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
19 Exercises • 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
PDF
1.1.7 Events
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1.1.8 Probability Definitions and Axioms
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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
00:02:31
1.2.2 Quiz
Exercise
1.2.3 Solved Problem 2
Video
00:02:18
1.2.3 Quiz
Exercise
1.2.4 Solved Problem 3
Video
00:02:34
1.2.4 Quiz
Exercise
1.2.5 Solved Problem 4
Video
00:02:00
1.2.5 Quiz
Exercise
1.2.6 Solved Problem 5
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1.2.7 Mathematical Tools
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1.2.8 Solved Problem 1
Video
00:04:31
1.2.8 Quiz
Exercise
1.2.9 Solved Problem 2
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1.2.10 Solved Problem 3
PDF
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
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1.3.3 Solved Problem 1
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1.4 Conditional Probability
1.4.1 Introduction of Conditional Probability
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1.4.2 Solved Problem 1
Video
00:04:09
1.4.2 Quiz
Exercise
1.4.3 Solved Problem 2
Video
00:04:34
1.4.3 Quiz
Exercise
1.4.4 Solved Problem 3
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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
00:08:10
1.5.3 Quiz
Exercise
1.5.4 Solved Problem 2
Video
00:09:48
1.5.4 Quiz
Exercise
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
00:01:31
1.6.2 Quiz
Exercise
1.6.3 Solved Problem 2
Video
00:02:01
1.6.3 Quiz
Exercise
1.6.4 Solved Problem 3
Video
00:03:30
1.6.4 Quiz
Exercise
1.6.5 Solved Problem 4
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1.6.6 Solved Problem 5
Video
00:05:00
1.6.6 Quiz
Exercise
1.6.7 Exercises
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1.7 Random Variable
1.7.1 Introduction of Random Variable
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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
00:09:52
1.7.8 Quiz
Exercise
1.7.9 Solved Problem 2
Video
00:03:55
1.7.9 Quiz
Exercise
1.7.10 Solved Problem 3
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1.7.11 Solved Problem 4
Video
00:05:32
1.7.11 Quiz
Exercise
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
00:03:17
1.8.4 Quiz
Exercise
1.8.5 Solved Problem 2
Video
00:07:59
1.8.5 Quiz
Exercise
1.8.6 Solved Problem 3
Video
00:07:07
1.8.6 Quiz
Exercise
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
00:11:05
1.9.6 Solved Problem 2
Video
00:09:24
1.9.7 Solved Problem 3
Video
00:06:27
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
00:06:28
1.10.8 Solved Problem 2
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00:07:02
1.10.9 Solved Problem 3
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00:08:28
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
00:04:39
1.11.3 Solved Problem 2
Video
00:09:06
1.11.4 Solved Problem 3
Video
00:05:15
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
00:08:23
1.12.4 Solved Problem 2
Video
00:03:35
1.12.5 Solved Problem 3
Video
00:09:26
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
00:02:58
1.13.6 Solved Problem 2
Video
00:05:09
1.13.7 Solved Problem 3
Video
00:13:30
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
00:06:55
1.14.4 Solved Problem 2
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00:04:46
1.14.5 Solved Problem 3
Video
00:05:54
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
00:10:35
2.2.3 Solved Problem 2
Video
00:10:14
2.2.4 Solved Problem 3
Video
00:10:56
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
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2.3.2 Solved Problem 1
Video
00:06:51
2.3.3 Solved Problem 2
Video
00:08:28
2.3.4 Solved Problem 3
Video
00:08:33
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
00:06:18
2.4.9 Solved Problem 2
Video
00:08:29
2.4.10 Solved Problem 3
Video
00:08:26
2.4.11 Solved problem 4
Video
00:09:09
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
00:15:07
2.5.3 Solved Problem 2
Video
00:12:46
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
00:03:42
2.6.3 Solved Problem 2
Video
00:09:06
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
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00:09:37
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
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00:09:45
2.7.5 Solved Problem 2
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00:15:28
2.7.6 Solved Problem 3
Video
00:07:03
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
00:04:12
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
00:09:38
2.8.3 Solved Problem 2
Video
00:10:07
2.8.4 Solved Problem 3
Video
00:13:50
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
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00:04:39
2.9.7 Solved Problem 2
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00:06:14
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
29 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
00:05:09
3.1.6 Quiz
Exercise
3.1.7 Solved Problem 2
Video
00:06:33
3.1.7 Quiz
Exercise
3.1.8 Solved Problem 3
Video
00:05:01
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
00:09:52
3.2.5 Quiz
Exercise
3.2.6 Solved Problem 2
Video
00:14:59
3.2.6 Quiz
Exercise
3.2.7 Solved Problem 3
Video
00:13:20
3.2.7 Quiz
Exercise
3.2.8 Solved Problem 4
Video
00:12:37
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
00:05:21
3.3.2 Quiz
Exercise
3.3.3 Solved Problem 2
Video
00:10:01
3.3.3 Quiz
Exercise
3.3.4 Solved Problem 3
Video
00:04:13
3.3.4 Quiz
Exercise
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
00:08:41
3.4.3 Quiz
Exercise
3.4.4 Solved Problem 2
Video
00:07:24
3.4.4 Quiz
Exercise
3.4.5 Solved Problem 3
Video
00:13:37
3.4.5 Quiz
Exercise
3.4.6 Solved Problem 4
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3.4.7 Solved Problem 5
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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
00:09:51
3.5.3 Quiz
Exercise
3.5.4 Solved Problem 2
Video
00:14:43
3.5.4 Quiz
Exercise
3.5.5 Solved Problem 3
Video
00:13:23
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 Solved Problem 1 (Problem based on w=c+z)
Video
00:04:45
3.6.8 Quiz
Exercise
3.6.9 Solved Problem 2
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3.6.10 Solved Problem 3 (Problem based on w=cz )
Video
00:06:02
3.6.10 Quiz
Exercise
3.6.11 Solved Problem 4
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3.6.12 Solved Problem 5 (Problem based on w=1/z)
Video
00:06:40
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 Solved Problem 8 (Problem based on w=z^2)
Video
00:04:46
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
00:07:58
3.7.6 Quiz
Exercise
3.7.7 Solved Problem 2
Video
00:06:23
3.7.7 Quiz
Exercise
3.7.8 Solved Problem 3
Video
00:05:05
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
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4.1.2 Solved Problem 1
Video
00:08:11
4.1.2 Quiz
Exercise
4.1.3 Solved Problem 2
Video
00:13:14
4.1.3 Quiz
Exercise
4.1.4 Solved Problem 3
Video
00:08:08
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
00:07:00
4.2.6 Quiz
Exercise
4.2.7 Solved Problem 2
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4.2.8 Solved Problem 3
Video
00:09:12
4.2.8 Quiz
Exercise
4.2.9 Solved Problem 4
Video
00:11:19
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
00:08:05
4.3.3 Quiz
Exercise
4.3.4 Solved Problem 2
Video
00:10:02
4.3.4 Quiz
Exercise
4.3.5 Solved Problem 3
Video
00:07:51
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
00:08:16
4.4.3 Quiz
Exercise
4.4.4 Solved Problem 2
Video
00:10:47
4.4.4 Quiz
Exercise
4.4.5 Solved Problem 3
Video
00:14:34
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
00:08:07
4.5.3 Quiz
Exercise
4.5.4 Solved Problem 2
Video
00:08:19
4.5.4 Quiz
Exercise
4.5.5 Solved Problem 3
Video
00:01:58
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
00:07:03
4.6.3 Quiz
Exercise
4.6.4 Solved Problem 2
Video
00:11:06
4.6.4 Quiz
Exercise
4.6.5 Solved Problem 3
Video
00:05:56
4.6.5 Quiz
Exercise
4.6.6 Solved Problem 4
Video
00:09:09
4.6.6 Quiz
Exercise
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 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
00:11:59
4.7.2 Quiz
Exercise
4.7.3 Solved Problem 2
Video
00:10:37
4.7.3 Quiz
Exercise
4.7.4 Solved Problem 3
Video
00:10:30
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
00:09:13
4.8.2 Quiz
Exercise
4.8.3 Solved Problem 2
Video
00:09:26
4.8.3 Quiz
Exercise
4.8.4 Solved Problem 3
Video
00:09:39
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
00:05:39
5.1.6 Quiz
Exercise
5.1.7 Solved Problem 2
Video
00:03:32
5.1.7 Quiz
Exercise
5.1.8 Solved Problem 3
Video
00:03:53
5.1.8 Quiz
Exercise
5.1.9 Solved Problem 4
PDF
5.1.10 Solved Problem 5
PDF
5.1.11 Solved Problem 6
PDF
5.1.12 Solved Problem 7
PDF
5.1.13 Solved Problem 8
PDF
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
PDF
5.1.18 Exercises
PDF
5.2 General Solution of f(D)y = e^ax
5.2.1 Particular Integral of f(D)y = e^ax
PDF
5.2.2 Solved Problem 1
Video
00:04:56
5.2.2 Quiz
Exercise
5.2.3 Solved Problem 2
Video
00:03:34
5.2.3 Quiz
Exercise
5.2.4 Solved Problem 3
Video
00:04:47
5.2.4 Quiz
Exercise
5.2.5 Solved Problem 4
Video
00:06:17
5.2.5 Quiz
Exercise
5.2.6 Solved Problem 5
Video
00:06:33
5.2.6 Quiz
Exercise
5.2.7 Solved problem 6
PDF
5.2.8 Solved problem 7
PDF
5.2.9 Solved problem 8
PDF
5.2.10 Solved problem 9
PDF
5.2.11 Solved problem 10
PDF
5.2.12 Exercises
PDF
5.3 General Solution of f(D)y = cos ax or sin ax
5.3.1 Particular Integral of f(D) = cosax or sinax
PDF
5.3.2 Working rule
PDF
5.3.3 Solved Problem 1
Video
00:06:26
5.3.3 Quiz
Exercise
5.3.4 Solved Problem 2
Video
00:05:22
5.3.4 Quiz
Exercise
5.3.5 Solved Problem 3
Video
00:06:24
5.3.5 Quiz
Exercise
5.3.6 Solved Problem 4
Video
00:06:47
5.3.6 Quiz
Exercise
5.3.7 Solved Problem 5
Video
00:05:06
5.3.7 Quiz
Exercise
5.3.8 Solved Problem 6
PDF
5.3.9 Solved Problem 7
PDF
5.3.10 Solved Problem 8
PDF
5.3.11 Exercises
PDF
5.4 General Solution of f(D)y = x^m
5.4.1 Particular Integral of f(D)y = xm
PDF
5.4.2 Solved Problem 1
Video
00:05:42
5.4.2 Quiz
Exercise
5.4.3 Solved Problem 2
Video
00:06:07
5.4.3 Quiz
Exercise
5.4.4 Solved Problem 3
Video
00:08:25
5.4.4 Quiz
Exercise
5.4.5 Solved problem 4
PDF
5.4.6 Solved problem 5
PDF
5.4.7 Solved problem 6
PDF
5.4.8 Solved problem 7
PDF
5.4.9 Solved Problem 8
PDF
5.4.10 Exercises
PDF
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)
PDF
5.5.2 Solved Problem 1
Video
00:07:16
5.5.2 Quiz
Exercise
5.5.3 Solved Problem 2
Video
00:09:52
5.5.3 Quiz
Exercise
5.5.4 Solved Problem 3
Video
00:10:19
5.5.4 Quiz
Exercise
5.5.5 Solved Problem 4
PDF
5.5.6 Solved Problem 5
PDF
5.5.7 Exercises
PDF
5.6 General Solution of f(D)y = x^m . f(x)
5.6.1 Particular integral = xm sinax or xm cosax
PDF
5.6.2 Solved Problem 1
Video
00:08:20
5.6.2 Quiz
Exercise
5.6.3 Solved Problem 2
Video
00:08:00
5.6.3 Quiz
Exercise
5.6.4 Solved Problem 3
Video
00:07:56
5.6.4 Quiz
Exercise
5.6.5 Solved Problem 4
PDF
5.6.6 Solved Problem 5
PDF
5.6.7 Solved Problem 6
PDF
5.6.8 Solved Problem 7
PDF
5.6.9 Exercises
PDF
5.7 Method of Variation of Parameters
5.7.1 Introduction
PDF
5.7.2 Method of Variation of Parameters
PDF
5.7.3 Solved Problem 1
Video
00:06:48
5.7.3 Quiz
Exercise
5.7.4 Solved Problem 2
Video
00:07:42
5.7.4 Quiz
Exercise
5.7.5 Solved Problem 3
Video
00:10:13
5.7.5 Quiz
Exercise
5.7.6 Solved Problem 4
PDF
5.7.7 Solved Problem 5
PDF
5.7.8 Solved Problem 6
PDF
5.7.9 Solved Problem 7
PDF
5.7.10 Solved Problem 8
PDF
5.7.11 Exercises
PDF
5.8 Cauchy's Differential Equations
5.8.1 Cauchy Euler homogeneous linear equation
PDF
5.8.2 Solved Problem 1
Video
00:07:40
5.8.2 Quiz
Exercise
5.8.3 Solved Problem 2
Video
00:08:11
5.8.3 Quiz
Exercise
5.8.4 Solved Problem 3
Video
00:08:22
5.8.4 Quiz
Exercise
5.8.5 Solved Problem 4
PDF
5.8.6 Solved Problem 5
PDF
5.8.7 Solved Problem 6
PDF
5.8.8 Solved Problem 7
PDF
5.8.9 Solved Problem 8
PDF
5.8.10 Solved Problem 9
PDF
5.8.11 Solved problem 10
PDF
5.8.12 Exercises
PDF
5.9 Legendre Differential Equations
5.9.1 Legendre Linear equations
PDF
5.9.2 Solved Problem 1
Video
00:07:07
5.9.2 Quiz
Exercise
5.9.3 Solved Problem 2
Video
00:06:02
5.9.3 Quiz
Exercise
5.9.4 Solved Problem 3
Video
00:07:21
6.9.4 Quiz
Exercise
5.9.5 Solved Problem 4
PDF
5.9.6 Solved Problem 5
PDF
5.9.7 Solved Problem 6
PDF
5.9.8 Solved Problem 7
PDF
5.9.9 Solved Problem 8
PDF
5.9.10 Exercises
PDF
5.10 Simultaneous First Order Linear Equations with Constant Coefficients
5.10.1 Introduction
PDF
5.10.2 Solved Problem 1
Video
00:09:03
5.10.2 Quiz
Exercise
5.10.3 Solved Problem 2
Video
00:07:06
5.10.3 Quiz
Exercise
5.10.4 Solved Problem 3
Video
00:05:25
5.10.4 Quiz
Exercise
5.10.5 Solved Problem 4
PDF
5.10.6 Solved Problem 5
PDF
5.10.7 Solved Problem 6
PDF
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
PDF
1.4 Part B: Q&A - 3
PDF
1.5 Part B: Q&A - 4
PDF
1.6 Part B: Q&A - 5
PDF
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
PDF
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
PDF
3.11 Part B: Q&A - 10
PDF
3.12 Part B: Q&A - 11
PDF
3.13 Part B: Q&A - 12
PDF
3.14 Part B: Q&A - 13
PDF
3.15 Part B: Q&A - 14
PDF
3.16 Part B: Q&A - 15
PDF
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
PDF
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
PDF
5.4 Part B: Q&A - 3
PDF
5.5 Part B: Q&A - 4
PDF
5.6 Part B: Q&A - 5
PDF
5.7 Part B: Q&A - 6
PDF
5.8 Part B: Q&A - 7
PDF
5.9 Part B: Q&A - 8
PDF
5.10 Part B: Q&A - 9
PDF
5.11 Part B: Q&A - 10
PDF
5.12 Part B: Q&A - 11
PDF
5.13 Part B: Q&A - 12
PDF
5.14 Part B: Q&A - 13
PDF
5.15 Part B: Q&A - 14
PDF
5.16 Part B: Q&A - 15
PDF
5.17 Part B: Q&A - 16
PDF
5.18 Part B: Q&A - 17
PDF
5.19 Part B: Q&A - 18
PDF
5.20 Part B: Q&A - 19
PDF
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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