NOC:Transform Calculus and its applications in Differential Equations

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