification of various declared exams and guidance to farm filling.
This document provides the syllabus for the B. Tech in Civil Engineering program at Maulana Abul Kalam Azad University of Technology, West Bengal for the academic year 2018-2019. It outlines the courses, course outcomes, modules, topics, and references for the Introduction to Fluid Mechanics and Introduction to Solid Mechanics courses in the second year, fourth semester. The courses cover topics such as fluid properties, fluid statics and dynamics, dimensional analysis, flow through pipes, solid mechanics concepts, stress and strain analysis, beam bending, trusses, and columns. The document lists the intended learning outcomes and prerequisites for each course.
BU (UVCE)5th Sem Electronics syllabus copy from Lohith kumar R UVCE
This document outlines the scheme of study and examination for the 5th semester of the Bachelor of Engineering program in Electronics and Communication Engineering under the 2006 scheme at University Visweswariah College of Engineering in Bangalore. It includes:
1. A list of 8 subjects to be taken in the 5th semester, along with the course code, number of hours per week, duration of exams, sessional marks and exam marks for both theory and practical components.
2. The syllabus for the Probability and Stochastic Processes course, outlining 10 topics to be covered along with reference books.
3. Details of the format and content but not the full text of the document. It provides an overview
This document outlines the syllabus for the Introduction to Fluid Mechanics course in the second year of the B. Tech Civil Engineering program at Maulana Abul Kalam Azad University of Technology. The course covers key topics in fluid mechanics over 6 modules, including fluid properties, fluid statics, fluid kinematics, fluid dynamics, dimensional analysis, and flow through pipes and pipelines. The course aims to help students understand and apply fundamental fluid mechanics concepts and analyze hydraulic problems and systems. Reference books on fluid mechanics are also listed.
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
This document outlines the syllabus and scheme for various courses at Dharmsinh Desai University. It includes topics like Mathematics I, Basic Electrical and Electronics Engineering, Elements of Linux OS and C Programming, Engineering Mechanics, and Workshop I. Some of the key topics covered are differential and integral calculus, electrical circuits, Linux commands, file systems, C programming basics, statics, dynamics, and carpentry skills. The document provides details of textbooks and reference books for different subjects. It specifies the teaching scheme with numbers of lectures, tutorials, and practical sessions along with the credit structure for each course.
The document provides information about the Engineering Mathematics - III course, including details about 8 units that will be covered in the course. It lists the topics that will be discussed in each unit, such as Fourier series, Fourier transforms, partial differential equations, curve fitting, numerical methods, difference equations, and Z-transforms. It also provides information about the course code, credit hours, examination hours and marks. Textbooks and reference books for the course are also specified.
The document describes a test for candidates pursuing an M.Tech in Computer Science. The test consists of two parts - Test MIII in the morning and Test CS in the afternoon. Test CS has two groups: Group A contains questions on analytical ability and mathematics at the BSc pass level. Group B contains questions testing knowledge in various subjects at higher levels, and candidates must choose one section to answer questions from. Sample questions are provided for both groups covering topics in mathematics, statistics, physics, computer science, and engineering.
The document describes a test for candidates seeking an M.Tech in Computer Science. It discusses the structure and content of the test, which includes two parts - an objective test in the morning and a short answer test in the afternoon. The short answer test contains two groups: Group A covers analytical ability and mathematics at the B.Sc. pass level, while Group B covers various subjects at higher levels and candidates must choose one section to answer questions from. Sample questions are provided covering a range of mathematical and technical topics that may appear on the test.
The document provides an overview of the syllabus for the BITSAT 2013 entrance exam, covering topics tested in mathematics, chemistry, and physics. Some of the main topics included are: algebra, trigonometry, coordinate geometry, calculus, probability, vectors, statistics, linear programming, atomic structure, chemical bonding, thermodynamics, equilibria, electrochemistry, and properties of matter. The syllabus outlines the specific concepts covered within each subject in detail to prepare students for the exam.
This document is a research essay presented by Canlin Zhang to the University of Waterloo in partial fulfillment of the requirements for a Master's degree in Pure Mathematics. The essay introduces some basic concepts in operator theory and their connections to quantum computation and information. It discusses topics such as quantum algorithms, quantum channels, quantum error correction, and noiseless subsystems. The essay is divided into six sections that cover these topics at a high-level introduction.
This document summarizes career opportunities in mathematics. It discusses higher education opportunities like MSc, MSc Applied Mathematics, and integrated MSc-PhD programs. It also outlines teaching careers requiring BSc, MSc, and PhD and research roles in organizations like IISc after PhD. Additionally, it discusses careers in government sectors like banking, insurance and railways requiring mathematics skills and competitive exams. Private sector careers mentioned include software companies, actuarial roles, and operation researcher. The document provides an overview of the wide range of opportunities available to mathematics graduates.
This document provides an overview of topics related to congruences that will be covered, including congruences, properties of congruences, linear congruences, and the Chinese remainder theorem.
This document contains the syllabus for the third semester of the B.E. degree in Electrical and Electronics Engineering at Anna University, Chennai. It lists the theory and practical courses offered in the semester. The theory courses include Transforms and Partial Differential Equations, Digital Logic Circuits, Electromagnetic Theory, Environmental Science and Engineering, and Electronic Devices and Circuits. The practical courses include Electronics Laboratory and Linear and Digital Integrated Circuits Laboratory. It then provides detailed course objectives and content outlines for some of the theory courses, including Transforms and Partial Differential Equations, Digital Logic Circuits, and Electromagnetic Theory. Recommended textbooks are also listed for some courses.
The document discusses the syllabus and exam details for AIEEE 2012. It provides information on the types of questions on the exam papers, dates for the online and offline exams, and syllabus details for mathematics, physics, and chemistry. Specifically, it outlines the topics covered in each subject, including units on algebra, calculus, mechanics, thermodynamics, electromagnetism, and modern physics. It also specifies the exam timing and duration for the two papers.
This document outlines the course requirements for a pre-PhD program in mathematics. It includes 1) a required 5-credit research methodology course covering skills like LaTeX, mathematical software, and reviewing papers; 2) an optional 5-credit participation in an advanced training mathematics school; and 3) a variety of 5-credit optional courses in areas like differential equations, Fourier analysis, complex analysis, and more. Students must complete 20 total credits, including the required methodology course, 10 credits from two other optional courses, and an additional 5-credit reading course with their research guide.
The document provides the syllabus for the 2013 EAMCET engineering entrance exam in the state of Andhra Pradesh, India. It outlines the syllabus for the mathematics and physics portions of the exam.
The mathematics syllabus covers topics in algebra, trigonometry, vector algebra, probability, and calculus. The physics syllabus covers 20 topics including measurements and units, mechanics, properties of matter, heat and thermodynamics, waves, optics, electricity and magnetism.
The syllabus is designed to be at the level of the intermediate course curriculum introduced by the state board of education for academic years 2011-2013. It indicates the scope of topics that will be included in the exam but is not
This document provides information about a course on molecular symmetry, group theory, and applications taught by Claire Vallance. It introduces some key concepts that will be covered in the course, including classifying molecular symmetry using point groups, and using group theory to understand molecular properties, bonding, vibrations, and spectroscopy. The document recommends textbooks for further reading and lists some useful websites for tutorials and interactive examples related to symmetry and group theory. It also includes an outline of topics that will be covered in the course lectures.
This document outlines the syllabus for a Strength of Materials course taught at Visvesvaraya Technological University. The course is a 3rd semester undergraduate class in Civil Engineering. It covers 5 modules: simple stresses and strains, compound stresses, shear force and bending moment in beams, torsion in circular shafts, and bending and shear stresses in beams. The course aims to teach students how to evaluate the strength of structural elements and materials. It will cover internal forces, failure concepts, torsion analysis, and beam design. Assessment includes class participation, exams, and a focus on applying concepts to solve engineering problems.
This document outlines the syllabus for the course MA3355 Random Processes and Linear Algebra taught in the third semester of the second year of the MREC/ECE program at Anna University, Chennai as per their 2021 regulations. The course covers five units: (1) probability and random variables, (2) two-dimensional random variables, (3) random processes, (4) vector spaces, and (5) linear transformations and inner product spaces. It includes topics such as probability distributions, random processes, vector spaces, linear transformations, and orthogonalization. The document also lists the textbooks and references for the course.
This document outlines the course outcomes and content for a 4-credit course on Topics in Probability. The course covers key concepts in probability including probability measures, random variables, distribution functions, expectation of random variables, convergence of random variables, independence, and characteristic functions. It is divided into 4 units that cover: probability measures and random variables, mathematical expectation and inequalities, modes of convergence, and independence and characteristic functions.
Advanced Linear Algebra (Third Edition) By Steven RomanLisa Cain
This document provides information about the Graduate Texts in Mathematics series published by Springer Science+Business Media, LLC. It lists 75 books in the series along with their authors and topics. It also provides the names of the editorial board members for the series, Steven Axler and Kenneth Ribet.
DA entrance exam is one of the highly anticipated and aspired examinations in India which offers the aspirants a large number of government job opportunities.
Competiton gurukul Coaching for NDA recruitment . Competition gurukul institute is the best coaching center for NDA in delhi India. NDA carry out selection and enrolment of Army , Navy, Air Force Officers . The National Defence Academy (NDA) admits students to the Army, Navy and Air Force wings through an entrance examination held twice a year, generally in the months of April and September. This examination is conducted by the Union Public Service Commission
Competition gurukul is a fine and promising institute for NDA coaching and our selection 75%. It provides all necessary resources of coaching for cracking NDA exam with marvelous ranking. The quality of coaching that competition gurukul provides is unique in various ways:
The syllabus is covered in specified duration with larger focus on concept development, knowledge building, through trick fusion frequent practice of formulas, facts and figures.
Wisely revised and highly graded study material.
Interactive, practical and sound approach conducted in classroom by highly qualified knowledge and dynamic professional teachers and experts.
Regular test and assessment as well as marks record keeping and maintenance system.
Time to time notification of various declared exams and guidance to farm filling.
This document provides the syllabus for the B. Tech in Civil Engineering program at Maulana Abul Kalam Azad University of Technology, West Bengal for the academic year 2018-2019. It outlines the courses, course outcomes, modules, topics, and references for the Introduction to Fluid Mechanics and Introduction to Solid Mechanics courses in the second year, fourth semester. The courses cover topics such as fluid properties, fluid statics and dynamics, dimensional analysis, flow through pipes, solid mechanics concepts, stress and strain analysis, beam bending, trusses, and columns. The document lists the intended learning outcomes and prerequisites for each course.
BU (UVCE)5th Sem Electronics syllabus copy from Lohith kumar R UVCE
This document outlines the scheme of study and examination for the 5th semester of the Bachelor of Engineering program in Electronics and Communication Engineering under the 2006 scheme at University Visweswariah College of Engineering in Bangalore. It includes:
1. A list of 8 subjects to be taken in the 5th semester, along with the course code, number of hours per week, duration of exams, sessional marks and exam marks for both theory and practical components.
2. The syllabus for the Probability and Stochastic Processes course, outlining 10 topics to be covered along with reference books.
3. Details of the format and content but not the full text of the document. It provides an overview
This document outlines the syllabus for the Introduction to Fluid Mechanics course in the second year of the B. Tech Civil Engineering program at Maulana Abul Kalam Azad University of Technology. The course covers key topics in fluid mechanics over 6 modules, including fluid properties, fluid statics, fluid kinematics, fluid dynamics, dimensional analysis, and flow through pipes and pipelines. The course aims to help students understand and apply fundamental fluid mechanics concepts and analyze hydraulic problems and systems. Reference books on fluid mechanics are also listed.
In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.
This document outlines the syllabus and scheme for various courses at Dharmsinh Desai University. It includes topics like Mathematics I, Basic Electrical and Electronics Engineering, Elements of Linux OS and C Programming, Engineering Mechanics, and Workshop I. Some of the key topics covered are differential and integral calculus, electrical circuits, Linux commands, file systems, C programming basics, statics, dynamics, and carpentry skills. The document provides details of textbooks and reference books for different subjects. It specifies the teaching scheme with numbers of lectures, tutorials, and practical sessions along with the credit structure for each course.
The document provides information about the Engineering Mathematics - III course, including details about 8 units that will be covered in the course. It lists the topics that will be discussed in each unit, such as Fourier series, Fourier transforms, partial differential equations, curve fitting, numerical methods, difference equations, and Z-transforms. It also provides information about the course code, credit hours, examination hours and marks. Textbooks and reference books for the course are also specified.
The document describes a test for candidates pursuing an M.Tech in Computer Science. The test consists of two parts - Test MIII in the morning and Test CS in the afternoon. Test CS has two groups: Group A contains questions on analytical ability and mathematics at the BSc pass level. Group B contains questions testing knowledge in various subjects at higher levels, and candidates must choose one section to answer questions from. Sample questions are provided for both groups covering topics in mathematics, statistics, physics, computer science, and engineering.
The document describes a test for candidates seeking an M.Tech in Computer Science. It discusses the structure and content of the test, which includes two parts - an objective test in the morning and a short answer test in the afternoon. The short answer test contains two groups: Group A covers analytical ability and mathematics at the B.Sc. pass level, while Group B covers various subjects at higher levels and candidates must choose one section to answer questions from. Sample questions are provided covering a range of mathematical and technical topics that may appear on the test.
The document provides an overview of the syllabus for the BITSAT 2013 entrance exam, covering topics tested in mathematics, chemistry, and physics. Some of the main topics included are: algebra, trigonometry, coordinate geometry, calculus, probability, vectors, statistics, linear programming, atomic structure, chemical bonding, thermodynamics, equilibria, electrochemistry, and properties of matter. The syllabus outlines the specific concepts covered within each subject in detail to prepare students for the exam.
This document is a research essay presented by Canlin Zhang to the University of Waterloo in partial fulfillment of the requirements for a Master's degree in Pure Mathematics. The essay introduces some basic concepts in operator theory and their connections to quantum computation and information. It discusses topics such as quantum algorithms, quantum channels, quantum error correction, and noiseless subsystems. The essay is divided into six sections that cover these topics at a high-level introduction.
This document summarizes career opportunities in mathematics. It discusses higher education opportunities like MSc, MSc Applied Mathematics, and integrated MSc-PhD programs. It also outlines teaching careers requiring BSc, MSc, and PhD and research roles in organizations like IISc after PhD. Additionally, it discusses careers in government sectors like banking, insurance and railways requiring mathematics skills and competitive exams. Private sector careers mentioned include software companies, actuarial roles, and operation researcher. The document provides an overview of the wide range of opportunities available to mathematics graduates.
This document provides an overview of topics related to congruences that will be covered, including congruences, properties of congruences, linear congruences, and the Chinese remainder theorem.
This document discusses prime numbers and Fermat numbers in mathematics. It covers prime numbers, the D algorithm theorem for finding prime numbers, the greatest common divisor (GCD) method, and the least common multiple (LCM) method.
This document outlines the topics covered in an elementary number theory course including basic definitions and concepts, divisibility and the division algorithm theorem, the greatest common divisor, and the least common multiple. The course is offered by the Department of Mathematics at Mahatma Gandhi College in Armori.
This document discusses homogeneous differential equations and Wronskian theory. It covers three main topics: homogeneous linear differential equations, the Wronskian, and calculus of variations.
This document outlines topics in higher order ordinary differential equations, including linear differential equations of higher orders with constant coefficients, complementary functions, particular integrals, and simultaneous differential equations.
This document provides an overview of topics covered in first order ordinary differential equations, including basic definitions, exact differential equations, linear differential equations, Bernoulli's differential equations, and orthogonal trajectory.
This document provides proposed syllabi for courses in the BSc Mathematics program at Mahatma Gandhi Arts, Science and Commerce College for semesters 5 and 6. It includes proposed courses, topics to be covered, reference materials, and exam details for Skill Enhancement Courses, Discipline Specific Electives, and other mathematics courses. Courses cover topics such as probability, mathematical modeling, linear algebra, matrices, numerical methods, graph theory, Boolean algebra, complex analysis, vector calculus, linear programming, and transportation problems. Exams will be conducted by the college for SEC courses and the university for DSE courses.
This document proposes a syllabus for Bachelor of Science in Mathematics at Maharaja Gandhi Arts, Science and Late N.P. Commerce College in Armori for semesters 3 and 4 under the Choice Based Credit System.
For semester 3, the proposed papers are Real Analysis (USMT-05) and Set Theory and Laplace Transform (USMT-06). For semester 4, the proposed papers are Algebra (USMT-07) and Elementary Number Theory (USMT-08). Each paper is divided into 4 units and includes topics such as real sequences, metric spaces, group theory, and prime numbers. Reference books are provided for each paper.
This document outlines the proposed syllabus for mathematics courses in the first and second semesters of a B.Sc. program under the Choice Based Credit System with effect from the 2017-18 academic year. It lists 4 courses to be offered each semester: Differential and Integral Calculus, Differential Calculus and Trigonometry, Ordinary Differential Equations and Difference Equations, and Partial Differential Equation. For each course, it provides the maximum marks, units of study, and list of reference books. The units cover topics in calculus, trigonometry, ordinary and partial differential equations, and difference equations.
More from DEPARTMENT OF MATHEMATICS MGC ARMORI (10)
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This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
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
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
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.
1. MAHATMA GANDHI ARTS, SCIENCE
AND LATE N.P. COMMERCE
COLLEGE ARMORI
Proposed Syllabus For
M.Sc. Mathematics Semester-III and
Semester-IV
Under Choice Based Credit System
(C.B.C.S.)
With effect from Academic Year:
2021-22
(Considered and approved by B.O.S. in Mathematics)
1
2. M.Sc. Mathematics
Semester wise Syllabus
M.Sc. Semester- III
CORE COURSES
2
PSCMTH11:
PSCMTH12 :
PSCMTH13:
ComplexAnalysis
FunctionalAnalysis
Mathematical Methods
PSCMTH14: CORE ELECTIVE COURSE (Opt any one of the following)
(a) Fluid Dynamics - I
(b) General Relativity
(c) Graph Theory
(d) CommutativeAlgebra
(e) Lattice Theory
PSCMTH15: FOUNDATION COURSE (Opt any one of the following)
Students from any post graduate program may opt any one of the following:
(a) Operations Research – I
(b) Business Mathematics
(c) MATLAB Programming
(d) Statistics
M.Sc. Semester- IV
CORE COURSE
PSCMTH16:
PSCMTH17:
PSCMTH18:
Dynamical Systems
Partial Differential Equations
Integral Equations
PSCMTH19: CORE ELECTIVE COURSE (Opt any one of the following)
(a) Fluid Dynamics - II
(b) Cosmology
(c) Combinatorics
(d) Representation Theory of the Symmetric Group
(e) Matroid Theory
PSCMTH20: FOUNDATION COURSE (Opt any one of the following)
Students from any post graduate program may opt any one of the following:
(a) Operations Research – II
(b) Elementary Discrete Mathematics
(c) Financial Mathematics
(d) C Programming
3. 3
SEMESTER-III
Core Course Code - PSCMTH11 Credit - 05
Complex Analysis
UNIT-I
Functions and Mappings, The Mappings u′ = z2 , Limits, Theorems on Limits,
Limits Involving the Point at Infinity, Continuity, Derivatives, Rules for
Differentiation, Cauchy–Riemann Equations, Sufficient Conditions for
Differentiability, Polar Coordinates, Analytic Functions, Harmonic Functions,
Uniquely Determined Analytic Functions, Reflection Principle, The Exponential
Function, The Logarithmic Function, Branches and Derivatives of Logarithms,
Some Identities involving Logarithms, The Power Function, Trigonometric
Functions, Zeros and singularities of Trigonometric Functions, Hyperbolic
Functions, Inverse Trigonometric and Hyperbolic Functions.
UNIT-II
Derivatives of Functions, Definite Integrals of Functions, Contours, Contour
Integrals with Examples, Examples involving Branch Cuts, Upper Bounds for
Moduli of Contour Integrals, Antiderivatives, Cauchy–Goursat Theorem, Simply
Connected Domains, Multiply connected Domains, Cauchy Integral Formula, An
Extension of Cauchy Integral Formula, Liouville’s Theorem and the Fundamental
Theorem of Algebra, Maximum Modulus Principle, Schwarz’s lemma(from
Ponnusammy’s book) Convergence of Sequences, Convergence of Series, Taylor
Series with Examples, Laurent Series with Examples, Absolute and Uniform
Convergence of Power Series.
UNIT-III
Isolated Singular Points, Residues, Cauchy’s Residue Theorem, Residue at Infinity,
The Three Types of Isolated Singular Points with Examples, Residues at Poles with
Examples, Zeros of Analytic Functions, Zeros and Poles, Behaviour of functions
near isolated singular points, Evaluation of Improper Integrals with Examples,
Jordan’s Lemma, Definite Integrals Involving Sines and Cosines, Argument
Principle, Rouche’s Theorem.
UNIT-IV
Linear Transformations, The Transformation w = 1/z, Mappings by 1/z, Linear
Fractional Transformations, An Implicit Form, Mappings of the Upper Half Plane
with Examples, Mapping Vertical Line Segments by w = sin z, Mapping Horizontal
Line Segments by w = sin z, Mappings by z2, Mapping by Branches of z1/2.
Text Books:
1. Complex Variables and Applications (Ninth edition): R. V
.Churchill and J. W.
Brown, Mc Graw Hill Publication.
4. 4
Scope:
Unit I – Chapter 2 and 3
Unit II - Chapter 4 and Chapter 5(excluding Continuity of Sums of Power Series,
Integration and Differentiation of Power Series, Uniqueness of Series
Representations, Multiplication and Division of Power Series)
Unit III - Chapter 6 and Chapter 7(excluding Improper Integrals from Fourier
Analysis, An Indented Path, An Indentation Around a Branch Point, Integration
along a branch cut, Inverse Laplace Transforms)
Unit IV – Chapter 8 (excluding Mapping by The Exponential Function, Square
Roots of Polynomials, Riemann surfaces, Surfaces for Related Functions)
2. Foundation of Complex Analysis (Second Edition): S.Ponnusamy, Narosa
Publication.
Reference Books:
1. Functions of One Complex Variable (Second edition): John B. Conway, Springer
international Student Edition.
2. ComplexAnalysis: L. V
.Ahlfors, Mc-Graw Hill, 1966.
5. 5
Core Course Code - PSCMTH12 Credit - 05
FunctionalAnalysis
UNIT-I
Definition and Some Examples of Banach Spaces, Continuous Linear
Transformations, The Hahn-Banach Theorem, The Natural embedding of N in N**.
UNIT-II
The Open Mapping Theorem, The Conjugate of an Operator, The Definition and
Some Simple Properties of Hilbert Spaces, Orthogonal Complements, Orthonormal
Sets.
UNIT-III
The conjugate space H*, The adjoint of an Operator, Self-adjoint Operators,
Normal and Unitary Operators, Projections.
UNIT-IV
Finite Dimensional Spectral Theory: Introduction, Matrices, Determinants and
Spectrum of an Operator, The Spectral Theorem.
Text Book:
Introduction to Topology and Modern Analysis: G. F. Simmons, Mc Graw Hill
International Student Edition, New York.
Scope:
Articles 46 to 62.
Reference Books:
1. Introduction to FunctionalAnalysis:A. E. Taylor and D. C. Lay, John Wiley and
Sons.
2. Introductory Functional Analysis with Applications: E. Kreyszig, John Wiley and
Sons.
3. Foundations of FunctionalAnalysis: S. Ponnusamy, Narosa Publishing House.
6. 6
Text Book:
An Introduction to Integral Transforms (First Edition): Baidyanath Patra, CRC
Press Taylor Francis Group, 2018.
Scope:
Unit I - Chapter 1 (1.1 to 1.16 with Exercices)
Unit II - Chapter 2 (2.1 to 2.7 with Exercices)
Unit III - Chapter 3 (3.1 to 3.19 with Exercices) and Chapter 4(4.1 to 4.4 with
Exercises)
Unit IV - Chapter 6 (6.1 to 6.6 with Exercices) and Chapter 8(8.1 to 8.7 with
Exercises)
References Books:
1. The Use of Integral Transforms: I N. Sneddon, Tata McGraw Hill Publishing
Company Ltd.
2. Modern Mathematics for Engineers: Edwin F Beckenbach, Second series,
McGraw Hill Book Company.
7. 7
Core Elective Course Code - PSCMTH14 (Opt any one of the following)
Credit - 05
(a) Fluid Dynamics-I
UNIT-I
Real Fluids and Ideal Fluids, Velocity of a Fluid at a Point, Stream Lines and Path
Lines, Steady and Unsteady Flows, Velocity Potential, Vorticity Vector, Local and
Particle Rates of Change, The Equation of Continuity, Worked Examples, Acceleration
of a Fluid, Condition at a Rigid Boundary, General Analysis of Fluid Motion, Euler’s
Equation of Motion, Bernoulli’s Equation, Worked Examples, Discussion of the Case
of Steady Motion Under Conservative Body Forces, Some Further Aspects of Vortex
Motion.
UNIT-II
Sources, Sinks and Doublets, Images in a Rigid Infinite Plane, Images in Solid
Spheres, Axisymmetric Flows, Stokes’ Stream Function. The Complex Potential for
Two-Dimensional Irrotational, Incompressible Flow, Complex Velocity Potential for
Standard Two Dimensional Flows, Uniform Stream, Line Source and Line Sinks,
Line Doublets, Line Vortices, Some Worked Examples, Two Dimensional Image
Systems, The Milne-Thomson Circle Theorem, Some applications of Circle
Theorem, Extension of the Circle Theorem, The Theorem of Blasius.
UNIT-III
The Equations of State of a Substance, The First Law of Thermodynamics, Internal
Energy of a Gas, Functions of State, Entropy, Maxwell’s Thermodynamic
Relations, Isothermal Adiabatic and Isentropic Processes, Compressibility Effects
in Real Fluids, The Elements of Wave Motion, One Dimensional Wave Equation,
Wave Equation in Two and Three Dimensions, Spherical Waves, Progressive and
Stationary Waves.
UNIT-IV
The Speed of Sound in a Gas, Equation of Motion of a Gas, Subsonic, Sonic,
Supersonic Flows, Isentropic Gas Flow, Reservoir Discharge Through a Channel of
Varying Section, Investigation of Maximum Mass Flow through a Nozzle, Shock
Waves, Formation of Shock Waves, ElementaryAnalysis of Normal Shock Waves.
Text Book:
Textbook of Fluid Dynamics: F. Chorlton, CBS Publishers, Delhi, 1985.
Reference Books:
1. An Introduction to Fluid Mechanics: G. K. Batchelor, Foundation Books, New
Delhi, 1994.
2. Fluid Mechanics: M. D. Raisinghania, S. Chand and Company, Delhi.
8. 8
(d) Commutative Algebra
UNIT-I
Rings and ring homomorphisms, Ideals, Quotient rings, Zero divisors, Nilpotent
elements, Units, Prime ideals and Maximal ideals, Nil radical and Jacobson radical,
Operations on ideals, Extension and contraction.
UNIT-II
Modules and module homomorphisms, Sub modules and Quotient modules,
Operations on sub modules, Direct sum and product, Finitely generated modules,
Exact sequences, Tensor product of modules, Restriction and extension of scalars,
Exactness properties of the tensor product,Algebras, Tensor product of algebras.
UNIT-III
Local properties, Extended and contracted ideals in ring of fractions, Primary
Decomposition. Integral dependence, The going-up theorem, Integrally closed
integral domains, The going- down theorem, Chain conditions.
UNIT-IV
Primary decomposition in Noetherian rings, Artin rings, Discrete valuation rings,
Dedekind domains, Fractional ideals.
Text Book:
Introduction to Commutative Algebra: M. F.Atiyah and I. G. Macdonald, Addison-
Wesley Publishing Company.
Scope:
Chapter 1 to Chapter 9.
Reference Books:
1. Commutative Ring Theory: H. Matsumura, Cambridge University Press.
2. CommutativeAlgebra: N. S. Gopalakrishnan.
3. AbstractAlgebra (Second Edition): D. S. Dummite and R. M. Foote, John Wiley
& Sons.
9. 9
Foundation Course Code - PSCMTH15 (Opt any one of the following)
Credit - 05
(a) Operations Research - I
UNIT-I
Linear Programming Problem - Simplex method, Duality in Linear Programming.
UNIT-II
Transportation Problem ,Assignment problems.
UNIT-III
Dynamic programming.
UNIT-IV
Games and Strategies.
Text Book:
Operations Research: Kanti Swarup, P. K. Gupta and Man Mohan, Sultan Chand
and Sons New Delhi.
Scope:
Unit I - Chapter 4 and 5
Unit II - Chapter 10 and 11
Unit III - Chapter 13
Unit IV - Chapter 17
Reference Books:
1. Linear Programming: G. Hadley, Narosa Publishing House,1995.
2. Introduction to Operations Research (Sixth Edition): F. S. Hillier and G. J.
Lieberman, Mc Graw Hill International Edition, 1995.
3. Operations Research – In Introduction: H.ATaha, Macmillan publishing company
Inc., New York
10. 10
Core Course Code - PSCMTH17 Credit - 05
Partial Differential Equations
UNIT-I
First order Partial Differential Equations :
Curves and Surfaces, Genesis of First Order P.D.E, Classification of Integrals,
Linear Equations of First Order, Pfaffian Differential Equations, Compatible
Systems, Charpit’s Method , Jacobi Method.
UNIT-II
Integral Surfaces Through a Given Curve, Quasi-Linear Equations, Non-linear First
Order Partial Differential Equations.
UNIT-III
Second order Partial Differential Equations :
Genesis of Second Order Partial Differential Equations, Classification of Second
Order Partial Differential Equations, One Dimensional Wave Equations.
UNIT-IV
Laplace’s Equation, Heat Conduction Problem, Duhamel’s Principle, Classification
in the Case of n variables, Families of Equipotential Surfaces.
Text Book:
An Elementary Course in Partial Differential Equations (Second Edition): T.
Amarnath, Narosa Publishing House.
Reference Books:
1. Partial Differential Equations: Phoolan Prasad and Renuka Ravindran; New Age
International (P) Limited.
2. Elements of Partial Differential Equations: I. N. Sneddon, McGraw Hill Book
Company
11. 11
Core Course Code – PSCMTH18 Credit - 05
Integral Equations
UNIT-I
Basic Concepts of Integral Equations: Introduction, Types of Kernels, Eigen values
and Eigen Functions, Differentiation under the Sign of Integration (Leibnitz’s
Rule), Connection with Differential Equation, Solution of an Integral Equation,
Conversion of Differential Equations to Integral Equations - Initial Value Problems,
Boundary Value Problems.
UNIT-II
Solution of Fredholm Integral Equations: Solution of Homogenous Fredholm
Integral Equations of the Second Kind with Separable (or Degenerate Kernel),
Orthogonality and Reality of Eigen Functions, Fredholm Integral Equations with
Separable Kernel.
UNIT-III
Hilbert - Schmidt Theory: Symmetric Kernel: Introduction, Complex Hilbert
Space, Othonormal System of Functions, Gram - Schmidt Orthonormalization
Process, Riesz - Fischer Theorem, Symmetric Kernel, Expansion of Symmetric
Kernel in Eigen Function, Hilbert - Schmidt Theorem, Solution of the Fredholm
Integral Equation of First Kind, Schmidt’s Solution of the Non-Homogenous
Fredholm Integral Equation of Second Kind.
UNIT-IV
Solution of Integral Equations of Second Kind: Successive Approximations and
Substitution Methods: Introduction, Solution of the Fredholm Integral Equation of
Second Kind by Successive Substitution, Solution of Volterra Integral Equation of
Second Kind by Successive Substitution, Solution of the Fredholm Integral
Equation of Second Kind by Successive Approximation, Reciprocal Functions,
Volterra’s Solution of Fredholm Integral Equation of the Second Kind, Solution of
Volterra Integral Equation of Second Kind by Successive Approximation:
Neumann Series, Some Particular Cases, Reduction of Volterra Integral Equation
into Differential Equation, Reduction of Volterra Integral Equation of First Kind to
a Volterra Integral Equation of Second Kind.
Text Book:
Mathematical Methods: Sudhir K. Pundir, Rimple Pundir, Pragati Prakashan,
Meerut.
Reference Book:
Integral Equations: A Short Course: LI. G. Chambers: International text book
company Ltd., 1976.
12. 12
Core Elective Course - PSCMTH19 (Opt any one of the following) Credit - 05
(a) Fluid Dynamics-II
UNIT-I
Stress components in a real fluid, Relation between Cartesian components of stress,
Translation motion of fluid elements, The rate of strain quadric and principal
stresses, Some further properties of the rate of the strain quadric, Stress analysis in
fluid motion, Relation between stress and rate of strain, The coefficient of viscosity
and laminar flow, The Navier-Stokes equations of motion of a viscous fluid, Some
solvable problems in viscous flow, Diffusion of vorticity, Energy dissipation due to
viscosity, Steady flow past a fixed sphere.
UNIT-II
Nature of magnetohydrodynamics, Maxwell electromagnetic field equations:
Medium at rest, Maxwell electromagnetic field equations: Medium in Motion,
Equation of motion of conducting fluid, Rate of flow of charge, Simplification of
electromagnetic field equations, Magnetic Reynold’s number; Alfven’s theorem,
The magnetic body force, Ferraro’s Law of Isorotation.
UNIT-III
Dynamical similarity, Buckingham Theorem. Reynold number. Prandtl’s boundary
layer, Boundary layer equation in two dimensions, Blasius solutions, Boundary
layer thickness, Displacement thickness. Karman integral conditions, Separation of
boundary layer flow.
UNIT-IV
Turbulence: Definition of turbulence and introductory concepts. Equations of
motion for turbulent flow. Reynolds Stresses Cylindrical coordinates. Equation for
the conservation of a transferable scalar quantity in a turbulent flow. Double
correlations between turbulence-velocity components. Change in double velocity
correlation with time. Introduction to triple velocity correlations. Features of the
double longitudinal and lateral correlations in a homogeneous turbulence. Integral
scale of turbulence.
Text Books:
1. Text book of Fluid Dynamics: F. Chorlton; CBS Publishers, Delhi, 1985.
2. Fluid Mechanics: Joseph Spurk, Springer.
3. Turbulence (Second edition): J. O. Hinze, Mc Graw-Hill, chapter 1 sections 1.1
to 1.7
Reference Books:
1. An Introduction to Fluid Mechanics: G. K. Batchelor; Foundation Books, New
Delhi, 1994.
2. Boundary Layer Theory: H. Schichting, Mc Graw Hill Book Company, New
York, 1971.
3. Fluid Mechanics: M.D. Raisinghania, S. Chand and Company, Delhi.
13. 13
Foundation Course Code - PSCMTH20 (Opt any one of the following)
Credit - 05
(a) Operations Research - II
UNIT-I
Integer programming.
UNIT-II
Goal Programming, Linear Programming Problem -Advanced Techniques.
UNIT-III
Sequencing Problem, Queueing Theory.
UNIT-IV
Non - Linear Programming, Non - Linear Programming Methods.
Text Book:
Operations Research: Kanti-Swarup, P.K. Gupta and Man Mohan, Sultan Chand
and Sons, New Delhi.
Scope:
Unit I - Chapter 7
Unit II - Chapter 8 and 9
Unit III - Chapter 12 and 21
Unit IV - Chapter 27 and 28
Reference Books:
1. Linear Programming: G. Hadley, Narosa Publishing House 1995.
2. Introduction to Operations Research (Sixth Edition), F. S. Hillier and G. J.
Lieberman, Mc Graw Hill, International Edition 1995.
3. Operations Research – An Introduction: H.A Taha, Macmillan publishing
Company inc, New York
14. 14
(b) Elementary Discrete Mathematics
UNIT-I
Mathematical Logic: Introduction, Proposition, Compound Proposition, Proposition
and truth tables, Logical equivalence, Algebra of Proposition, conditional
Proposition, Converse, contrapositive & Inverse, Bi-conditional statement,
Negation of compound statements, Tautologies & contradictions, normal forms,
Logic in proof.
UNIT-II
Lattice: Lattice as partially ordered sets, Their properties, Lattices as algebraic
systems, Sub lattices, and Some special lattices eg. Complete, Complemented and
Distributive lattices.
UNIT-III
Boolean algebra and Logic Circuits: Boolean algebra, Basic operations, Boolean
functions, De-Morgan’s theorem, Logic gate, Sum of products and Product of sum
forms, Normal form, Expression of Boolean function as a canonical form,
Simplification of Boolean expression by algebraic method, Boolean expression
form logic & Switching network.
UNIT-IV
Graph Theory: Basic terminology, Simple graph, Multigraph, Degree of a vertex,
Types of a graph, Sub graphs of isomorphic graphs, Matrix representation of
graphs, Euler’s theorem on the existence of Eulerian path & Circuits, Directed
graph, Weighted graphs, Strong connectivity, Chromatic number.
Text Book:
Discrete Mathematical structures with applications to computer science by J. P.
Tremblay and R. Manohar, McGraw-Hill book company, 1997.
Reference Book:
1. Discrete Mathematics and Its Applications (Eighth Edition): Kenneth Rosen,
McGraw - Hill Higher Education, 2018.
2. Essential Discrete Mathematics for Computer Science: Harry Lewis, Rachel
Zax, Princeton University Press, 2019.
3. A Beginner’s Guide to Discrete Mathematics (Second Edition): W. D. Wallis,
Birkhauser Basel, 2012.