Transform Calculus and its applications in Differential Equations 4KX0C5RYZZ

URI	`m2://res/4KX0C5RYZZ`
Kind	course
Creators	Adrijit Goswami (instructor)
Date	2019-01-14
Scope	in
Ids	course 03w5sq511:111105123

Expressions

e1: edition

Language	en
Date	2019-01-14

m1: page, IIT Kharagpur (record). nptel 111105123
m2: page, 2019-01-14 (record). nptel 111105123

Contents

part 1: Week 1 :
session 1: Lecture 1 : Introduction to Integral Transform and Laplace Transform
session 2: Lecture 2 : Existence of Laplace Transform
session 3: Lecture 3 : Shifting Properties of Laplace Transform
session 4: Lecture 4 : Laplace Transform of Derivatives and Integration of a Function - I
session 5: Lecture 5 : Laplace Transform of Derivatives and Integration of a Function - II
part 2: Week 2 :
session 6: Lecture 06: Explanation of properties of Laplace Transform using Examples
session 7: Lecture 07: Laplace Transform of Periodic Function
session 8: Lecture 08: Laplace Transform of some special Functions
session 9: Lecture 09: Error Function, Dirac Delta Function and their Laplace Transform
session 10: Lecture 10: Bessel Function and its Laplace Transform
part 3: Week 3 :
session 11: Lecture 11: Introduction to Inverse Laplace Transform
session 12: Lecture 12: Properties of Inverse Laplace Transform
session 13: Lecture 13: Convolution and its Applications
session 14: Lecture 14: Evaluation of Integrals using Laplace Transform
session 15: Lecture 15: Solution of Ordinary Differential Equations with constant coefficients using Laplace Transform
part 4: Week 4 :
session 16: Lecture 16 : Solution of Ordinary Differential Equations with variable coefficients using Laplace Transform
session 17: Lecture 17 : Solution of Simultaneous Ordinary Differential Equations using Laplace Transform
session 18: Lecture 18 : Introduction to Integral Equation and its Solution Process
session 19: Lecture 19 : Introduction to Fourier Series
session 20: Lecture 20 : Fourier Series for Even and Odd Functions
part 5: Week 5 :
session 21: Lecture 21: Fourier Series of Functions having arbitrary period - I
session 22: Lecture 22: Fourier Series of Functions having arbitrary period - II
session 23: Lecture 23: Half Range Fourier Series
session 24: Lecture 24: Parseval's Theorem and its Applications
session 25: Lecture 25: Complex form of Fourier Series
part 6: Week 6 :
session 26: Lecture 26: Fourier Integral Representation
session 27: Lecture 27: Introduction to Fourier Transform
session 28: Lecture 28: Derivation of Fourier Cosine Transform and Fourier Sine Transform of Functions
session 29: Lecture 29: Evaluation of Fourier Transform of various functions
session 30: Lecture 30: Linearity Property and Shifting Properties of Fourier Transform
part 7: Week 7 :
session 31: Lecture 31: Change of Scale and Modulation Properties of Fourier Transform
session 32: Lecture 32: Fourier Transform of Derivative and Integral of a Function
session 33: Lecture 33: Applications of Properties of Fourier Transform - I
session 34: Lecture 34: Applications of Properties of Fourier Transform - II
session 35: Lecture 35: Fourier Transform of Convolution of two functions
part 8: Week 8 :
session 36: Lecture 36: Parseval's Identity and its Application
session 37: Lecture 37: Evaluation of Definite Integrals using Properties of Fourier Transform
session 38: Lecture 38: Fourier Transform of Dirac Delta Function
session 39: Lecture 39: Representation of a function as Fourier Integral
session 40: Lecture 40: Applications of Fourier Transform to Ordinary Differential Equations - I
part 9: Week 9 :
session 41: Lecture 41 : Applications of Fourier Transform to Ordinary Differential Equations - II
session 42: Lecture 42 : Solution of Integral Equations using Fourier Transform
session 43: Lecture 43 : Introduction to Partial Differential Equations
session 44: Lecture 44 : Solution of Partial Differential Equations using Laplace Transform
session 45: Lecture 45 : Solution of Heat Equation and Wave Equation using Laplace Transform
part 10: Week 10 :
session 46: Lecture 46 : Criteria for choosing Fourier Transform, Fourier Sine Transform, Fourier Cosine Transform in solving Partial Differential Equations
session 47: Lecture 47 : Solution of Partial Differential Equations using Fourier Cosine Transform and Fourier Sine Transform
session 48: Lecture 48 : Solution of Partial Differential Equations using Fourier Transform - I
session 49: Lecture 49 : Solution of Partial Differential Equations using Fourier Transform - II
session 50: Lecture 50 : Solving problems on Partial Differential Equations using Transform Techniques
part 11: Week 11 :
session 51: Lecture 51: Introduction to Finite Fourier Transform
session 52: Lecture 52: Solution of Boundary Value Problems using Finite Fourier Transform - I
session 53: Lecture 53: Solution of Boundary Value Problems using Finite Fourier Transform - II
session 54: Lecture 54: Introduction to Mellin Transform
session 55: Lecture 55: Properties of Mellin Transform
part 12: Week 12 :
session 56: Lecture 56: Examples of Mellin Transform - I
session 57: Lecture 57: Examples of Mellin Transform - II
session 58: Lecture 58: Introduction to Z-Transform
session 59: Lecture 59: Properties of Z-Transform
session 60: Lecture 60: Evaluation of Z-Transform of some functions
part 13: Live Session
session 61: Live Session 26-02-2021
session 62: Live Session 10-03-2021
session 63: Live Session 05-04-2021
session 64: Live Session 22-02-2020
session 65: Live Session 13-03-2020
session 66: Live Session 25-02-2022
session 67: Live Session 25-03-2022
session 68: Live Session 11-04-2022

Catalogue records

nptel: 111105123 (manifestation)
nptel_video: 111105123 (manifestation)