Transforms and Partial Differential Equations (MA3351) - Anna University
Course Instructor
Promath
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Course Overview
Schedule of Classes
Course Curriculum
6 Subjects
Unit - I : Partial Differential Equations
113 Learning Materials
1.1 Formation of PDE by elimination the Arbitrary Constant
1.1.1 Introduction
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1.1.2 Formation of PDE by elimination of arbitrary constant
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1.1.3 Application of PDEs by Eliminating Arbitrary Constants
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1.1.4 Solved Problem 1
Video
3:2
1.1.5 Solved Problem 2
Video
4:15
1.1.6 Solved Problem 3
Video
4:24
1.1.7 Solved Problem 4
Video
3:38
1.1.8 Solved Problem 5
Video
5:48
1.1.9 Solved Problem 6
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1.1.10 Solved Problem 7
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1.1.11 Solved Problem 8
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1.1.12 Solved Problem 9
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1.1.13 Solved Problem 10
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1.1.14 Solved Problem 11
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1.1.15 Solved Problem 12
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1.1.16 Exercises
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1.2 Formation of PDE by elimination the Arbitrary functions
1.2.1 Introduction
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1.2.2 Application of PDEs by Eliminating Arbitrary Functions
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1.2.3 Solved Problem 1
Video
3:42
1.2.4 Solved Problem 2
Video
4:6
1.2.5 Solved Problem 3
Video
5:32
1.2.6 Solved Problem 4
Video
3:23
1.2.7 Solved Problem 5
Video
7:16
1.2.8 Solved Problem 6
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1.2.9 Solved Problem 7
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1.2.10 Solved Problem 8
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1.2.11 Solved Problem 9
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1.2.12 Solved Problem 10
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1.2.13 Solved Problem 11
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1.2.14 Solved Problem 12
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1.2.15 Exercises
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1.3 Solutions of standard first order PDEs
1.3.1 Introduction
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1.3.2 Complete Solution of First Order Non-Linear PDEs
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1.3.3 Application of first order non-linear PDEs
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1.3.4 Type I f(p, q) = 0
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1.3.5 Solved Problem 1
Video
4:5
1.3.6 Solved Problem 2
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3:47
1.3.7 Solved Problem 3
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4:52
1.3.8 Solved Problem 4
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1.3.9 Solved Problem 5
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1.3.10 Type II z = px+qy+f(p,q) [Clairaut’s form]
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1.3.11 Solved Problem 6
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5:31
1.3.12 Solved Problem 7
Video
5:33
1.3.13 Solved Problem 8
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1.3.14 Solved Problem 9
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1.3.15 Solved Problem 10
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1.3.16 Solved Problem 11
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1.3.17 Type III f(z,p,q)=0, f(x,p,q)=0, f(y,p,q)=0
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1.3.18 Solved Problem 12
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5:5
1.3.19 Solved Problem 13
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4:18
1.3.20 Solved Problem 14
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1.3.21 Solved Problem 15
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1.3.22 Solved Problem 16
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1.3.23 Solved Problem 17
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1.3.24 Type IV f(x,p) = g(y,q)
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1.3.25 Solved Problem 18
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4:36
1.3.26 Solved Problem 19
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3:50
1.3.27 Solved Problem 20
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1.3.28 Exercises
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1.4 Equations Reducible to standard types
1.4.1 Introduction
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1.4.2 Application of PDEs Reducible to Standard Solution Types-Transforming Complexity
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1.4.3 Solved Problem 1
Video
6:1
1.4.4 Solved Problem 2
Video
5:17
1.4.5 Solved Problem 3
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1.4.6 Solved Problem 4
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1.4.7 Exercises
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1.5 First Order Lagrange's Linear Equation
1.5.1 Introduction
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1.5.2 Linear Partial differential eqautions of the first order
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1.5.3 Solved Problem 1
Video
5:33
1.5.4 Solved Problem 2
Video
4:59
1.5.5 Solved Problem 3
Video
6:49
1.5.6 Solved Problem 4
Video
6:26
1.5.7 Solved Problem 5
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1.5.8 Solved Problem 6
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1.5.9 Solved Problem 7
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1.5.10 Solved Problem 8
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1.5.11 Solved Problem 9
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1.5.12 Solved Problem 10
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1.5.13 Solved Problem 11
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1.5.14 Solved Problem 12
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1.5.15 Solved Problem 13
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1.5.16 Exercises
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1.6 Higher Order PDE
1.6.1 Introduction
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1.6.2 Solved Problem 1
Video
2:58
1.6.3 Solved Problem 2
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4:11
1.6.4 Solved Problem 3
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3:52
1.6.5 Solved Problem 4
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4:56
1.6.6 Solved Problem 5
Video
5:55
1.6.7 Solved Problem 6
Video
7:6
1.6.8 Solved Problem 7
Video
6:35
1.6.9 Solved Problem 8
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1.6.10 Solved Problem 9
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1.6.11 Solved Problem 10
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1.6.12 Solved Problem 11
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1.6.13 Solved Problem 12
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1.6.14 Solved Problem 13
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1.6.15 Solved Problem 14
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1.6.16 Solved Problem 15
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1.6.17 Solved Problem 16
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1.6.18 Solved Problem 17
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1.6.19 Exercises
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1.7 Complementary Function for a Non-homogenous Linear Equation
1.7.1 Introduction
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1.7.2 Solved Problem 1
Video
7:45
1.7.3 Solved Problem 2
Video
6:35
1.7.4 Solved Problem 3
Video
7:22
1.7.5 Solved Problem 4
Video
7:8
1.7.6 Solved Problem 5
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1.7.7 Solved Problem 6
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1.7.8 Solved Problem 7
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1.7.9 Solved Problem 8
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1.7.10 Solved Problem 9
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1.7.11 Solved Problem 10
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1.7.12 Exercises
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Unit - II : Fourier Series
78 Learning Materials
2.1 Fourier series
2.1.1 Introduction
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2.1.2 Periodic Function
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2.1.3 Even and odd functions
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2.1.4 Examples
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2.1.5 Trigonometric Series
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2.1.6 Dirichlet Conditions
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2.1.7 Definition of Fourier Series
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2.1.8 Convergence of Fourier Series at specific point
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2.1.9 Continuity and Discontinuity in open and closed interval
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2.1.10 Solved Problem 1
Video
13:1
2.1.11 Solved Problem 2
Video
13:49
2.1.12 Solved Problem 3
Video
23:58
2.1.13 Solved Problem 4
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2.1.14 Solved Problem 5
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2.1.15 Solved Problem 6
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2.1.16 Solved Problem 7
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2.1.17 Exercises
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2.2 Function having points of discontinuity
2.2.1 Fourier Series for discontinuous functions
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2.2.2 Solved Problem 1
Video
16:44
2.2.3 Solved Problem 2
Video
19:37
2.2.4 Solved Problem 3
Video
16:16
2.2.5 Solved Problem 4
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2.2.6 Solved Problem 5
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2.2.7 Exercises
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2.3 Change of variable
2.3.1 Change of variable
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2.3.2 Solved Problem 1
Video
17:52
2.3.3 Solved Problem 2
Video
9:24
2.3.4 Solved Problem 3
Video
14:44
2.3.5 Solved Problem 4
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2.3.6 Solved Problem 5
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2.3.7 Solved Problem 6
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2.3.8 Exercises
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2.4 Even and odd functions
2.4.1 Even and odd functions
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2.4.2 Fourier Series For Even And Odd Function
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2.4.3 Solved Problem 1
Video
14:9
2.4.4 Solved Problem 2
Video
10:28
2.4.5 Solved Problem 3
Video
11:25
2.4.6 Solved Problem 4
Video
13:30
2.4.7 Solved Problem 5
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2.4.8 Solved Problem 6
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2.4.9 Solved Problem 7
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2.4.10 Exercises
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2.5 Half range fourier series
2.5.1 Introduction to Half–Range Fourier Series
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2.5.2 Solved Problem 1
Video
9:55
2.5.3 Solved Problem 2
Video
11:42
2.5.4 Solved Problem 3
Video
11:30
2.5.5 Solved Problem 4
Video
10:49
2.5.6 Solved Problem 5
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2.5.7 Solved Problem 6
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2.5.8 Solved Problem 7
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2.5.9 Solved Problem 8
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2.5.10 Solved Problem 9
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2.5.11 Solved Problem 10
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2.5.12 Exercises
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2.6 Complex form
2.6.1 Complex form of Fourier series
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2.6.2 Solved Problem 1
Video
6:16
2.6.3 Solved Problem 2
Video
7:6
2.6.4 Solved Problem 3
Video
4:57
2.6.5 Solved Problem 4
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2.6.6 Exercises
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2.7 Parseval’s Theorem
2.7.1 Parseval’s Theorem
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2.7.2 Solved Problem 1
Video
12:12
2.7.3 Solved Problem 2
Video
7:12
2.7.4 Solved Problem 3
Video
12:49
2.7.5 Solved Problem 4
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2.7.6 Solved Problem 5
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2.7.7 Solved Problem 6
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2.7.8 Solved Problem 7
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2.7.9 Solved Problem 8
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2.7.10 Exercises
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2.8 Harmonic analysis
2.8.1 Harmonic analysis
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2.8.2 Solved Problem 1
Video
10:13
2.8.3 Solved Problem 2
Video
8:14
2.8.4 Solved Problem 3
Video
9:19
2.8.5 Solved Problem 4
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2.8.6 Solved Problem 5
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2.8.7 Solved Problem 6
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2.8.8 Exercises
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Unit - III : Applications of Partial Differential Equations
69 Learning Materials
3.1 Classification of second order PDE
3.1.1 Introduction
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3.1.2 Solved Problem 1
Video
5:20
3.1.3 Solved Problem 2
Video
3:8
3.1.4 Solved Problem 3
Video
3:3
3.1.5 Solved Problem 4
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3.1.6 Solved Problem 5
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3.1.7 Solved Problem 6
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3.1.8 Solved Problem 7
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3.1.9 Solved Problem 8
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3.1.10 Solved Problem 9
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3.1.11 Solved Problem 10
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3.1.12 Exercises
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3.2 Method of separation of variables
3.2.1 Introduction
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3.2.2 Solved Problem 1
Video
9:32
3.2.3 Solved Problem 2
Video
5:19
3.2.4 Solved Problem 3
Video
7:49
3.2.5 Solved Problem 4
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3.2.6 Solved Problem 5
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3.2.7 Solved Problem 6
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3.2.8 Solved Problem 7
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3.2.9 Solved Problem 8
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3.2.10 Exercises
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3.3 Solution of one dimensional Wave equation
3.3.1 Introduction
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3.3.2 Transverse vibrations of a stretched string - one dimesional wave equation
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3.3.3 Transmission line equations
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3.3.4 Variable separable solutions of the wave
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3.3.5 Choice of proper solution
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3.3.6 Solution of a damped vibrating string equation
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3.3.7 Problems on vibrating string with non-zero initial velocity
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3.3.8 Solved Problem 1
Video
9:22
3.3.9 Solved Problem 2
Video
13:00
3.3.10 Solved Problem 3
Video
10:32
3.3.11 Solved Problem 4
Video
12:50
3.3.12 Solved Problem 5
Video
12:11
3.3.13 Solved Problem 6
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3.3.14 Solved Problem 7
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3.3.15 Solved Problem 8
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3.3.16 Solved Problem 9
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3.3.17 Solved Problem 10
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3.3.18 Solved Problem 11
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3.3.19 Solved Problem 12
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3.3.20 Exercises
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3.4 Solution of one dimensional Heat equation
3.4.1 Introduction
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3.4.2 Equation of variable heat flow in one dimension
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3.4.3 Variable separable solutions of the heat equation
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3.4.4 Choice of proper solution
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3.4.5 One dimensional heat equation
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3.4.6 Solved Problem 1
Video
9:1
3.4.7 Solved Problem 2
Video
9:20
3.4.8 Solved Problem 3
Video
8:5
3.4.9 Solved Problem 4
Video
7:5
3.4.10 Solved Problem 5
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3.4.11 Solved Problem 6
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3.4.12 Solved Problem 7
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3.4.13 Solved Problem 8
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3.4.14 Exercises
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3.5 Two dimensional Heat equation
3.5.1 Steady state heat flow two dimenstions[cartesian coordinates]
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3.5.2 Equation of variable heat flow in two dimensions in cartesian coordinates
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3.5.3 Variable separable solutions of laplace equation
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3.5.4 Choice of proper solution
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3.5.5 Two dimensional heat equation
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3.5.6 Solved Problem 1
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3.5.7 Solved Problem 2
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3.5.8 Solved Problem 3
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3.5.9 Solved Problem 4
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3.5.10 Solved Problem 5
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3.5.11 Solved Problem 6
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3.5.12 Solved Problem 7
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3.5.13 Exercises
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Unit- IV : Fourier Transforms
57 Learning Materials
4.1 Fourier Integral Theorem
4.1.1 Fourier integral theorem
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4.1.2 Complex form of the Fourier integrals
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4.1.3 Fourier sine and cosine Integrals
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4.1.4 Solved Problem 1
Video
7:20
4.1.5 Solved Problem 2
Video
5:2
4.1.6 Solved Problem 3
Video
9:50
4.1.7 Solved Problem 4
Video
4:20
4.1.8 Solved Problem 5
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4.1.9 Solved Problem 6
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4.1.10 Exercises
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4.2 Fourier Transform
4.2.1 Introduction
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4.2.2 Solved Problem 1
Video
4:3
4.2.3 Solved Problem 2
Video
13:26
4.2.4 Solved Problem 3
Video
11:44
4.2.5 Solved Problem 4
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4.2.6 Solved Problem 5
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4.2.7 Solved Problem 6
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4.2.8 Solved Problem 7
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4.2.9 Solved Problem 8
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4.2.10 Solved Problem 9
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4.2.11 Exercises
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4.3 Fourier sine Transform
4.3.1 Introduction
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4.3.2 Solved Problem 1
Video
4:1
4.3.3 Solved Problem 2
Video
5:51
4.3.4 Solved Problem 3
Video
6:26
4.3.5 Solved Problem 4
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4.3.6 Solved Problem 5
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4.3.7 Solved Problem 6
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4.3.8 Solved Problem 7
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4.3.9 Exercises
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4.4 Fourier cosine Transform
4.4.1 Introduction
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4.4.2 Solved Problem 1
Video
8:19
4.4.3 Solved Problem 2
Video
5:53
4.4.4 Solved Problem 3
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4.4.5 Solved Problem 4
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4.4.6 Solved Problem 5
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4.4.7 Exercises
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4.5 Properties of Fourier Transform
4.5.1 Introduction
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4.5.2 Modulation Theorem and Some Other Properties
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4.5.3 Properties of Fourier sine and cosine Transform
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4.5.4 Solved Problem 1
Video
4:34
4.5.5 Solved Problem 2
Video
4:55
4.5.6 Solved Problem 3
Video
7:10
4.5.7 Solved Problem 4
Video
15:11
4.5.8 Solved Problem 5
Video
8:59
4.5.9 Solved Problem 6
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4.5.10 Exercises
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4.6 Convolution Theorem and Parseval’s Identity
4.6.1 Introduction
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4.6.2 Parseval’s Identity
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4.6.3 Solved Problem 1
Video
6:38
4.6.4 Solved Problem 2
Video
15:40
4.6.5 Solved Problem 3
Video
12:34
4.6.6 Solved Problem 4
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4.6.7 Solved Problem 5
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4.6.8 Solved Problem 6
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4.6.9 Solved Problem 7
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4.6.10 Exercises
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Unit - V : Z - Transforms and Difference Equations
130 Learning Materials
5.1 Z-Transform
5.1.1 Introduction
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5.1.2 Definition of Z-Transform
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5.1.3 Solved Problem 1
Video
3:34
5.1.4 Solved Problem 2
Video
3:55
5.1.5 Solved Problem 3
Video
4:33
5.1.6 Solved Problem 4
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5.1.7 Solved Problem 5
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5.1.8 Solved Problem 6
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5.1.9 Solved Problem 7
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5.1.10 Solved Problem 8
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5.1.11 Solved Problem 9
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5.1.12 Problems based on bilateral Z-transform
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5.1.13 Solved Problem 11
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5.1.14 Solved Problem 12
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5.1.15 Solved Problem 13
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5.1.16 Solved Problem 14
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5.1.17 Exercises
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5.2 Linear Property
5.2.1 Linear Property
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5.2.2 Example
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5.2.3 Solved Problem 1
Video
6:8
5.2.4 Solved Problem 2
Video
6:53
5.2.5 Solved Problem 3
Video
3:18
5.2.6 Solved Problem 4
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5.2.7 Solved Problem 5
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5.2.8 Solved Problem 6
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5.2.9 Solved Problem 7
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5.2.10 Solved Problem 8
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5.2.11 Solved Problem 9
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5.2.12 Solved Problem 10
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5.2.13 Solved Problem 11
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5.2.14 Exercises
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5.3 Shifting and Damping rule
5.3.1 Shifting and Damping rule
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5.3.2 Solved Problem 1
Video
2:27
5.3.3 Solved Problem 2
Video
2:43
5.3.4 Solved Problem 3
Video
3:13
5.3.5 Solved Problem 4
Video
2:51
5.3.6 Solved Problem 5
Video
2:35
5.3.7 Solved Problem 6
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5.3.8 Solved Problem 7
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5.3.9 Solved Problem 8
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5.3.10 Solved Problem 9
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5.3.11 Solved Problem 10
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5.3.12 Solved Problem 11
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5.3.13 Exercises
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5.4 Differentiation in the Z domain
5.4.1 Differentiation in the z-domain
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5.4.2 Solved Problem 1
Video
5:11
5.4.3 Solved Problem 2
Video
5:25
5.4.4 Solved Problem 3
Video
4:14
5.4.5 Solved Problem 4
Video
4:28
5.4.6 Solved Problem 5
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5.4.7 Solved Problem 6
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5.4.8 Solved Problem 7
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5.4.9 Solved Problem 8
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5.4.10 Solved Problem 9
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5.4.11 Exercises
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5.5 Second Shifting Theorem
5.5.1 Second shifting theorem
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5.5.2 Solved Problem 1
Video
4:27
5.5.3 Solved Problem 2
Video
3:44
5.5.4 Solved Problem 3
Video
3:38
5.5.5 Solved Problem 4
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5.5.6 Solved Problem 5
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5.5.7 Exercises
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5.6 Unit sample sequences and Unit step sequences
5.6.1 Unit sample sequence and unit step sequence
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5.6.2 Solved Problem 1
Video
2:28
5.6.3 Solved Problem 2
Video
4:12
5.6.4 Solved Problem 3
Video
7:38
5.6.5 Solved Problem 4
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5.6.6 Solved Problem 5
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5.6.7 Solved Problem 6
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5.6.8 Exercises
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5.7 Initial value and Final Theorems
5.7.1 Initial and final value theorems
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5.7.2 Solved Problem 1
Video
11:42
5.7.3 Solved Problem 2
Video
9:46
5.7.4 Solved Problem 3
Video
8:37
5.7.5 Solved Problem 4
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5.7.6 Solved Problem 5
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5.7.7 Solved Problem 6
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5.7.8 Differentiation
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5.7.9 Solved Problem 7
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5.7.10 Solved Problem 8
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5.7.11 Exercises
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5.8 Partial fraction method
5.8.1 Partial Fractions Method
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5.8.2 Solved Problem 1
Video
5:54
5.8.3 Solved Problem 2
Video
11:51
5.8.4 Solved Problem 3
Video
6:51
5.8.5 Solved Problem 4
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5.8.6 Solved Problem 5
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5.8.7 Solved Problem 6
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5.8.8 Solved Problem 7
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5.8.9 Exercises
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5.9 Convolution Theorem
5.9.1 Convolution Theorem
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5.9.2 Z-transform of f(x) g(x)type
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5.9.3 Solved Problem 1
Video
6:40
5.9.4 Solved Problem 2
Video
7:34
5.9.5 Solved Problem 3
Video
6:39
5.9.6 Solved Problem 4
Video
5:28
5.9.7 Solved Problem 5
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5.9.8 Solved Problem 6
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5.9.9 Solved Problem 7
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5.9.10 Solved Problem 8
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5.9.11 Solved Problem 9
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5.9.12 Solved Problem 10
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5.9.13 Exercises
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5.10 Formation of Difference equation
5.10.1 Formation of difference equations
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5.10.2 Solved Problem 1
Video
5:44
5.10.3 Solved Problem 2
Video
6:9
5.10.4 Solved Problem 3
Video
4:9
5.10.5 Solved Problem 4
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5.10.6 Solved Problem 5
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5.10.7 Solved Problem 6
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5.10.8 Exercises
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5.11 Solution of Difference equation using z-transform
5.11.1 Solution of difference equations using z-transform
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5.11.2 Solved Problem 1
Video
11:26
5.11.3 Solved Problem 2
Video
10:2
5.11.4 Solved Problem 3
Video
10:11
5.11.5 Solved Problem 4
Video
16:25
5.11.6 Solved Problem 5
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5.11.7 Solved Problem 6
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5.11.8 Solved Problem 7
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5.11.9 Solved Problem 8
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5.11.10 Solved Problem 9
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5.11.11 Solved Problem 10
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5.11.12 Solved Problem 11
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5.11.13 Solved Problem 12
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5.11.14 Solved Problem 13
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5.11.15 Solved Problem 14
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5.11.16 Solved Problem 15
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5.11.17 Solved Problem 16
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5.11.18 Solved Problem 17
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5.11.19 Exercises
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Important Q&A
74 Learning Materials
1. Partial Differential Equations
1.1 Part A: Q&A
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1.2 Part B: Q&A - 1
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1.3 Part B: Q&A - 2
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1.4 Part B: Q&A - 3
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1.5 Part B: Q&A - 4
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1.6 Part B: Q&A - 5
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1.7 Part B: Q&A - 6
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1.8 Part B: Q&A - 7
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1.9 Part B: Q&A - 8
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1.10 Part B: Q&A - 9
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1.11 Part B: Q&A - 10
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1.12 Part B: Q&A - 11
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1.13 Part B: Q&A - 12
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1.14 Part B: Q&A - 13
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2. Fourier Series
2.1 Part A: Q&A
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2.2 Part B: Q&A - 1
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2.3 Part B: Q&A - 2
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2.4 Part B: Q&A - 3
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2.5 Part B: Q&A - 4
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2.6 Part B: Q&A - 5
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2.7 Part B: Q&A - 6
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2.8 Part B: Q&A - 7
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2.9 Part B: Q&A - 8
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2.10 Part B: Q&A - 9
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2.11 Part B: Q&A - 10
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2.12 Part B: Q&A - 11
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2.13 Part B: Q&A - 12
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2.14 Part B: Q&A - 13
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2.15 Part B: Q&A - 14
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2.16 Part B: Q&A - 15
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2.17 Part B: Q&A - 16
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2.18 Part B: Q&A - 17
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2.19 Part B: Q&A - 18
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3. Applications of Partial Differential Equations
3.1 Part A: Q&A
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3.2 Part B: Q&A - 1
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3.3 Part B: Q&A - 2
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3.4 Part B: Q&A - 3
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3.5 Part B: Q&A - 4
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3.6 Part B: Q&A - 5
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3.7 Part B: Q&A - 6
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3.8 Part B: Q&A - 7
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3.9 Part B: Q&A - 8
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4. Fourier Transforms
4.1 Part A: Q&A
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4.2 Part B: Q&A - 1
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4.3 Part B: Q&A - 2
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4.4 Part B: Q&A - 3
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4.5 Part B: Q&A - 4
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4.6 Part B: Q&A - 5
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4.7 Part B: Q&A - 6
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4.8 Part B: Q&A - 7
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4.9 Part B: Q&A - 8
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4.10 Part B: Q&A - 9
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4.11 Part B: Q&A - 10
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4.12 Part B: Q&A - 11
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4.13 Part B: Q&A - 12
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4.14 Part B: Q&A - 13
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4.15 Part B: Q&A - 14
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4.16 Part B: Q&A - 15
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4.17 Part B: Q&A - 16
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4.18 Part B: Q&A - 17
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4.19 Part B: Q&A - 18
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4.20 Part B: Q&A - 19
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5. Z - Transforms and Difference Equations
5.1 Part A: (Q&A)
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5.2 Part B: Q&A - 1
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5.3 Part B: Q&A - 2
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5.4 Part B: Q&A - 3
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5.5 Part B: Q&A - 4
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5.6 Part B: Q&A - 5
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5.7 Part B: Q&A - 6
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5.8 Part B: Q&A - 7
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5.9 Part B: Q&A - 8
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5.10 Part B: Q&A - 9
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5.11 Part B: Q&A - 10
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5.12 Part B: Q&A - 11
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