NOC:Transform Calculus and its applications in Differential Equations (USB)

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof. A. Goswami

NPTEL Co-ordinating Institute : IIT Kharagpur

NPTEL Lecture Count : 60

NPTEL Course Size : 16 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

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