1 Transform Calculus and its applications in Differential Equations
2 Lecture 01: Introduction to Integral Transform and Laplace Transform
3 Lecture 02: Existence of Laplace Transform
4 Lecture 03: Shifting properties of Laplace Transform
5 Lecture 04: Laplace Transform of Derivative and Integration of a Function - I
6 Lecture 05: Laplace Transform of Derivative and Integration of a Function - II
7 Lecture 06: Explanation of properties of Laplace Transform using Examples
8 Lecture 07: Laplace Transform of Periodic Function
9 Lecture 08: Laplace Transform of some special Functions
10 Lecture 09: Error Function, Dirac Delta Function and their Laplace Transform
11 Lecture 10: Bessel Function and its Laplace Transform
12 Lecture 11: Introduction to Inverse Laplace Transform
13 Lecture 12: Properties of Inverse Laplace Transform
14 Lecture 13: Convolution and its Applications
15 Lecture 14: Evaluation of Integrals using Laplace Transform
16 Lecture 15
17 Lecture 16
18 Lecture 17: Solution of Simultaneous Ordinary Differential Equations using Laplace Transform
19 Lecture 18: Introduction to Integral Equation and its Solution Process
20 Lecture 19: Introduction to Fourier Series
21 Lecture 20: Fourier Series for Even and Odd Functions
22 Lecture 21: Fourier Series of Functions having arbitrary period - I
23 Lecture 22: Fourier Series of Functions having arbitrary period - II
24 Lecture 23: Half Range Fourier Series
25 Lecture 24: Parseval's Theorem and its Applications
26 Lecture 25: Complex form of Fourier Series
27 Lecture 26: Fourier Integral Representation
28 Lecture 27: Introduction to Fourier Transform
29 Lecture 28: Derivation of Fourier Cosine Transform and Fourier Sine Transform of Functions
30 Lecture 29: Evaluation of Fourier Transform of various functions
31 Lecture 30: Linearity Property and Shifting Properties of Fourier Transform
32 Lecture 31: Change of Scale and Modulation Properties of Fourier Transform
33 Lecture 32: Fourier Transform of Derivative and Integral of a Function
34 Lecture 33: Applications of Properties of Fourier Transform - I
35 Lecture 34: Applications of Properties of Fourier Transform - II
36 Lecture 35: Fourier Transform of Convolution of two functions
37 Lecture 36: Parseval's Identity and its Application
38 Lecture 37: Evaluation of Definite Integrals using Properties of Fourier Transform
39 Lecture 38: Fourier Transform of Dirac Delta Function
40 Lecture 39: Representation of a function as Fourier Integral
41 Lecture 40: Applications of Fourier Transform to Ordinary Differential Equations - I
42 Lecture 41: Applications of Fourier Transform to Ordinary Differential Equations - II
43 Lecture 42: Solution of Integral Equations using Fourier Transform
44 Lecture 43: Introduction to Partial Differential Equations
45 Lecture 44: Solution of Partial Differential Equations using Laplace Transform
46 Lecture 45: Solution of Heat Equation and Wave Equation using Laplace Transform
47 Lecture 46:
48 Lecture 47:
49 Lecture 48: Solution of Partial Differential Equations using Fourier Transform - I
50 Lecture 49: Solution of Partial Differential Equations using Fourier Transform - II
51 Lecture 50: Solving problems on Partial Differential Equations using Transform Techniques
52 Lecture 51: Introduction to Finite Fourier Transform
53 Lecture 52: Solution of Boundary Value Problems using Finite Fourier Transform - I
54 Lecture 53: Solution of Boundary Value Problems using Finite Fourier Transform - II
55 Lecture 54: Introduction to Mellin Transform
56 Lecture 55: Properties of Mellin Transform
57 Lecture 56: Examples of Mellin Transform - I
58 Lecture 57: Examples of Mellin Transform - II
59 Lecture 58: Introduction to Z-Transform
60 Lecture 59: Properties of Z-Transform
61 Lecture 60: Evaluation of Z-Transform of some functions