Mathematical Methods and its Applications 6Q1DW4B01S

URI	`m2://res/6Q1DW4B01S`
Kind	course
Creators	P.N. Agarwal (instructor), S. K. Gupta (instructor)
Date	2017-01-17
Scope	in
Ids	course 00582g326:111107098

Expressions

e1: edition

Language	en
Date	2017-01-17

m1: page, IIT Roorkee (record). nptel 111107098
m2: page, 2017-01-17 (record). nptel 111107098

Contents

part 1: Week 1
session 1: Introduction to linear differential equations
session 2: Linear dependence, independence and Wronskian of functions, Existence and Uniqueness theorem
session 3: Solution of second order homogeneous linear differential equations with constant coefficient-
session 4: Solution of second order homogeneous linear differential equations with constant coefficient-II
session 5: Methods of Undetermined coefficients
part 2: Week 2
session 6: Methods for finding particular integrals for second order linear differential equations with constant coefficients I
session 7: Methods for finding particular integrals for second order linear differential equations with constant coefficients II
session 8: Methods for finding particular integrals for second order linear differential equations with constant coefficients III
session 9: Cauchy-Euler equation
session 10: Methods of reduction for second order-linear differential equations
part 3: Week 3
session 11: Methods of variation of parameters
session 12: Solution of second order differential equations by changing dependent variables
session 13: Solution of second order differential equations by changing independent variable
session 14: Solution of higher-order homogeneous linear differential equations with constant coefficients
session 15: Methods for finding particular integral for higher-order linear differential equations with constant coefficient s
part 4: Week 4
session 16: Formulation of partial differential equations
session 17: Solution of Lagrange's equation I
session 18: Solution of Lagranage's equations II
session 19: Solution of first order non-linear equation I
session 20: Solution of first order non-linear equation II
part 5: Week 5
session 21: Solution of first order non linear equation III
session 22: Solution of first order non linear equation IV
session 23: Introduction to Laplace transforms
session 24: Laplace transforms of some standard functions
session 25: Existence theorem for Laplace transforms
part 6: Week 6
session 26: Properties of Laplace transforms-I
session 27: Properties of Laplace transforms-II
session 28: Properties of Laplace transforms-III
session 29: Properties of Laplace transforms-IV
session 30: Convolution Theorem for Laplace Transforms-I
part 7: Week 7
session 31: Convolution Theorem for Laplace Transforms-II
session 32: Initial and Final Value Theorems for Laplace Transforms
session 33: Laplace Transforms of Periodic Functions
session 34: Laplace Transforms of Unit Step Function
session 35: Laplace Transforms of Dirac delta Functions
part 8: Week 8
session 36: Applications of Laplace Transforms-I
session 37: Applications of Laplace Transforms-II
session 38: Applications of Laplace Transforms-III
session 39: Z- transform and inverse Z- transform of elemetary functions
session 40: Properties of Z-transforms-I
part 9: Week 9
session 41: Properties of Z - transformatons - II
session 42: Initial and final theorems for Z- transforms
session 43: Convolution theorem for Z-transforms
session 44: Convergence of Z- transform
session 45: Application of Z-transforms-I
part 10: Week 10
session 46: Applications of Z- transform- II
session 47: Fourier Series and its Convergence-I
session 48: Fourier Series and its Convergence-II
session 49: Fourier Series of Even and Odd functions
session 50: Fourier half-range series
part 11: Week 11
session 51: Parseval’s Identity
session 52: Complex form of Fourier series
session 53: Fourier integrals
session 54: Fourier sine and cosine integrals
session 55: Fourier transforms
part 12: Week 12
session 56: Fourier sine and cosine transforms
session 57: Convolution theorem for Fourier transforms
session 58: Applications of Fourier transforms to BVP–I
session 59: Applications of Fourier transforms to BVP–II
session 60: Applications of Fourier transforms to BVP–III

Catalogue records

nptel: 111107098 (manifestation)
nptel_video: 111107098 (manifestation)