Probability and Complex Functions (MA3303) - Anna University
Course Instructor
Promath
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Course Overview
Schedule of Classes
Course Curriculum
7 Subjects
Unit - I : Probability and Random Variables
131 Learning Materials
1.1 Probability and Random Variable
1.1.1 Introduction of Probability
PDF
1.1.2 Set definitions
PDF
1.1.3 Operations on sets
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1.1.4 Laws of algebra of sets
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1.1.5 Experiments and sample spaces
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1.1.6 Discrete and Continuous sample spaces
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1.1.7 Events
PDF
1.1.8 Probability Definitions and axioms
PDF
1.1.9 Theorems on probability
PDF
1.1.10 Exercises
PDF
1.2 Mathematical model of experiments
1.2.1 Mathematical (or) classical definition of probability
PDF
1.2.2 Solved Problem 1
Video
2:31
1.2.3 Solved Problem 2
Video
2:18
1.2.4 Solved Problem 3
Video
2:34
1.2.5 Solved Problem 4
Video
2:00
1.2.6 Solved Problem 5
PDF
1.2.7 Mathematical tools
PDF
1.2.8 Solved Problem 1
Video
4:31
1.2.9 Solved Problem 2
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1.2.10 Solved Problem 3
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1.2.11 Exercises
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1.3 Joint probability
1.3.1 Joint Probability
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1.3.2 Introduction to Probability as Relative Frequency
PDF
1.3.3 Solved Problem 1
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1.4 Conditional probability
1.4.1 Introduction of conditional probability
PDF
1.4.2 Solved Problem 1
Video
4:9
1.4.3 Solved Problem 2
Video
4:34
1.4.4 Solved Problem 4
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1.5 Total probability and baye's theorem
1.5.1 Theorem of Total Probability
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1.5.2 Baye's theorem
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1.5.3 Solved Problem 1
Video
8:10
1.5.4 Solved Problem 2
Video
9:48
1.5.5 Solved Problem 3
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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 Exercises
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1.6 Independent Events
1.6.1 Independent Events (multiplication law of probability)
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1.6.2 Solved Problem 1
Video
1:31
1.6.3 Solved Problem 2
Video
2:1
1.6.4 Solved Problem 3
Video
3:30
1.6.5 Solved Problem 4
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1.6.6 Solved Problem 5
Video
5:00
1.6.7 Exercises
PDF
1.7 Random Variable
1.7.1 Introduction of Random variable
PDF
1.7.2 Definition of Random variable
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1.7.3 Discrete continuous and mixed random variable
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1.7.4 conditions for a function to be a random variable
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1.7.5 Probability distribution function
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1.7.6 Probability of mass function
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1.7.7 Probability of discrete random variable
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1.7.8 Solved Problem 1
Video
9:52
1.7.9 Solved Problem 2
Video
3:55
1.7.10 Solved Problem 3
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1.7.11 Solved Problem 4
Video
5:32
1.7.12 Solved Problem 5
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1.7.13 Exercises
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1.8 Continuous Random Variable
1.8.1 Probability distribution function
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1.8.2 Probability density function
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1.8.3 Probability of continuous random variable
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1.8.4 Solved Problem 1
Video
3:17
1.8.5 Solved Problem 2
Video
7:59
1.8.6 Solved Problem 3
Video
7:7
1.8.7 Solved Problem 4
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1.8.8 Solved Problem 5
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1.8.9 Solved Problem 6
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1.8.10 Exercises
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1.9 Binomial distribution
1.9.1 Introduction to binomial Distribution
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1.9.2 Mean of binomial distribution
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1.9.3 Variance of binomial distribution
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1.9.4 Moment generating function
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1.9.5 Solved Problem 1
Video
11:5
1.9.6 Solved Problem 2
Video
9:24
1.9.7 Solved Problem 3
Video
6:27
1.9.8 Solved problem 4
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1.9.9 Solved problem 5
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1.9.10 Solved problem 6
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1.9.11 Solved problem 7
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1.9.12 Solved problem 8
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1.9.13 Exercises
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1.10 Poisson distribution
1.10.1 Introduction to poisson distribution
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1.10.2 Mean of poisson distribution
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1.10.3 Variance of poisson distribution
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1.10.4 Moment of generating function
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1.10.5 Properties of poisson distribution 1
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1.10.6 Properties of poisson distribution 2
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1.10.7 Solved Problem 1
Video
6:28
1.10.8 Solved problem 2
Video
7:2
1.10.9 Solved Problem 3
Video
8:28
1.10.10 Solved Problem 4
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1.10.11 Solved Problem 5
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1.10.12 Solved Problem 6
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1.10.13 Solved Problem 7
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1.10.14 Solved Problem 8
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1.10.15 Exercises
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1.11 Geometric Distribution
1.11.1 Introduction to Geometric Distribution
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1.11.2 Solved Problem 1
Video
4:39
1.11.3 Solved Problem 2
Video
9:6
1.11.4 Solved Problem 3
Video
5:15
1.11.5 Solved problem 4
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1.11.6 Solved problem 5
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1.11.7 Solved problem 6
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1.11.8 Solved problem 7
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1.11.9 Solved problem 8
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1.11.10 Exercises
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1.12 Uniform distribution
1.12.1 Introduction to uniform distribution
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1.12.2 Moment generating function of uniform distribution
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1.12.3 Solved Problem 1
Video
8:23
1.12.4 Solved Problem 2
Video
3:35
1.12.5 Solved Problem 3
Video
9:26
1.12.6 Solved Problem 4
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1.12.7 Exercises
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1.13 Normal/Gaussian Distribution
1.13.1 Introduction to gaussian or Normal distribution
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1.13.2 Application of gaussian distribution
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1.13.3 Characteristics of the gaussian distribution
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1.13.4 Normal distribution as a limiting form of binomial distribution
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1.13.5 Solved Problem 1
Video
2:58
1.13.6 Solved Problem 2
Video
5:9
1.13.7 Solved Problem 3
Video
13:30
1.13.8 Solved Problem 4
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1.13.9 Solved Problem 5
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1.13.10 Exercises
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1.14 Exponential Distribution
1.14.1 Introduction to Exponential Distribution
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1.14.2 Exponential Distribution
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1.14.3 Solved Problem 1
Video
6:55
1.14.4 Solved Problem 2
Video
4:46
1.14.5 Solved Problem 3
Video
5:54
1.14.6 Memoryless Property of the exponential distribution
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1.14.7 Solved Problem 4
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1.14.8 Solved Problem 5
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1.14.9 Exercises
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Unit - II : Two-Dimensional Random Variables
105 Learning Materials
2.1 Two Dimensional Random Variables
2.1.1 Introduction
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2.1.2 Joint Probability Distribution
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2.1.3 Joint Cumulative Distribution Function
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2.1.4 Marginal Probability Distribution Function
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2.1.5 Conditional Probability Distribution Function
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2.1.6 Expectation of a Function g(X, Y)
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2.2 Problems based on Discrete Random Variables
2.2.1 Introduction
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2.2.2 Solved Problem 1
Video
10:35
2.2.3 Solved Problem 2
Video
10:14
2.2.4 Solved Problem 3
Video
10:56
2.2.5 Solved Problem 4
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2.2.6 Solved Problem 5
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2.2.7 Solved Problem 6
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2.2.8 Solved Problem 7
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2.2.9 Exercises
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2.3 Problems based on Continuous Random Variables
2.3.1 Introduction
PDF
2.3.2 Solved Problem 1
Video
6:51
2.3.3 Solved Problem 2
Video
8:28
2.3.4 Solved Problem 3
Video
8:33
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 Solved Problem 7
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2.3.9 Solved Problem 8
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2.3.10 Solved Problem 9
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2.3.11 Solved Problem 10
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2.3.12 Solved Problem 11
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2.3.13 Exercises
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2.4 Correlation
2.4.1 Covariance
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2.4.2 Correlation
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2.4.3 Types of Correlation
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2.4.4 Methods of studying correlation
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2.4.5 Scatter Diagram & Simple Graph Method
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2.4.6 Karl Pearson's Coefficient of Correlation
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2.4.7 Properties of Correlation Coefficient
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2.4.8 Solved problem 1
Video
6:18
2.4.9 Solved problem 2
Video
8:29
2.4.10 Solved problem 3
Video
8:26
2.4.11 Solved problem 4
Video
9:9
2.4.12 Solved problem 5
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2.4.13 Solved problem 6
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2.4.14 Solved problem 7
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2.4.15 Solved problem 8
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2.4.16 Solved problem 9
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2.4.17 Solved problem 10
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2.4.18 Solved problem 11
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2.4.19 Solved problem 12
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2.4.20 Solved problem 13
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2.4.21 Solved problem 14
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2.4.22 Solved problem 15
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2.4.23 Solved problem 16
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2.4.24 Solved problem 17
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2.4.25 Exercises
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2.5 Correlation and Grouped data
2.5.1 Correlation of Grouped Data
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2.5.2 Solved problem 1
Video
15:7
2.5.3 Solved problem 2
Video
12:46
2.5.4 Solved problem 3
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2.5.5 Exercises
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2.6 Rank Correlation Coefficient
2.6.1 Rank Correlation Coefficient
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2.6.2 Solved problem 1
Video
3:42
2.6.3 Solved problem 2
Video
9:6
2.6.4 Solved problem 3
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2.6.5 Solved problem 4
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2.6.6 Solved problem 5
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2.6.7 Equal or Repeated Ranks
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2.6.8 Solved problem 3
Video
9:37
2.6.9 Solved problem 2
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2.6.10 Exercises
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2.7 Regression
2.7.1 Introduction
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2.7.2 Methods of studying Regression
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2.7.3 Regression Lines
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2.7.4 Solved problem 1
Video
9:45
2.7.5 Solved problem 2
Video
15:28
2.7.6 Solved problem 3
Video
7:3
2.7.7 Solved problem 4
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2.7.8 Solved problem 5
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2.7.9 Solved problem 6
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2.7.10 Solved problem 7
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2.7.11 Angle Between Two Regression Lines
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2.7.12 Solved problem 1
Video
4:12
2.7.13 Solved problem 2
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2.7.14 Solved problem 3
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2.7.15 Exercises
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2.8 Transformation of Random Variables
2.8.1 Transformation of Random Variables
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2.8.2 Solved problem 1
Video
9:38
2.8.3 Solved problem 2
Video
10:7
2.8.4 Solved problem 3
Video
13:50
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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2.9 Central Limit Theorem
2.9.1 Central Limit Theorem [Lindberg-Levy’s form]
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2.9.2 Convergence
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2.9.3 Normal area Property
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2.9.4 Uses of Central Limit Theorem
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2.9.5 Theorem
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2.9.6 Solved problem 1
Video
4:39
2.9.7 Solved problem 2
Video
6:14
2.9.8 Solved problem 3
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2.9.9 Solved problem 4
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2.9.10 Solved problem 5
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2.9.11 Solved problem 6
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2.9.12 Solved problem 7
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2.9.13 Area under the Standard Normal Probability Curve
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2.9.14 Exercises
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Unit - III : Analytic Functions
26 Exercises • 79 Learning Materials
3.1 Analytic Functions
3.1.1 Analytic function
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3.1.2 Cauchy Riemann Equation
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3.1.3 The Necessary condition for f(z) to be analytic (in Cartesian form)
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3.1.4 Sufficient condition for f(z) to be analytic
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3.1.5 Cauchy Riemann equations In polar coordinates
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3.1.6 Solved Problem 1
Video
5:9
3.1.6 Quiz
Exercise
3.1.7 Solved Problem 2
Video
6:33
3.1.7 Quiz
Exercise
3.1.8 Solved Problem 3
Video
5:1
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 Exercises
Exercise
3.2 Harmonic Property
3.2.1 Property of Analytic functions
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3.2.2 Harmonic Functions - Laplace Equation
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3.2.3 Harmonic Function
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3.2.4 Harmonic Conjugates
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3.2.5 Solved Problem 1
Video
9:55
3.2.5 Quiz
Exercise
3.2.6 Solved Problem 2
Video
14:59
3.2.6 Quiz
Exercise
3.2.7 Solved Problem 3
Video
13:20
3.2.7 Quiz
Exercise
3.2.8 Solved Problem 4
Video
12:37
3.2.8 Quiz
Exercise
3.2.9 Solved Problem 5
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3.2.10 Solved Problem 6
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3.2.11 Solved Problem 7
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3.2.12 Solved Problem 8
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3.2.13 Solved Problem 9
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3.2.14 Exercises
Exercise
3.3 Orthogonal Property
3.3.1 Orthogonal system
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3.3.2 Solved Problem 1
Video
5:21
3.3.3 Solved Problem 2
Video
10:1
3.3.4 Solved Problem 3
Video
4:13
3.3.5 Solved Problem 4
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3.3.6 Solved Problem 5
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3.3.7 Solved Problem 6
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3.3.8 Exercises
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3.4 Construction of Analytic functions
3.4.1 Construction of Analytic functions
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3.4.2 Method 1 Construction of Analytic function whose real or imaginary part is known
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3.4.3 Solved Problem 1
Video
8:41
3.4.3 Quiz
Exercise
3.4.4 Solved Problem 2
Video
7:24
3.4.4 Quiz
Exercise
3.4.5 Solved Problem 3
Video
13:37
3.4.5 Quiz
Exercise
3.4.6 Solved problem 4
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3.4.7 Solved problem 5
PDF
3.4.8 Exercises
Exercise
3.5 Milne Thomson Method
3.5.1 Milne Thomson Method (To Construct an analytic function)
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3.5.2 Working rule To Construct an analytic function by Milne Thomson Method
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3.5.3 Solved Problem 1
Video
9:51
3.5.3 Quiz
Exercise
3.5.4 Solved Problem 2
Video
14:43
3.5.4 Quiz
Exercise
3.5.5 Solved Problem 3
Video
13:23
3.5.5 Quiz
Exercise
3.5.6 Solved Problem 4
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3.5.7 Solved Problem 5
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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 Exercises
Exercise
3.6 Conformal Mapping
3.6.1 Conformal mapping
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3.6.2 Translation w=c+z
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3.6.3 Magnification w=cz
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3.6.4 Magnification and Rotation
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3.6.5 Magnification, Rotation and Translation
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3.6.6 Inversion and Reflection w=1/z
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3.6.7 Transformation w=z^2
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3.6.8 Problem based on w=c+z _ Solved Problem 1
Video
4:45
3.6.8 Quiz
Exercise
3.6.9 Solved Problem 2
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3.6.10 Problem based on w=cz _ Solved Problem 3
Video
6:2
3.6.10 Quiz
Exercise
3.6.11 Solved Problem 4
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3.6.12 Problem based on w=1/z _ Solved Problem 5
Video
6:40
3.6.12 Quiz
Exercise
3.6.13 Solved Problem 6
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3.6.14 Solved Problem 7
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3.6.15 Problem based on w=z^2 _ Solved Problem 8
Video
4:46
3.6.15 Quiz
Exercise
3.6.16 Solved Problem 9
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3.6.17 Exercises
Exercise
3.7 Bilinear Transformation (Mobius Transformation)
3.7.1 Bilinear Transformation
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3.7.2 Theorem 1
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3.7.3 Fixed points (or) Invariant points
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3.7.4 Theorem 2
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3.7.5 Cross Ratio
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3.7.6 Solved Problem 1
Video
7:58
3.7.6 Quiz
Exercise
3.7.7 Solved Problem 2
Video
6:23
3.7.7 Quiz
Exercise
3.7.8 Solved Problem 3
Video
5:5
3.7.8 Quiz
Exercise
3.7.9 Solved Problem 4
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3.7.10 Solved Problem 5
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3.7.11 Solved Problem 6
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3.7.12 Solved Problem 7
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3.7.13 Solved Problem 8
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3.7.14 Exercises
Exercise
Unit - IV : Complex Integration
25 Exercises • 88 Learning Materials
4.1 Line Integral
4.1.1 Line integral
PDF
4.1.2 Solved Problem 1
Video
8:11
4.1.2 Quiz
Exercise
4.1.3 Solved Problem 2
Video
13:14
4.1.3 Quiz
Exercise
4.1.4 Solved Problem 3
Video
8:8
4.1.4 Quiz
Exercise
4.1.5 Solved Problem 4
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4.1.6 Solved Problem 5
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4.1.7 Solved Problem 6
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4.1.8 Solved Problem 7
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4.1.9 Exercises
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4.2 Cauchy's Integral Theorem and Integral Formula
4.2.1 Introduction
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4.2.2 The Cauchy's theorem
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4.2.3 Cauchy's theorem for multiply connected region
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4.2.4 Cauchy's integral formula
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4.2.5 Cauchy's integral formula for derivative
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4.2.6 Solved Problem 1
Video
7:00
4.2.6 Quiz
Exercise
4.2.7 Solved Problem 2
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4.2.8 Solved Problem 3
Video
9:12
4.2.8 Quiz
Exercise
4.2.9 Solved Problem 4
Video
11:19
4.2.9 Quiz
Exercise
4.2.10 Solved Problem 5
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4.2.11 Solved Problem 6
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4.2.12 Solved Problem 7
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4.2.13 Solved Problem 8
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4.2.14 Solved Problem 9
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4.2.15 Solved Problem 10
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4.2.16 Solved Problem 11
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4.2.17 Solved Problem 12
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4.2.18 Exercises
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4.3 Taylor’s Series
4.3.1 Taylor's series
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4.3.2 Some important results
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4.3.3 Solved Problem 1
Video
8:5
4.3.3 Quiz
Exercise
4.3.4 Solved Problem 2
Video
10:2
4.3.4 Quiz
Exercise
4.3.5 Solved Problem 3
Video
7:51
4.3.5 Quiz
Exercise
4.3.6 Solved Problem 4
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4.3.7 Solved Problem 5
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4.3.8 Solved Problem 6
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4.3.9 Solved Problem 7
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4.3.10 Exercises
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4.4 Laurent’s Series
4.4.1 Laurent's series
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4.4.2 Some important results
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4.4.3 Solved Problem 1
Video
8:16
4.4.3 Quiz
Exercise
4.4.4 Solved Problem 2
Video
10:47
4.4.4 Quiz
Exercise
4.4.5 Solved Problem 3
Video
14:34
4.4.5 Quiz
Exercise
4.4.6 Solved Problem 4
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4.4.7 Solved Problem 5
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4.4.8 Solved Problem 6
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4.4.9 Exercises
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4.5 Classification of Singularities
4.5.1 Singularities and Classification
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4.5.2 Types of singularities
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4.5.3 Solved Problem 1
Video
8:7
4.5.3 Quiz
Exercise
4.5.4 Solved Problem 2
Video
8:19
4.5.4 Quiz
Exercise
4.5.5 Solved Problem 3
Video
1:58
4.5.5 Quiz
Exercise
4.5.6 Solved Problem 4
PDF
4.5.7 Exercises
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4.6 Cauchy's Residue Theorem
4.6.1 Residues
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4.6.2 Cauchy's residue theorem
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4.6.3 Solved Problem 1
Video
7:3
4.6.3 Quiz
Exercise
4.6.4 Solved Problem 2
Video
11:6
4.6.4 Quiz
Exercise
4.6.5 Solved Problem 3
Video
5:56
4.6.5 Quiz
Exercise
4.6.6 Solved Problem 4
Video
9:9
4.6.6 Quiz
Exercise
4.6.7 Solved Problem 5
PDF
4.6.8 Solved Problem 6
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4.6.9 Solved Problem 7
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4.6.10 Solved Problem 8
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4.6.11 Solved Problem 9
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4.6.12 Solved Problem 10
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4.6.13 Solved Problem 11
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4.6.14 Solved Problem 12
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4.6.15 Solved Problem 13
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4.6.16 Solved Problem 14
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4.6.17 Solved Problem 15
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4.6.18 Solved Problem 16
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4.6.19 Solved Problem 17
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4.6.20 Solved Problem 18
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4.6.21 Exercises
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4.7 Integration around the Unit Circle
4.7.1 Contour integration type I
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4.7.2 Solved Problem 1
Video
11:59
4.7.2 Quiz
Exercise
4.7.3 Solved Problem 2
Video
10:37
4.7.3 Quiz
Exercise
4.7.4 Solved Problem 3
Video
10:30
4.7.4 Quiz
Exercise
4.7.5 Solved Problem 4
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4.7.6 Solved Problem 5
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4.7.7 Exercises
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4.8 Integration around the semi - circle
4.8.1 Contour integration type II
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4.8.2 Solved Problem 1
Video
9:13
4.8.2 Quiz
Exercise
4.8.3 Solved Problem 2
Video
9:26
4.8.3 Quiz
Exercise
4.8.4 Solved Problem 3
Video
9:39
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 Exercises
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Unit - V : Ordinary Differential Equations
34 Exercises • 108 Learning Materials
5.1 Linear Differential Equations of Higher Order
5.1.1 What is Ordinary Differential Equations?
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5.1.2 What are the applications of higher order ODEs in Engineering?
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5.1.3 Linear differential equations of higher order
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5.1.4 Operator D
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5.1.5 To find the General solution of f(D)y = 0
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5.1.6 Solved Problem 1
Video
5:39
5.1.6 Quiz
Exercise
5.1.7 Solved Problem 2
Video
3:32
5.1.7 Quiz
Exercise
5.1.8 Solved Problem 3
Video
3:53
5.1.8 Quiz
Exercise
5.1.9 Solved Problem 4
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5.1.10 Solved Problem 5
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5.1.11 Solved problem 6
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5.1.12 Solved problem 7
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5.1.13 Solved problem 8
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5.1.14 Solved problem 9
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5.1.15 Solved problem 10
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5.1.16 Solved problem 11
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5.1.17 Solved problem 12
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5.1.18 Exercises
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5.2 General solution of f(D)y = e^ax
5.2.1 Particular Integral of f(D)y = e^ax
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5.2.2 Solved Problem 1
Video
4:56
5.2.2 Quiz
Exercise
5.2.3 Solved Problem 2
Video
3:34
5.2.3 Quiz
Exercise
5.2.4 Solved Problem 3
Video
4:47
5.2.4 Quiz
Exercise
5.2.5 Solved Problem 4
Video
6:17
5.2.5 Quiz
Exercise
5.2.6 Solved Problem 5
Video
6:33
5.2.6 Quiz
Exercise
5.2.7 Solved problem 6
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5.2.8 Solved problem 7
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5.2.9 Solved problem 8
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5.2.10 Solved problem 9
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5.2.11 Solved problem 10
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5.2.12 Exercises
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5.3 General solution of f(D)y = cos ax or sin ax
5.3.1 Particular Integral of f(D) = cosax or sinax
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5.3.2 Working rule
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5.3.3 Solved Problem 1
Video
6:26
5.3.3 Quiz
Exercise
5.3.4 Solved Problem 2
Video
5:22
5.3.4 Quiz
Exercise
5.3.5 Solved Problem 3
Video
6:24
5.3.5 Quiz
Exercise
5.3.6 Solved Problem 4
Video
6:47
5.3.6 Quiz
Exercise
5.3.7 Solved Problem 5
Video
5:6
5.3.7 Quiz
Exercise
5.3.8 Solved Problem 6
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5.3.9 Solved Problem 7
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5.3.10 Solved Problem 8
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5.3.11 Exercises
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5.4 General solution of f(D)y = x^m
5.4.1 Particular Integral of f(D)y = xm
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5.4.2 Solved Problem 1
Video
5:42
5.4.2 Quiz
Exercise
5.4.3 Solved Problem 2
Video
6:7
5.4.3 Quiz
Exercise
5.4.4 Solved Problem 3
Video
8:25
5.4.4 Quiz
Exercise
5.4.5 Solved problem 4
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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 Exercises
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5.5 General solution of f(D)y = e^ax . f(x)
5.5.1 Particular Integral of f(D)y = e^ax f(x)
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5.5.2 Solved Problem 1
Video
7:16
5.5.2 Quiz
Exercise
5.5.3 Solved Problem 2
Video
9:52
5.5.3 Quiz
Exercise
5.5.4 Solved Problem 3
Video
10:19
5.5.4 Quiz
Exercise
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 General solution of f(D)y = x^m . f(x)
5.6.1 Particular integral = xm sinax or xm cosax
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5.6.2 Solved Problem 1
Video
8:20
5.6.2 Quiz
Exercise
5.6.3 Solved Problem 2
Video
8:00
5.6.3 Quiz
Exercise
5.6.4 Solved Problem 3
Video
7:56
5.6.4 Quiz
Exercise
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 Solved Problem 7
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5.6.9 Exercises
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5.7 Method of variation of parameters
5.7.1 Introduction
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5.7.2 Method of variation of parameters
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5.7.3 Solved Problem 1
Video
6:48
5.7.3 Quiz
Exercise
5.7.4 Solved Problem 2
Video
7:42
5.7.4 Quiz
Exercise
5.7.5 Solved Problem 3
Video
10:13
5.7.5 Quiz
Exercise
5.7.6 Solved problem 4
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5.7.7 Solved problem 5
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5.7.8 Solved problem 6
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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 Cauchy's Differential Equations
5.8.1 Cauchy Euler homogeneous linear equation
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5.8.2 Solved Problem 1
Video
7:40
5.8.2 Quiz
Exercise
5.8.3 Solved Problem 2
Video
8:11
5.8.3 Quiz
Exercise
5.8.4 Solved Problem 3
Video
8:22
5.8.4 Quiz
Exercise
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 Solved Problem 8
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5.8.10 Solved Problem 9
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5.8.11 Solved problem 10
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5.8.12 Exercises
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5.9 Legendre Differential Equations
5.9.1 Legendre Linear equations
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5.9.2 Solved Problem 1
Video
7:7
5.9.2 Quiz
Exercise
5.9.3 Solved Problem 2
Video
6:2
5.9.3 Quiz
Exercise
5.9.4 Solved Problem 3
Video
7:21
6.9.4 Quiz
Exercise
5.9.5 Solved Problem 4
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5.9.6 Solved Problem 5
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5.9.7 Solved Problem 6
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5.9.8 Solved Problem 7
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5.9.9 Solved Problem 8
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5.9.10 Exercises
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5.10 Simultaneous First Order Linear Equations with Constant Coefficients
5.10.1 Introduction
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5.10.2 Solved Problem 1
Video
9:3
5.10.2 Quiz
Exercise
5.10.3 Solved Problem 2
Video
7:6
5.10.3 Quiz
Exercise
5.10.4 Solved Problem 3
Video
5:25
5.10.4 Quiz
Exercise
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
PDF
Important Q&A
85 Learning Materials
1. Probability and Random Variables
1.1 Part A: Q&A
PDF
1.2 Part B: Q&A - 1
PDF
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
PDF
1.8 Part B: Q&A - 7
PDF
1.9 Part B: Q&A - 8
PDF
1.10 Part B: Q&A - 9
PDF
1.11 Part B: Q&A - 10
PDF
1.12 Part B: Q&A - 11
PDF
1.13 Part B: Q&A - 12
PDF
1.14 Part B: Q&A - 13
PDF
1.15 Part B: Q&A - 14
PDF
1.16 Part B: Q&A - 15
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1.17 Part B: Q&A - 16
PDF
2. Two-Dimensional Random Variables
2.1 Part A: Q&A
PDF
2.2 Part B: Q&A - 1
PDF
2.3 Part B: Q&A - 2
PDF
2.4 Part B: Q&A - 3
PDF
2.5 Part B: Q&A - 4
PDF
2.6 Part B: Q&A - 5
PDF
2.7 Part B: Q&A - 6
PDF
2.8 Part B: Q&A - 7
PDF
2.9 Part B: Q&A - 8
PDF
2.10 Part B: Q&A - 9
PDF
2.11 Part B: Q&A - 10
PDF
2.12 Part B: Q&A - 11
PDF
2.13 Part B: Q&A - 12
PDF
2.14 Part B: Q&A - 13
PDF
3. Analytic Functions
3.1 Part A: Q&A
PDF
3.2 Part B: Q&A - 1
PDF
3.3 Part B: Q&A - 2
PDF
3.4 Part B: Q&A - 3
PDF
3.5 Part B: Q&A - 4
PDF
3.6 Part B: Q&A - 5
PDF
3.7 Part B: Q&A - 6
PDF
3.8 Part B: Q&A - 7
PDF
3.9 Part B: Q&A - 8
PDF
3.10 Part B: Q&A - 9
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3.11 Part B: Q&A - 10
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3.12 Part B: Q&A - 11
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3.13 Part B: Q&A - 12
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3.14 Part B: Q&A - 13
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3.15 Part B: Q&A - 14
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3.16 Part B: Q&A - 15
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3.17 Part B: Q&A - 16
PDF
4. Complex Integration
4.1 Part A: Q&A
PDF
4.2 Part B: Q&A - 1
PDF
4.3 Part B: Q&A - 2
PDF
4.5 Part B: Q&A - 4
PDF
4.6 Part B: Q&A - 5
PDF
4.7 Part B: Q&A - 6
PDF
4.8 Part B: Q&A - 7
PDF
4.9 Part B: Q&A - 8
PDF
4.10 Part B: Q&A - 9
PDF
4.11 Part B: Q&A - 10
PDF
4.12 Part B: Q&A - 11
PDF
4.13 Part B: Q&A - 12
PDF
4.14 Part B: Q&A - 13
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4.15 Part B: Q&A - 14
PDF
4.16 Part B: Q&A - 15
PDF
5. Ordinary Differential Equations
5.1 Part A: Q&A
PDF
5.2 Part B: Q&A - 1
PDF
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
PDF
5.11 Part B: Q&A - 10
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5.12 Part B: Q&A - 11
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5.13 Part B: Q&A - 12
PDF
5.14 Part B: Q&A - 13
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5.15 Part B: Q&A - 14
PDF
5.16 Part B: Q&A - 15
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5.17 Part B: Q&A - 16
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5.18 Part B: Q&A - 17
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5.19 Part B: Q&A - 18
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5.20 Part B: Q&A - 19
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5.21 Part B: Q&A - 20
PDF
5.22 Part B: Q&A - 21
PDF
University Solved Question Paper
24 Learning Materials
April/May 2024
Part A
PDF
Part B: Q&A - 11
PDF
Part B: Q&A - 12
PDF
Part B: Q&A - 13
PDF
Part B: Q&A - 14
PDF
Part B: Q&A - 15
PDF
November/December 2023
Part A
PDF
Part B: Q&A - 11
PDF
Part B: Q&A - 12
PDF
Part B: Q&A - 13
PDF
Part B: Q&A - 14
PDF
Part B: Q&A - 15
PDF
April/May 2023
Part A
PDF
Part B: Q&A - 11
PDF
Part B: Q&A - 12
PDF
Part B: Q&A - 13
PDF
Part B: Q&A - 14
PDF
Part B: Q&A - 15
PDF
November/December 2022
Part A
PDF
Part B: Q&A - 11
PDF
Part B: Q&A - 12
PDF
Part B: Q&A - 13
PDF
Part B: Q&A - 14
PDF
Part B: Q&A - 15
PDF
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