Transform Calculus and Its Applications in Differential Equation

Lecture 02: Existence of Laplace Transform.
Lecture 03: Shifting properties of Laplace Transform.
Lecture 04: Laplace Transform of Derivative and Integration of a Function - I.
Lecture 05: Laplace Transform of Derivative and Integration of a Function - II.
Lecture 06: Explanation of properties of Laplace Transform using Examples.
Lecture 07: Laplace Transform of Periodic Function.
Lecture 08: Laplace Transform of some special Functions.
Lecture 09: 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.
Lecture 16.
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:.
Lecture 47:.
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.