Complex Analysis and Ordinary Differential Equations (U23MA202) - Vivekananda Faculties
Course Instructor
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Course Overview
Schedule of Classes
Course Curriculum
5 Subjects
Unit I - Analytic Functions (VCEWM2) staff
26 Exercises • 79 Learning Materials
1.1 Analytic Functions
1.1.1 Analytic function
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1.1.2 Cauchy Riemann Equation
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1.1.3 The Necessary condition for f(z) to be analytic (in Cartesian form)
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1.1.4 Sufficient condition for f(z) to be analytic
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1.1.5 Cauchy Riemann equations In polar coordinates
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1.1.6 Solved Problem 1
Video
5:9
1.1.6 Quiz
Exercise
1.1.7 Solved Problem 2
Video
6:33
1.1.7 Quiz
Exercise
1.1.8 Solved Problem 3
Video
5:1
1.1.8 Quiz
Exercise
1.1.9 Solved Problem 4
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1.1.10 Solved Problem 5
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1.1.11 Solved Problem 6
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1.1.12 Solved Problem 7
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1.1.13 Exercises
Exercise
1.2 Harmonic Property
1.2.1 Property of Analytic functions
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1.2.2 Harmonic Functions - Laplace Equation
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1.2.3 Harmonic Function
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1.2.4 Harmonic Conjugates
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1.2.5 Solved Problem 1
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9:55
1.2.5 Quiz
Exercise
1.2.6 Solved Problem 2
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14:59
1.2.6 Quiz
Exercise
1.2.7 Solved Problem 3
Video
13:20
1.2.7 Quiz
Exercise
1.2.8 Solved Problem 4
Video
12:37
1.2.8 Quiz
Exercise
1.2.9 Solved Problem 5
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1.2.10 Solved Problem 6
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1.2.11 Solved Problem 7
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1.2.12 Solved Problem 8
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1.2.13 Solved Problem 9
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1.2.14 Exercises
Exercise
1.3 Orthogonal Property
1.3.1 Orthogonal system
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1.3.2 Solved Problem 1
Video
5:21
1.3.3 Solved Problem 2
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10:1
1.3.4 Solved Problem 3
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4:13
1.3.5 Solved Problem 4
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1.3.6 Solved Problem 5
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1.3.7 Solved Problem 6
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1.3.8 Exercises
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1.4 Construction of Analytic functions
1.4.1 Construction of Analytic functions
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1.4.2 Method 1 Construction of analytic function whose real or imaginary part is known
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1.4.3 Solved Problem 1
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8:41
1.4.3 Quiz
Exercise
1.4.4 Solved Problem 2
Video
7:24
1.4.4 Quiz
Exercise
1.4.5 Solved Problem 3
Video
13:37
1.4.5 Quiz
Exercise
1.4.6 Solved problem 4
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1.4.7 Solved problem 5
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1.4.8 Exercises
Exercise
1.5 Milne Thomson Method
1.5.1 Milne Thomson Method (To Construct an analytic function)
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1.5.2 Working rule To Construct an analytic function by Milne Thomson Method
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1.5.3 Solved Problem 1
Video
9:51
1.5.3 Quiz
Exercise
1.5.4 Solved Problem 2
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14:43
1.5.4 Quiz
Exercise
1.5.5 Solved Problem 3
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13:23
1.5.5 Quiz
Exercise
1.5.6 Solved Problem 4
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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 Exercises
Exercise
1.6 Conformal Mapping
1.6.1 Conformal mapping
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1.6.2 Translation w=c+z
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1.6.3 Magnification w=cz
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1.6.4 Magnification and Rotation
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1.6.5 Magnification, Rotation and Translation
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1.6.6 Inversion and Reflection w=1/z
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1.6.7 Transformation w=z^2
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1.6.8 Problem based on w=c+z _ Solved Problem 1
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4:45
1.6.8 Quiz
Exercise
1.6.9 Solved Problem 2
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1.6.10 Problem based on w=cz _ Solved Problem 3
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6:2
1.6.10 Quiz
Exercise
1.6.11 Solved Problem 4
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1.6.12 Problem based on w=1/z _ Solved Problem 5
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6:40
1.6.12 Quiz
Exercise
1.6.13 Solved Problem 6
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1.6.14 Solved Problem 7
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1.6.15 Problem based on w=z^2 _ Solved Problem 8
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4:46
1.6.15 Quiz
Exercise
1.6.16 Solved Problem 9
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1.6.17 Exercises
Exercise
1.7 Bilinear Transformation (Mobius Transformation)
1.7.1 Bilinear Transformation
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1.7.2 Theorem 1
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1.7.3 Fixed points (or) Invariant points
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1.7.4 Theorem 2
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1.7.5 Cross Ratio
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1.7.6 Solved Problem 1
Video
7:58
1.7.6 Quiz
Exercise
1.7.7 Solved Problem 2
Video
6:23
1.7.7 Quiz
Exercise
1.7.8 Solved Problem 3
Video
5:5
1.7.8 Quiz
Exercise
1.7.9 Solved Problem 4
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1.7.10 Solved Problem 5
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1.7.11 Solved Problem 6
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1.7.12 Solved Problem 7
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1.7.13 Solved Problem 8
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1.7.14 Exercises
Exercise
Unit II - Complex Integration (VCEWM2) staff
25 Exercises • 88 Learning Materials
2.1 Line Integral
2.1.1 Line integral
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2.1.2 Solved Problem 1
Video
8:11
2.1.2 Quiz
Exercise
2.1.3 Solved Problem 2
Video
13:14
2.1.3 Quiz
Exercise
2.1.4 Solved Problem 3
Video
8:8
2.1.4 Quiz
Exercise
2.1.5 Solved Problem 4
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2.1.6 Solved Problem 5
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2.1.7 Solved Problem 6
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2.1.8 Solved Problem 7
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2.1.9 Exercises
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2.2 Cauchy's Integral Theorem and Integral Formula
2.2.1 Introduction
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2.2.2 The Cauchy's theorem
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2.2.3 Cauchy's theorem for multiply connected region
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2.2.4 Cauchy's integral formula
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2.2.5 Cauchy's integral formula for derivative
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2.2.6 Solved Problem 1
Video
7:00
2.2.6 Quiz
Exercise
2.2.7 Solved Problem 2
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2.2.8 Solved Problem 3
Video
9:12
2.2.8 Quiz
Exercise
2.2.9 Solved Problem 4
Video
11:19
2.2.9 Quiz
Exercise
2.2.10 Solved Problem 5
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2.2.11 Solved Problem 6
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2.2.12 Solved Problem 7
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2.2.13 Solved Problem 8
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2.2.14 Solved Problem 9
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2.2.15 Solved Problem 10
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2.2.16 Solved Problem 11
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2.2.17 Solved Problem 12
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2.2.18 Exercises
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2.3 Taylor’s Series
2.3.1 Taylor's series
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2.3.2 Some important results
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2.3.3 Solved Problem 1
Video
8:5
2.3.3 Quiz
Exercise
2.3.4 Solved Problem 2
Video
10:2
2.3.4 Quiz
Exercise
2.3.5 Solved Problem 3
Video
7:51
2.3.5 Quiz
Exercise
2.3.6 Solved Problem 4
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2.3.7 Solved Problem 5
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2.3.8 Solved Problem 6
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2.3.9 Solved Problem 7
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2.3.10 Exercises
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2.4 Laurent’s Series
2.4.1 Laurent's series
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2.4.2 Some important results
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2.4.3 Solved Problem 1
Video
8:16
2.4.3 Quiz
Exercise
2.4.4 Solved Problem 2
Video
10:47
2.4.4 Quiz
Exercise
2.4.5 Solved Problem 3
Video
14:34
2.4.5 Quiz
Exercise
2.4.6 Solved Problem 4
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2.4.7 Solved Problem 5
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2.4.8 Solved Problem 6
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2.4.9 Exercises
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2.5 Classification of Singularities
2.5.1 Singularities and Classification
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2.5.2 Types of singularities
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2.5.3 Solved Problem 1
Video
8:7
2.5.3 Quiz
Exercise
2.5.4 Solved Problem 2
Video
8:19
2.5.4 Quiz
Exercise
2.5.5 Solved Problem 3
Video
1:58
2.5.5 Quiz
Exercise
2.5.6 Solved Problem 4
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2.5.7 Exercises
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2.6 Cauchy's Residue Theorem
2.6.1 Residues
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2.6.2 Cauchy's residue theorem
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2.6.3 Solved Problem 1
Video
7:3
2.6.3 Quiz
Exercise
2.6.4 Solved Problem 2
Video
11:6
2.6.4 Quiz
Exercise
2.6.5 Solved Problem 3
Video
5:56
2.6.5 Quiz
Exercise
2.6.6 Solved Problem 4
Video
9:9
2.6.6 Quiz
Exercise
2.6.7 Solved Problem 5
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2.6.8 Solved Problem 6
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2.6.9 Solved Problem 7
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2.6.10 Solved Problem 8
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2.6.11 Solved Problem 9
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2.6.12 Solved Problem 10
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2.6.13 Solved Problem 11
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2.6.14 Solved Problem 12
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2.6.15 Solved Problem 13
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2.6.16 Solved Problem 14
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2.6.17 Solved Problem 15
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2.6.18 Solved Problem 16
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2.6.19 Solved Problem 17
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2.6.20 Solved Problem 18
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2.6.21 Exercises
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2.7 Integration around the Unit Circle
2.7.1 Contour integration type I
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2.7.2 Solved Problem 1
Video
11:59
2.7.2 Quiz
Exercise
2.7.3 Solved Problem 2
Video
10:37
2.7.3 Quiz
Exercise
2.7.4 Solved Problem 3
Video
10:30
2.7.4 Quiz
Exercise
2.7.5 Solved Problem 4
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2.7.6 Solved Problem 5
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2.7.7 Exercises
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2.8 Integration around the semi - circle
2.8.1 Contour integration type II
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2.8.2 Solved Problem 1
Video
9:13
2.8.2 Quiz
Exercise
2.8.3 Solved Problem 2
Video
9:26
2.8.3 Quiz
Exercise
2.8.4 Solved Problem 3
Video
9:39
2.8.4 Quiz
Exercise
2.8.5 Solved Problem 4
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2.8.6 Solved Problem 5
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2.8.7 Exercises
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Unit III - Vector Differentiation & Integration (VCEWM2) staff
38 Exercises • 106 Learning Materials
3.1 Gradient
3.1.1 Introduction
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3.1.2 Graphical representation of vector fields
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3.1.3 Scalar and vector fields
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3.1.4 Gradient of a scalar
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3.1.5 Geometrical interpretation
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3.1.6 Solved Problem 1
Video
4:20
3.1.6 Quiz
Exercise
3.1.7 Solved Problem 2
Video
8:1
3.1.7 Quiz
Exercise
3.1.8 Solved Problem 3
Video
8:13
3.1.8 Quiz
Exercise
3.1.9 Solved Problem 4
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3.1.10 Solved Problem 5
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3.1.11 Solved Problem 6
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3.1.12 Solved Problem 7
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3.1.13 Solved Problem 8
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3.1.14 Exercises
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3.2 Directional Derivatives
3.2.1 Introduction
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3.2.2 Solved problem 1
Video
6:54
3.2.2 Quiz
Exercise
3.2.3 Solved problem 2
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3.2.4 Solved problem 3
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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 Exercises
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3.3 Curl & Divergence
3.3.1 Introduction
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3.3.2 Laplacian of a scalar field
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3.3.3 Properties
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3.3.4 Curl of a vector field
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3.3.5 Properties
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3.3.6 Vector Identities
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3.3.7 Solved Problem 1
Video
3:17
3.3.7 Quiz
Exercise
3.3.8 Solved Problem 2
Video
7:34
3.3.8 Quiz
Exercise
3.3.9 Solved Problem 3
Video
7:21
3.3.9 Quiz
Exercise
3.3.10 Solved Problem 4
Video
6:36
3.3.10 Quiz
Exercise
3.3.11 Solved Problem 5
Video
5:2
3.3.11 Quiz
Exercise
3.3.12 Solved Problem 6
Video
5:39
3.3.12 Quiz
Exercise
3.3.13 Solved Problem 7
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3.3.14 Solved Problem 8
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3.3.15 Solved Problem 9
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3.3.16 Solved Problem 10
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3.3.17 Solved Problem 11
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3.3.18 Solved Problem 12
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3.3.19 Solved Problem 13
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3.3.20 Solved Problem 14
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3.3.21 Exercises
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3.4 Solenoidal & Irrotational
3.4.1 Introduction
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3.4.2 Solved Problem 1
Video
3:45
3.4.2 Quiz
Exercise
3.4.3 Solved Problem 2
Video
2:20
3.4.3 Quiz
Exercise
3.4.4 Solved Problem 3
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3.4.5 Solved Problem 4
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3.4.6 Solved Problem 5
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3.4.7 Solved Problem 6
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3.4.8 Solved Problem 7
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3.4.9 Solved Problem 8
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3.4.10 Solved Problem 9
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3.4.11 Solved Problem 10
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3.4.12 Exercises
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3.5 Line Integral
3.5.1 Introduction
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3.5.2 Conservative vector field
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3.5.3 Solved Problem 1
Video
5:50
3.5.3 Quiz
Exercise
3.5.4 Solved Problem 2
Video
4:38
3.5.4 Quiz
Exercise
3.5.5 Solved Problem 3
Video
5:1
3.5.5 Quiz
Exercise
3.5.6 Solved Problem 4
Video
4:24
3.5.6 Quiz
Exercise
3.5.7 Solved Problem 5
Video
4:31
3.5.7 Quiz
Exercise
3.5.8 Solved Problem 6
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3.5.9 Solved Problem 7
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3.5.10 Solved Problem 8
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3.5.11 Solved Problem 9
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3.5.12 Exercises
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3.6 Surface Integral
3.6.1 Introduction
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3.6.2 Solved Problem 1
Video
8:00
3.6.2 Quiz
Exercise
3.6.3 Solved Problem 2
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3.6.4 Solved Problem 3
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3.6.5 Exercises
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3.7 Volume Integral
3.7.1 Introduction
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3.7.2 Solved Problem 1
Video
6:15
3.7.2 Quiz
Exercise
3.7.3 Solved Problem 2
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3.7.4 Exercises
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3.8 Greens Theorem
3.8.1 Introduction
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3.8.2 Solved Problem 1
Video
6:50
3.8.2 Quiz
Exercise
3.8.3 Solved Problem 2
Video
12:6
3.8.3 Quiz
Exercise
3.8.4 Solved Problem 3
Video
8:55
3.8.4 Quiz
Exercise
3.8.5 Solved Problem 4
Video
9:41
3.8.5 Quiz
Exercise
3.8.6 Solved Problem 5
Video
7:50
3.8.6 Quiz
Exercise
3.8.7 Solved Problem 6
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3.8.8 Solved Problem 7
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3.8.9 Solved Problem 8
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3.8.10 Exercises
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3.9 Gauss Divergence Theorem
3.9.1 Introduction
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3.9.2 Solved Problem 1
Video
15:7
3.9.2 Quiz
Exercise
3.9.3 Solved Problem 2
Video
5:24
3.9.3 Quiz
Exercise
3.9.4 Solved Problem 3
Video
4:15
3.9.4 Quiz
Exercise
3.9.5 Solved Problem 4
Video
6:53
3.9.5 Quiz
Exercise
3.9.6 Solved Problem 5
Video
13:58
3.9.6 Quiz
Exercise
3.9.7 Solved Problem 6
Video
8:16
3.9.7 Quiz
Exercise
3.9.8 Solved Problem 7
Video
10:21
3.9.8 Quiz
Exercise
3.9.9 Solved Problem 8
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3.9.10 Exercises
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3.10 Stokes Theorem
3.10.1 Introduction
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3.10.2 Solved Problem 1
Video
10:3
3.10.2 Quiz
Exercise
3.10.3 Solved Problem 2
Video
9:19
3.10.3 Quiz
Exercise
3.10.4 Solved Problem 3
Video
14:11
3.10.4 Quiz
Exercise
3.10.5 Solved Problem 4
Video
7:31
3.10.5 Quiz
Exercise
3.10.6 Solved Problem 5
Video
6:45
3.10.6 Quiz
Exercise
3.10.7 Solved Problem 6
Video
6:38
3.10.7 Quiz
Exercise
3.10.8 Solved Problem 7
Video
8:35
3.10.8 Quiz
Exercise
3.10.9 Exercises
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Unit IV - Ordinary Differential Equations (VCEWM2) staff
31 Exercises • 100 Learning Materials
4.1 Linear Differential Equations of Higher Order
4.1.1 What is Ordinary Differential Equations?
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4.1.2 What are the applications of higher order ODEs in Engineering?
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4.1.3 Linear differential equations of higher order
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4.1.4 Operator D
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4.1.5 To find the General solution of f(D)y = 0
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4.1.6 Solved Problem 1
Video
5:39
4.1.6 Quiz
Exercise
4.1.7 Solved Problem 2
Video
3:32
4.1.7 Quiz
Exercise
4.1.8 Solved Problem 3
Video
3:53
4.1.8 Quiz
Exercise
4.1.9 Solved Problem 4
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4.1.10 Solved Problem 5
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4.1.11 Solved problem 6
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4.1.12 Solved problem 7
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4.1.13 Solved problem 8
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4.1.14 Solved problem 9
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4.1.15 Solved problem 10
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4.1.16 Solved problem 11
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4.1.17 Solved problem 12
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4.1.18 Exercise
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4.2 General solution of f(D)y = e^ax
4.2.1 Particular Integral of f(D)y = e^ax
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4.2.2 Solved Problem 1
Video
4:56
4.2.2 Quiz
Exercise
4.2.3 Solved Problem 2
Video
3:34
4.2.3 Quiz
Exercise
4.2.4 Solved Problem 3
Video
4:47
4.2.4 Quiz
Exercise
4.2.5 Solved Problem 4
Video
6:17
4.2.5 Quiz
Exercise
4.2.6 Solved Problem 5
Video
6:33
4.2.6 Quiz
Exercise
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 Solved problem 10
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4.2.12 Exercises
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4.3 General solution of f(D)y = cos ax or sin ax
4.3.1 Particular Integral of f(D) = cosax or sinax
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4.3.2 Working rule
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4.3.3 Solved Problem 1
Video
6:26
4.3.3 Quiz
Exercise
4.3.4 Solved Problem 2
Video
5:22
4.3.4 Quiz
Exercise
4.3.5 Solved Problem 3
Video
6:24
4.3.5 Quiz
Exercise
4.3.6 Solved Problem 4
Video
6:47
4.3.6 Quiz
Exercise
4.3.7 Solved Problem 5
Video
5:6
4.3.7 Quiz
Exercise
4.3.8 Solved Problem 6
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4.3.9 Solved Problem 7
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4.3.10 Solved Problem 8
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4.3.11 Exercises
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4.4 General solution of f(D)y = x^m
4.4.1 Particular Integral of f(D)y = xm
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4.4.2 Solved Problem 1
Video
5:42
4.4.2 Quiz
Exercise
4.4.3 Solved Problem 2
Video
6:7
4.4.3 Quiz
Exercise
4.4.4 Solved Problem 3
Video
8:25
4.4.4 Quiz
Exercise
4.4.5 Solved problem 4
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4.4.6 Solved problem 5
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4.4.7 Solved problem 6
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4.4.8 Solved problem 7
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4.4.9 Solved Problem 8
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4.4.10 Exercises
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4.5 General solution of f(D)y = e^ax . f(x)
4.5.1 Particular Integral of f(D)y = e^ax f(x)
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4.5.2 Solved Problem 1
Video
7:16
4.5.2 Quiz
Exercise
4.5.3 Solved Problem 2
Video
9:52
4.5.3 Quiz
Exercise
4.5.4 Solved Problem 3
Video
10:19
4.5.4 Quiz
Exercise
4.5.5 Solved Problem 4
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4.5.6 Solved Problem 5
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4.5.7 Exercise
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4.6 General solution of f(D)y = x^m . f(x)
4.6.1 Particular integral = xm sinax or xm cosax
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4.6.2 Solved Problem 1
Video
8:20
4.6.2 Quiz
Exercise
4.6.3 Solved Problem 2
Video
8:00
4.6.3 Quiz
Exercise
4.6.4 Solved Problem 3
Video
7:56
4.6.4 Quiz
Exercise
4.6.5 Solved Problem 4
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4.6.6 Solved Problem 5
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4.6.7 Solved Problem 6
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4.6.8 Solved Problem 7
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4.6.9 Exercises
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4.7 Method of variation of parameters
4.7.1 Introduction
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4.7.2 Method of variation of parameters
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4.7.3 Solved Problem 1
Video
6:48
4.7.3 Quiz
Exercise
4.7.4 Solved Problem 2
Video
7:42
4.7.4 Quiz
Exercise
4.7.5 Solved Problem 3
Video
10:13
4.7.5 Quiz
Exercise
4.7.6 Solved problem 4
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4.7.7 Solved problem 5
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4.7.8 Solved problem 6
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4.7.9 Solved problem 7
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4.7.10 Solved problem 8
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4.7.11 Exercises
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4.8 Cauchy's Differential Equations
4.8.1 Cauchy euler homogeneous linear equation
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4.8.2 Solved Problem 1
Video
7:40
4.8.2 Quiz
Exercise
4.8.3 Solved Problem 2
Video
8:11
4.8.3 Quiz
Exercise
4.8.4 Solved Problem 3
Video
8:22
4.8.4 Quiz
Exercise
4.8.5 Solved Problem 4
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4.8.6 Solved Problem 5
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4.8.7 Solved Problem 6
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4.8.8 Solved Problem 7
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4.8.9 Solved Problem 8
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4.8.10 Solved Problem 9
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4.8.11 Solved problem 10
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4.8.12 Exercises
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4.9 Legendre Differential Equations
4.9.1 Legendre Linear equations
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4.9.2 Solved Problem 1
Video
7:7
4.9.2 Quiz
Exercise
4.9.3 Solved Problem 2
Video
6:2
4.9.3 Quiz
Exercise
4.9.4 Solved Problem 3
Video
7:21
4.9.4 Quiz
Exercise
4.9.5 Solved Problem 4
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4.9.6 Solved Problem 5
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4.9.7 Solved Problem 6
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4.9.8 Solved Problem 7
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4.9.9 Solved Problem 8
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4.9.10 Exercises
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Unit V - Laplace Transforms (VCEWM2) staff
138 Learning Materials
5.1 Laplace Transform
5.1.1 Introduction
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5.1.2 Sufficient Conditions for Existence
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5.1.3 Solved Problem 1
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5.1.4 Exponential Order
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5.2 Laplace Transform of Some Standard Functions
5.2.1 Introduction
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5.2.2 Laplace Transform of e^at
Video
5:12
5.2.3 Laplace Transform of 1
Video
3:54
5.2.4 Laplace Transform of sinat and cosat
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5:28
5.2.5 Laplace Transform of sinhat and coshat
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7:21
5.2.6 Laplace Transform of t^n
Video
4:52
5.2.7 Solved Problem 1
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6:15
5.2.8 Solved Problem 2
Video
8:2
5.2.9 Solved Problem 3
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8:36
5.2.10 Solved Problem 4
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5.2.11 Solved Problem 5
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5.2.12 Solved Problem 6
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5.2.13 Solved Problem 7
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5.2.14 Solved Problem 8
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5.2.15 Solved Problem 9
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5.2.16 Exercises
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5.3 First, Second Shifting Theorem and Change of Scale Property
5.3.1 First Shifting Theorem
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5.3.2 Solved Problem 1
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5:39
5.3.3 Solved Problem 2
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5:17
5.3.4 Solved Problem 3
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3:50
5.3.5 Solved Problem 4
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5.3.6 Solved Problem 5
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5.3.7 Second Shifting Theorem
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5.3.8 Solved Problem 1
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4:9
5.3.9 Solved Problem 2
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5.3.10 Solved Problem 3
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5.3.11 Change of Scale Property
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5.3.12 Solved Problem 1
Video
5:38
5.3.13 Solved Problem 2
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5.3.14 Solved Problem 3
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5.3.15 Exercises
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5.4 Transforms of Derivatives
5.4.1 Transforms of Derivatives
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5.4.2 Derivatives of Transforms
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5.4.3 Solved Problem 1
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10:2
5.4.4 Solved Problem 2
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7:43
5.4.5 Solved Problem 3
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5.4.6 Solved Problem 4
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5.4.7 Solved Problem 5
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7:34
5.4.8 Solved Problem 6
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5.4.9 Exercises
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5.5 Transforms of Integrals
5.5.1 Transforms of Integrals
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5.5.2 Integrals of Transforms
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5.5.3 Solved Problem 1
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10:00
5.5.4 Solved Problem 2
Video
10:53
5.5.5 Solved Problem 3
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10:52
5.5.6 Solved Problem 4
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5.5.7 Solved Problem 5
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5.5.8 Solved Problem 6
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5.5.9 Solved Problem 7
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5.5.10 Solved Problem 8
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5.5.11 Solved Problem 9
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5.5.12 Exercises
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5.6 Laplace Transform of Periodic Functions
5.6.1 Laplace Transform of Periodic Functions
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5.6.2 Solved Problem 1
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6:56
5.6.3 Solved Problem 2
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12:12
5.6.4 Solved Problem 3
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5.6.5 Solved Problem 4
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5.6.6 Solved Problem 5
Video
9:9
5.6.7 Exercises
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5.7 Laplace Transform of Unit Step and Unit Impulse Functions
5.7.1 Laplace Transform of Unit Step Functions
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5.7.2 Laplace Transform of Unit Impulse Functions
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5.7.3 Solved Problem 1
Video
4:28
5.7.4 Solved Problem 2
Video
12:39
5.7.5 Solved Problem 3
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11:17
5.7.6 Solved Problem 4
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5.7.7 Solved Problem 5
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5.7.8 Exercises
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5.8 Inverse Laplace Transform
5.8.1 Introduction
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5.8.2 Solved Problem 1
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3:41
5.8.3 Solved Problem 2
Video
6:3
5.8.4 Solved Problem 3
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5.8.5 Solved Problem 4
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5.8.6 Solved Problem 5
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5.8.7 Method of Partial Fraction
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5.8.8 Solved Problem 2
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6:5
5.8.9 Solved Problem 3
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5.8.10 Solved Problem 4
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5.8.11 Solved Problem 5
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5.8.12 Solved Problem 6
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5.8.13 Solved Problem 7
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5.8.14 Solved Problem 8
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5.8.15 Exercise
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5.9 First and Second Shifting Theorem, Change of scale of property
5.9.1 First Shifting Theorem
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5.9.2 Solved Problem 2
Video
7:9
5.9.3 Solved Problem 3
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5.9.4 Second Shifting Theorem
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5.9.5 Solved Problem 1
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4:48
5.9.6 Solved Problem 2
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5.9.7 Solved Problem 3
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5.9.8 Change of Scale of Property
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5.9.9 Solved Problem 1
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4:50
5.9.10 Solved Problem 2
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5.9.11 Solved Problem 3
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5.9.12 Exercises
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5.10 Inverse Laplace Transform of Derivatives and Integrals
5.10.1 Inverse Laplace Transform of Derivatives
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5.10.2 Solved Problem 1
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6:14
5.10.3 Solved Problem 2
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5.10.4 Solved Problem 3
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5.10.5 Solved Problem 4
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5.10.6 Solved Problem 5
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5.10.7 Inverse Laplace Transform of Integrals
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5.10.8 Solved Problem 1
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4:26
5.10.9 Solved Problem 2
Video
6:10
5.10.10 Solved Problem 3
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5.10.11 Solved Problem 4
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5.10.12 Exercises
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5.11 Multiplication by power of 's' and Division by 's'
5.11.1 Multiplication by Power of ‘s’
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5.11.2 Solved Problem 1
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4:3
5.11.3 Solved Problem 2
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5.11.4 Solved Problem 3
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5.11.5 Division by ‘s’
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5.11.6 Solved Problem 2
Video
2:1
5.11.7 Solved Problem 3
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6:30
5.11.8 Exercises
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5.12 Convolution Theorem
5.12.1 Convolution theorem
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5.12.2 Solved Problem 1
Video
7:12
5.12.3 Solved Problem 2
Video
8:29
5.12.4 Solved Problem 3
Video
8:28
5.12.5 Solved Problem 4
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5.12.6 Solved Problem 5
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5.12.7 Solved Problem 6
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5.12.8 Solved Problem 7
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5.12.9 Solved Problem 8
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5.12.10 Exercises
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5.13 Solving ordinary equations by laplace transform
5.13.1 Introduction
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5.13.2 Solved Problem 2
Video
10:22
5.13.3 Solved Problem 3
Video
10:2
5.13.4 Solved Problem 4
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10:48
5.13.5 Solved Problem 5
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5.13.6 Solved Problem 6
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5.13.7 Solved Problem 7
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5.13.8 Solved Problem 8
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5.13.9 Solved Problem 9
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5.13.10 Exercise
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