Matrices and Calculus (MA3151) - Anna University
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Course Overview
Schedule of Classes
Course Curriculum
7 Subjects
Unit 1: Matrices
33 Exercises • 82 Learning Materials
Maths.Engineering Platform Walkthrough
Maths Engineering Platform Walkthrough
Video
1:11
1.1 Matrix Introduction
1.1.1 Introduction
PDF
1.1.2 Key Concepts
PDF
1.1.3 Types of Matrices
PDF
1.1.4 Types of Matrices
PDF
1.1.5 Application of Matrices
PDF
1.1.6 Matrix Introduction
Video
8:3
1.1.6 Quiz
Exercise
1.1.7 Matrix Addition
Video
2:10
1.1.7 Quiz
Exercise
1.1.8 Matrix Multiplication
Video
4:38
1.1.8 Quiz
Exercise
1.1.9 Determinant of Matrix
Video
3:8
1.1.9 Quiz
Exercise
1.1.10 Inverse of a Matrix
Video
5:13
1.1.10 Quiz
Exercise
1.1.11 Application of Matrices
Video
5:50
1.2 Characteristic equation
1.2.1 Introduction
Video
5:41
1.2.2 Eigen values and Eigen vectors
PDF
1.2.3 Applications Eigenvalues and Eigenvectors in Engineering
PDF
1.2.4 Characteristic equation
PDF
1.2.5 Solved problem 1
Video
2:15
1.2.5 Quiz
Exercise
1.2.6 Solved problem 2
Video
4:9
1.2.6 Quiz
Exercise
1.2.7 Solved problem 3
PDF
1.2.8 Solved problem 4
PDF
1.2.9 Exercises
Exercise
1.3 Eigen values and Eigen vectors of a matrix
1.3.1 Introduction
PDF
1.3.2 Eigen vectors
PDF
1.3.3 Solved problem 1
Video
12:41
1.3.3 Quiz
Exercise
1.3.4 Solved problem 2
PDF
1.3.5 Solved problem 3
Video
11:48
1.3.5 Quiz
Exercise
1.3.6 Solved problem 4
PDF
1.3.7 Solved problem 5
PDF
1.3.8 Solved problem 6
Video
12:35
1.3.8 Quiz
Exercise
1.3.9 Solved problem 7
PDF
1.3.10 Solved problem 8
PDF
1.3.11 Solved problem 9
PDF
1.3.12 Solved problem 10
PDF
1.3.13 Solved problem 11
Video
11:57
1.3.13 Quiz
Exercise
1.3.14 Exercises
Exercise
1.4 Properties of Eigen values and Eigen vectors
1.4.1 Introduction
PDF
1.4.2 Properties of Eigen values
PDF
1.4.3 Solved Problem 1
Video
1:53
1.4.3 Quiz
Exercise
1.4.4 Solved problem 2
PDF
1.4.5 Solved problem 3
Video
1:58
1.4.5 Quiz
Exercise
1.4.6 Solved problem 4
PDF
1.4.7 Solved problem 5
PDF
1.4.8 Solved problem 6
Video
1:45
1.4.8 Quiz
Exercise
1.4.9 Solved problem 7
PDF
1.4.10 Solved problem 8
Video
2:45
1.4.10 Quiz
Exercise
1.4.11 Solved problem 9
PDF
1.4.12 Solved problem 10
PDF
1.4.13 Solved problem 11
Video
2:34
1.4.13 Quiz
Exercise
1.4.14 Solved problem 12
PDF
1.4.15 Solved problem 13
PDF
1.4.16 Solved problem 14
PDF
1.4.17 Properties of Eigen vectors
PDF
1.4.18 Exercises
Exercise
1.5 Cayley - Hamilton Theorem
1.5.1 Introduction
PDF
1.5.2 Solved problem 1
Video
10:15
1.5.2 Quiz
Exercise
1.5.3 Solved problem 2
Video
8:7
1.5.3 Quiz
Exercise
1.5.4 Solved problem 3
Video
7:26
1.5.4 Quiz
Exercise
1.5.5 Solved problem 4
PDF
1.5.6 Solved problem 5
PDF
1.5.7 Solved problem 6
PDF
1.5.8 Solved problem 7
PDF
1.5.9 Solved problem 8
PDF
1.5.10 Solved problem 9
PDF
1.5.11 Solved problem 10
PDF
1.5.12 Exercises
Exercise
1.6 Diagonalisation of matrix (Orthogonal Transformation)
1.6.1 Introduction
PDF
1.6.2 Solved problem 1
Video
16:34
1.6.2 Quiz
Exercise
1.6.3 Solved problem 2
Video
17:48
1.6.3 Quiz
Exercise
1.6.4 Solved problem 3
Video
21:48
1.6.4 Quiz
Exercise
1.6.5 Solved problem 4
PDF
1.6.6 Solved problem 5
PDF
1.6.7 Exercises
Exercise
1.7 Reduction of Quadratic form to Canonical form
1.7.1 Introduction
PDF
1.7.2 Nature of a Quadratic form
PDF
1.7.3 Canonical Form
PDF
1.7.4 Applications in Engineering
PDF
1.7.5 Solved problem 1
Video
20:41
1.7.5 Quiz
Exercise
1.7.6 Solved problem 2
Video
19:58
1.7.6 Quiz
Exercise
1.7.7 Solved problem 3
PDF
1.7.8 Solved problem 4
PDF
1.7.9 Solved problem 5
PDF
1.7.10 Solved problem 6
PDF
1.7.11 Exercises
Exercise
1.8 Stretching of an Elastic Membrane
1.8.1 Introduction
PDF
1.8.2 Solved problem 1
Video
8:59
1.8.2 Quiz
Exercise
1.8.3 Solved problem 2
Video
8:39
1.8.3 Quiz
Exercise
1.8.4 Solved problem 3
PDF
1.8.5 Solved problem 4
PDF
1.8.6 Exercises
Exercise
Unit 2: Differential Calculus
128 Learning Materials
2.1 Representation of Functions
2.1.1 Introduction
PDF
2.1.2 Representation of Functions
PDF
2.1.3 Piecewise defined Functions
PDF
2.1.4 Solved Problem 1
Video
6:49
2.1.5 Solved Problem 2
Video
5:7
2.1.6 Solved Problem 3
PDF
2.1.7 Solved Problem 4
PDF
2.1.8 Solved Problem 5
PDF
2.1.9 Solved Problem 6
Video
3:41
2.1.10 Solved Problem 7
Video
3:12
2.1.11 Solved Problem 8
PDF
2.1.12 Solved Problem 9
PDF
2.1.13 Exercises
PDF
2.2 Limit of a function
2.2.1 Introduction
PDF
2.2.2 Solved Problem 1
Video
2:10
2.2.3 Solved Problem 2
Video
1:53
2.2.4 Solved Problem 3
PDF
2.2.5 Solved Problem 4
PDF
2.2.6 Solved Problem 5
PDF
2.2.7 Solved Problem 6
PDF
2.2.8 Limit laws
PDF
2.2.9 Standard Limits
PDF
2.2.10 Direct Substitution property
PDF
2.2.11 Solved Problem 7
Video
2:38
2.2.12 Solved Problem 8
Video
2:22
2.2.13 Solved Problem 9
Video
1:49
2.2.14 Solved Problem 10
Video
2:3
2.2.15 Solved Problem 11
Video
1:59
2.2.16 Solved Problem 12
PDF
2.2.17 Solved Problem 13
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2.2.18 Solved Problem 14
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2.2.19 Solved Problem 15
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2.2.20 Solved Problem 16
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2.2.21 Solved Problem 17
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2.2.22 Solved Problem 18
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2.2.23 Solved Problem 19
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2.2.24 Solved Problem 20
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2.2.25 Solved Problem 21
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2.2.26 Solved Problem 22
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2.2.27 Solved Problem 23
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2.2.28 Exercises
PDF
2.3 Continuity
2.3.1 Continuity
PDF
2.3.2 Theorem
PDF
2.3.3 Application
PDF
2.3.4 Solved Problem 1
Video
4:40
2.3.5 Solved Problem 2
PDF
2.3.6 Solved Problem 3
PDF
2.3.7 Solved Problem 4
PDF
2.3.8 Solved Problem 5
PDF
2.3.9 Solved Problem 6
PDF
2.3.10 Solved Problem 7
Video
7:4
2.3.11 Solved Problem 8
Video
3:36
2.3.12 Solved Problem 9
PDF
2.3.13 Solved Problem 10
PDF
2.3.14 Exercises
PDF
2.4 Derivatives
2.4.1 Introduction
PDF
2.4.2 Solved Problem 1
Video
4:29
2.4.3 Solved Problem 2
Video
2:37
2.4.4 Solved Problem 3
PDF
2.4.5 Solved Problem 4
PDF
2.4.6 Solved Problem 5
PDF
2.4.7 Exercises
PDF
2.5 Differentiation Rules
2.5.1 Introduction
PDF
2.5.2 Differentiation Rules
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2.5.3 Important Differentiation Rules
PDF
2.5.4 Sum rule
PDF
2.5.5 Solved Problem 1
Video
2:38
2.5.6 Solved Problem 2
Video
5:4
2.5.7 Solved Problem 3
PDF
2.5.8 Solved Problem 4
PDF
2.5.9 Solved Problem 5
PDF
2.5.10 Product rule
PDF
2.5.11 Solved Problem 6
Video
3:18
2.5.12 Solved Problem 7
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2.5.13 Solved Problem 8
PDF
2.5.14 Solved Problem 9
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2.5.15 Quotient rule
PDF
2.5.16 Solved Problem 10
Video
3:59
2.5.17 Solved Problem 11
PDF
2.5.18 Solved Problem 12
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2.5.19 Chain rule
PDF
2.5.20 Solved Problem 13
Video
2:27
2.5.21 Solved Problem 14
Video
3:10
2.5.22 Solved Problem 15
PDF
2.5.23 Solved Problem 16
PDF
2.5.24 Solved Problem 17
PDF
2.5.25 Solved Problem 18
PDF
2.5.26 Exercises
PDF
2.6 Implicit Differentiation
2.6.1 Introduction
PDF
2.6.2 Implicit Differentiation
PDF
2.6.3 General Differentiation formulae
PDF
2.6.4 Solved Problem 1
Video
4:9
2.6.5 Solved Problem 2
Video
4:5
2.6.6 Solved Problem 3
Video
4:46
2.6.7 Solved Problem 4
Video
5:34
2.6.8 Solved Problem 5
Video
7:20
2.6.9 Solved problem 6
PDF
2.6.10 Solved problem 7
PDF
2.6.11 Solved problem 8
PDF
2.6.12 Solved problem 9
PDF
2.6.13 Solved problem 10
PDF
2.6.14 Exercises
PDF
2.7 Logarithmic Differentiation
2.7.1 Logarithmic Differentiation
PDF
2.7.2 Logarithmic Differentiation Formula
PDF
2.7.3 Solved Problem 1
Video
3:35
2.7.4 Solved Problem 2
Video
3:30
2.7.5 Solved Problem 3
Video
4:5
2.7.6 Solved Problem 4
PDF
2.7.7 Solved Problem 5
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2.7.8 Solved problem 6
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2.7.9 Solved problem 7
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2.7.10 Solved problem 8
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2.7.11 Exercises
PDF
2.8 Maxima and Minima of functions of one variable
2.8.1 Maxima and minima
PDF
2.8.2 Extreme value Theorem
PDF
2.8.3 Increasing-Decreasing Test
PDF
2.8.4 Solved Problem 1
Video
4:00
2.8.5 Solved Problem 2
Video
4:28
2.8.6 Solved Problem 3
Video
14:57
2.8.7 Solved Problem 4
Video
12:32
2.8.8 Solved Problem 5
Video
10:13
2.8.9 Solved problem 6
PDF
2.8.10 Solved problem 7
PDF
2.8.11 Solved problem 8
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2.8.12 Solved problem 9
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2.8.13 Solved problem 10
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2.8.14 Solved problem 11
PDF
2.8.15 Exercises
PDF
Unit 3: Functions of Several Variables
25 Exercises • 106 Learning Materials
3.1 Partial Differentiation
3.1.1 Introduction
PDF
3.1.2 Solved Problem 1
Video
000
3.1.2 Quiz
Exercise
3.1.3 Solved Problem 2
Video
000
3.1.3 Quiz
Exercise
3.1.4 Solved Problem 3
Video
000
3.1.4 Quiz
Exercise
3.1.5 Solved Problem 4
PDF
3.1.6 Solved Problem 5
PDF
3.1.7 Solved Problem 6
PDF
3.1.8 Solved Problem 7
PDF
3.1.9 Solved Problem 8
PDF
3.1.10 Solved Problem 9
PDF
3.1.11 Exercises
PDF
3.2 Homogeneous Function and Euler's Theorem
3.2.1 Introduction
PDF
3.2.2 Euler's Theorem
PDF
3.2.3 Solved Problem 1
Video
000
3.2.3 Quiz
Exercise
3.2.4 Solved Problem 2
Video
000
3.2.4 Quiz
Exercise
3.2.5 Solved Problem 3
Video
000
3.2.5 Quiz
Exercise
3.2.6 Solved Problem 4
PDF
3.2.7 Solved Problem 5
PDF
3.2.8 Solved Problem 6
PDF
3.2.9 Solved Problem 7
PDF
3.2.10 Solved Problem 8
PDF
3.2.11 Solved Problem 9
PDF
3.2.12 Exercises
PDF
3.3 Total Derivative
3.3.1 Introduction
PDF
3.3.2 Solved Problem 1
Video
000
3.3.2 Quiz
Exercise
3.3.3 Solved Problem 2
Video
000
3.3.3 Quiz
Exercise
3.3.4 Solved Problem 3
PDF
3.3.5 Solved Problem 4
PDF
3.3.6 Solved Problem 5
PDF
3.3.7 Solved Problem 6
PDF
3.3.8 Solved Problem 7
PDF
3.3.9 Solved Problem 8
PDF
3.3.10 Exercises
PDF
3.4 Partial Differentiation of Implicit Functions
3.4.1 Introduction
PDF
3.4.2 Implicit function of three variables
PDF
3.4.3 Solved Problem 1
Video
000
3.4.3 Quiz
Exercise
3.4.4 Solved Problem 2
PDF
3.4.5 Solved Problem 3
PDF
3.4.6 Solved Problem 4
PDF
3.4.7 Solved Problem 5
PDF
3.4.8 Solved Problem 6
PDF
3.4.9 Solved Problem 7
PDF
3.4.10 Exercises
PDF
3.5 Change of Variables
3.5.1 Introduction
PDF
3.5.2 Solved Problem 1
Video
000
3.5.2 Quiz
Exercise
3.5.3 Solved Problem 2
Video
000
3.5.3 Quiz
Exercise
3.5.4 Solved Problem 3
Video
000
3.5.4 Quiz
Exercise
3.5.5 Solved Problem 4
Video
000
3.5.5 Quiz
Exercise
3.5.6 Solved Problem 5
Video
000
3.5.6 Quiz
Exercise
3.5.7 Solved Problem 6
PDF
3.5.8 Solved Problem 7
PDF
3.5.9 Solved Problem 8
PDF
3.5.10 Solved Problem 9
PDF
3.5.11 Solved Problem 10
PDF
3.5.12 Solved Problem 11
PDF
3.5.13 Exercises
PDF
3.6 Jacobians
3.61 Introduction
PDF
3.6.2 Properties of Jacobian
PDF
3.6.3 Jacobian of implicit functions
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3.6.4 Partial derivatives using Jacobian
PDF
3.6.5 Solved Problem 1
Video
000
3.6.5 Quiz
Exercise
3.6.6 Solved Problem 2
Video
000
3.6.6 Quiz
Exercise
3.6.7 Solved Problem 3
PDF
3.6.8 Solved Problem 4
PDF
3.6.9 Solved Problem 5
PDF
3.6.10 Solved Problem 6
PDF
3.6.11 Solved Problem 7
PDF
3.6.12 Solved Problem 8
PDF
3.6.13 Solved Problem 9
PDF
3.6.14 Exercises
PDF
3.7 Taylor's series for functions of two variables
3.7.1 Introduction
PDF
3.7.2 Solved Problem 1
Video
7:45
3.7.2 Quiz
Exercise
3.7.3 Solved Problem 2
Video
9:50
3.7.3 Quiz
Exercise
3.7.4 Solved Problem 3
Video
9:40
3.7.4 Quiz
Exercise
3.7.5 Solved Problem 4
PDF
3.7.6 Solved Problem 5
PDF
3.7.7 Solved Problem 6
PDF
3.7.8 Solved Problem 7
PDF
3.7.9 Solved Problem 8
PDF
3.7.10 Solved Problem 9
PDF
3.7.11 Solved Problem 10
PDF
3.7.12 Solved Problem 11
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3.7.13 Solved Problem 12
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3.7.14 Solved Problem 13
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3.7.15 Solved Problem 14
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3.7.16 Exercises
PDF
3.8 Maxima and minima of functions of two variables
3.8.1 Introduction
PDF
3.8.2 Solved Problem 1
Video
9:7
3.8.2 Quiz
Exercise
3.8.3 Solved Problem 2
Video
17:17
3.8.3 Quiz
Exercise
3.8.4 Solved Problem 3
Video
12:24
3.8.4 Quiz
Exercise
3.8.5 Solved Problem 4
PDF
3.8.6 Solved Problem 5
PDF
3.8.7 Solved Problem 6
PDF
3.8.8 Solved Problem 7
PDF
3.8.9 Solved Problem 8
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3.8.10 Solved Problem 9
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3.8.11 Solved Problem 10
PDF
3.8.12 Solved Problem 11
PDF
3.8.13 Exercises
PDF
3.9 Lagrange's method of undetermined multipliers
3.9.1 Introduction
PDF
3.9.2 Solved Problem 1
Video
9:50
3.9.2 Quiz
Exercise
3.9.3 Solved Problem 2
Video
10:25
3.9.3 Quiz
Exercise
3.9.4 Solved Problem 3
Video
7:55
3.9.4 Quiz
Exercise
3.9.5 Solved Problem 4
PDF
3.9.6 Solved Problem 5
PDF
3.9.7 Exercises
PDF
Unit 4: Integral Calculus
23 Exercises • 181 Learning Materials
4.1 Definite Integral
4.1.1 Introduction
Video
6:11
4.1.2 Introduction to Integral calculus
PDF
4.1.3 The Definite Integral
PDF
4.1.4 Standard formulae
PDF
4.1.5 Applications
PDF
4.1.6 Solved Problem 1
Video
2:43
4.1.6 Quiz
Exercise
4.1.7 Solved Problem 2
Video
2:47
4.1.7 Quiz
Exercise
4.1.8 Solved Problem 3
Video
3:20
4.1.8 Quiz
Exercise
4.1.9 Solved problem 4
PDF
4.1.10 Solved problem 5
PDF
4.1.11 Solved problem 6
PDF
4.1.12 Solved problem 7
PDF
4.1.13 Solved problem 8
PDF
4.1.14 Solved problem 9
PDF
4.1.15 Exercises
Exercise
4.2 Definite Integral - Reimann Sum
4.2.1 The Definite Integral
PDF
4.2.2 Applications
PDF
4.2.3 Solved Problem 1
Video
6:57
4.2.4 Solved Problem 2
Video
6:12
4.2.5 Solved problem 3
PDF
4.2.6 Solved problem 4
PDF
4.2.7 Solved problem 5
PDF
4.2.8 Solved problem 6
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4.2.9 Solved problem 7
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4.2.10 Solved problem 8
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4.2.11 Solved problem 9
PDF
4.2.12 Exercises
PDF
4.3 Indefinite Integral
4.3.1 Indefinite Integral
PDF
4.3.2 Formulae
PDF
4.3.3 Applications
PDF
4.3.4 Solved Problem 1
Video
2:44
4.3.5 Solved Problem 2
Video
1:54
4.3.6 Solved Problem 3
Video
3:24
4.3.7 Solved problem 4
PDF
4.3.8 Solved problem 5
PDF
4.3.9 Solved problem 6
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4.3.10 Solved problem 7
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4.3.11 Solved problem 8
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4.3.12 Solved problem 9
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4.3.13 Exercises
PDF
4.4 Properties of Definite Integral
4.4.1 Properties of Definite Integral
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4.4.2 Applications
PDF
4.4.3 Solved Problem 1
Video
4:10
4.4.3 Quiz
Exercise
4.4.4 Solved Problem 2
Video
4:12
4.4.4 Quiz
Exercise
4.4.5 Solved Problem 3
Video
3:49
4.4.5 Quiz
Exercise
4.4.6 Solved Problem 4
Video
3:22
4.4.6 Quiz
Exercise
4.4.7 Solved problem 5
PDF
4.4.8 Solved problem 6
PDF
4.4.9 Solved problem 7
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4.4.10 Solved problem 8
PDF
4.4.11 Solved problem 9
PDF
4.4.12 Solved problem 10
PDF
4.4.13 Exercises
Exercise
4.5 Substitution Rule
4.5.1 Introduction
Video
5:55
4.5.2 Substitution Rule
PDF
4.5.3 Why we need substitution rule in integration
PDF
4.5.4 Applications
PDF
4.5.5 Type I - Algebraic functions - Solved problem 1
Video
2:30
4.5.5 Quiz
Exercise
4.5.6 Solved problem 2
Video
2:43
4.5.6 Quiz
Exercise
4.5.7 Solved problem 3
PDF
4.5.8 Solved problem 4
PDF
4.5.9 Type II - Logarithmic functions - Solved problem 5
Video
1:59
4.5.9 Quiz
Exercise
4.5.10 Solved problem 6
Video
2:30
4.5.10 Quiz
Exercise
4.5.11 Solved problem 7
PDF
4.5.12 Solved problem 8
PDF
4.5.13 Type III - Exponential functions - Solved problem 9
Video
3:17
4.5.13 Quiz
Exercise
4.5.14 Solved problem 10
Video
2:26
4.5.14 Quiz
Exercise
4.5.15 Solved problem 11
PDF
4.5.16 Solved problem 12
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4.5.17 Solved problem 13
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4.5.18 Type IV - Trigonometric functions - Solved problem 14
Video
2:30
4.5.18 Quiz
Exercise
4.5.19 Solved problem 15
Video
3:25
4.5.19 Quiz
Exercise
4.5.20 Solved problem 16
PDF
4.5.21 Solved problem 17
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4.5.22 Solved problem 18
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4.5.23 Solved problem 19
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4.5.24 Exercises
Exercise
4.6 Integration by Parts
4.6.1 Integration by parts
Video
5:27
4.6.2 Bernoullis formula for Integration by parts
Video
6:40
4.6.3 Why we need Integration by Parts
PDF
4.6.4 Applications
PDF
4.6.5 Solved Problem 1
Video
3:33
4.6.5 Quiz
Exercise
4.6.6 Solved Problem 2
Video
3:33
4.6.6 Quiz
Exercise
4.6.7 Solved Problem 3
Video
5:45
4.6.7 Quiz
Exercise
4.6.8 Solved Problem 4
Video
6:45
4.6.8 Quiz
Exercise
4.6.9 Type I - Problems on Integration by Parts - Solved Problem 1
PDF
4.6.10 Solved Problem 2
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4.6.11 Solved Problem 3
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4.6.12 Solved Problem 4
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4.6.13 Solved Problem 5
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4.6.14 Solved Problem 6
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4.6.15 Solved Problem 7
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4.6.16 Solved Problem 8
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4.6.17 Type II - Problems on Bernoulli's Formula - Solved Problem 9
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4.6.18 Solved Problem 10
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4.6.19 Reduction Formula
PDF
4.6.20 Type III - Problems on Reduction Formula - Solved Problem 11
PDF
4.6.21 Solved Problem 12
PDF
4.6.22 Exercises
Exercise
4.7 Trigonometric Integrals
4.7.1 Type I
PDF
4.7.2 Type II
PDF
4.7.3 Type III
PDF
4.7.4 Solved Problem 1
Video
4:48
4.7.5 Solved Problem 2
Video
5:37
4.7.6 Solved Problem 3
Video
4:25
4.7.7 Solved Problem 4
Video
2:20
4.7.8 Type I - Solved Problem 5
PDF
4.7.9 Solved Problem 6
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4.7.10 Solved Problem 7
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4.7.11 Solved Problem 8
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4.7.12 Solved Problem 9
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4.7.13 Type II - Solved Problem 10
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4.7.14 Solved Problem 11
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4.7.15 Solved Problem 12
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4.7.16 Type III -Solved Problem 13
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4.7.17 Solved Problem 14
PDF
4.7.18 Exercises
PDF
4.8 Trigonometric Substitutions
4.8.1 Trigonometric Substitution
PDF
4.8.2 Solved Problem 1
Video
2:50
4.8.3 Solved Problem 2
Video
7:14
4.8.4 Solved Problem 3
Video
5:00
4.8.5 Solved Problem 4
Video
3:50
4.8.6 Type I - Solved problem 5
PDF
4.8.7 Solved problem 6
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4.8.8 Type II - Solved problem 7
PDF
4.8.9 Solved problem 8
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4.8.10 Type III - Solved problem 9
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4.8.11 Solved problem 10
PDF
4.8.12 Exercises
PDF
4.9 Integration of rational functions by partial fraction
4.9.1 Integration of Rational functions by partial fraction
PDF
4.9.2 Applications
PDF
4.9.3 Solved Problem 1
Video
5:27
4.9.4 Solved Problem 2
Video
3:52
4.9.5 Solved Problem 3
Video
5:15
4.9.6 Solved Problem 4
Video
9:5
4.9.7 Solved Problem 5
Video
4:34
4.9.8 Type 1 Solved problem 6
PDF
4.9.9 Solved problem 7
PDF
4.9.10 Type 2 Solved problem 8
PDF
4.9.11 Solved problem 9
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4.9.12 Type 3 Solved problem 10
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4.9.13 Solved problem 11
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4.9.14 Type 4 Solved problem 12
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4.9.15 Solved problem 13
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4.9.16 Solved problem 14
PDF
4.9.17 Solved problem 15
PDF
4.9.18 Solved problem 16
PDF
4.9.19 Exercises
PDF
4.10 Improper Integrals
4.10.1 Improper Integrals
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4.10.2 I. Definition of an Improper Integral of Type I
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4.10.3 II. Definition of an Improper Integral of Type II
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4.10.4 Examples of Infinite limits of Integration
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4.10.5 Solved Problem 1
Video
2:00
4.10.6 Solved Problem 2
Video
3:7
4.10.7 Solved Problem 3
Video
3:18
4.10.8 Solved Problem 4
Video
3:4
4.10.9 Solved Problem 5
Video
3:19
4.10.10 Solved problem 6
PDF
4.10.11 Solved problem 7
PDF
4.10.12 Solved problem 8
PDF
4.10.13 Solved problem 9
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4.10.14 Solved problem 10
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4.10.15 Solved problem 11
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4.10.16 Solved problem 12
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4.10.17 III. A comparison test for improper integrals
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4.10.18 Solved problem 13
PDF
4.10.19 Solved problem 14
PDF
4.10.20 Exercises
PDF
4.11 Applications - Hydrostatic force and Pressure
4.11.1 Hydrostatic Force and Pressure
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4.11.2 Hydrostatic Force of a submerged plate
PDF
4.11.3 Strategy for finding Hydrostatic Force
PDF
4.11.4 Solved Problem 1
Video
9:41
4.11.5 Solved Problem 2
Video
6:57
4.11.6 Solved Problem 3
PDF
4.11.7 Solved Problem 4
PDF
4.11.8 Solved Problem 5
PDF
4.11.9 Exercises
PDF
4.12 Applications - Moments and center of mass
4.12.1 Moments and center of mass
PDF
4.12.2 Solved Problem 1
Video
5:5
4.12.3 Solved Problem 2
Video
7:50
4.12.4 Solved Problem 3
Video
7:41
4.12.5 Solved Problem 4
PDF
4.12.6 Solved Problem 5
PDF
4.12.7 Solved Problem 6
PDF
4.12.8 Exercises
PDF
Unit 5: Multiple Integrals
33 Exercises • 74 Learning Materials
5.1 Double Integrals
5.1.1 Introduction
PDF
5.1.2 Applications of Multiple Integral in Engineering
PDF
5.1.3 Evaluation of Double Integration in Cartesian Coordinates
PDF
5.1.4 Evaluation of Double Integration in Polar Coordinates
PDF
5.1.5 Properties of Double integrals
PDF
5.1.6 Problem based on Cartesian Form
Video
2:46
5.1.6 Quiz
Exercise
5.1.7 Solved problem 2
Video
5:13
5.1.7 Quiz
Exercise
5.1.8 Solved problem 3
Video
2:30
5.1.8 Quiz
Exercise
5.1.9 Solved problem 4
PDF
5.1.10 Solved problem 5
PDF
5.1.11 Problem based on Region Given
Video
5:36
5.1.11 Quiz
Exercise
5.1.12 Solved problem 7
PDF
5.1.13 Solved problem 8
PDF
5.1.14 Solved problem 9
PDF
5.1.15 Problem based on Polar Form
Video
2:49
5.1.15 Quiz
Exercise
5.1.16 Solved problem 11
Video
3:49
5.1.16 Quiz
Exercise
5.1.17 Solved problem 12
PDF
5.1.18 Exercises
Exercise
5.2 Triple Integrals
5.2.1 Triple integrals
PDF
5.2.2 Problem based on Cartesian Form
Video
4:41
5.2.2 Quiz
Exercise
5.2.3 Solved problem 2
Video
3:40
5.2.3 Quiz
Exercise
5.2.4 Solved problem 3
PDF
5.2.5 Solved problem 4
PDF
5.2.6 Solved problem 5
PDF
5.2.7 Problem based on Region Given
Video
4:40
5.2.7 Quiz
Exercise
5.2.8 Solved problem 7
PDF
5.2.9 Solved Problem 8
Video
4:19
5.2.9 Quiz
Exercise
5.2.10 Exercises
Exercise
5.3 Change of Order of Integration
5.3.1 Change of order of integration
PDF
5.3.2 Solved problem 1
Video
4:57
5.3.2 Quiz
Exercise
5.3.3 Solved problem 2
Video
9:15
5.3.3 Quiz
Exercise
5.3.4 Solved problem 3
Video
6:34
5.3.4 Quiz
Exercise
5.3.5 Solved problem 4
Video
11:58
5.3.6 Solved problem 5
PDF
5.3.7 Solved problem 6
PDF
5.3.8 Exercise
Exercise
5.4 Change of Variables (Double Integral)
5.4.1 Change of Variables (Double Integral)
PDF
5.4.2 Changing cartesian to polar coordinates
PDF
5.4.3 Solved problem 1
Video
5:39
5.4.3 Quiz
Exercise
5.4.4 Solved problem 2
Video
5:21
5.4.4 Quiz
Exercise
5.4.5 Solved problem 3
Video
5:20
5.4.5 Quiz
Exercise
5.4.6 Solved problem 4
PDF
5.4.7 Solved problem 5
PDF
5.4.8 Exercise
Exercise
5.5 Change of Variables (Triple Integral)
5.5.1 Change of Variables (Triple Integral)
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5.5.2 Change of Cartesian to Spherical Co-Ordinates
PDF
5.5.3 Change of Cartesian to Cylindrical Co-Ordinates
PDF
5.5.4 problem based on Cylindrical Co-Ordinates
Video
4:54
5.5.4 Quiz
Exercise
5.5.5 Solved problem 2
Video
5:35
5.5.5 Quiz
Exercise
5.5.6 Solved problem 3
PDF
5.5.7 problem based on Spherical Co-Ordinates
Video
5:27
5.5.7 Quiz
Exercise
5.5.8 Solved problem 5
Video
6:22
5.5.8 Quiz
Exercise
5.5.9 Solved problem 6
PDF
5.5.10 Exercise
Exercise
5.6 Application of Double Integral (Area)
5.6.1 Area as Double integral
PDF
5.6.2 problem based on Cartesian Form
Video
5:16
5.6.2 Quiz
Exercise
5.6.3 Solved problem 2
Video
5:55
5.6.3 Quiz
Exercise
5.6.4 Solved problem 3
PDF
5.6.5 Solved problem 4
PDF
5.6.6 Solved problem 5
PDF
5.6.7 problem based on Polar Form
Video
4:1
5.6.7 Quiz
Exercise
5.6.8 Solved problem 7
PDF
5.6.9 Solved problem 8
PDF
5.6.10 Exercise
Exercise
5.7 Application of Triple Integral (Volume)
5.7.1 Volume as Triple Integral
PDF
5.7.2 Solved problem 1
Video
5:1
5.7.2 Quiz
Exercise
5.7.3 Solved problem 2
Video
5:55
5.7.3 Quiz
Exercise
5.7.4 Solved problem 3
Video
5:46
5.7.4 Quiz
Exercise
5.7.5 Solved problem 4
PDF
5.7.6 Solved problem 5
PDF
5.7.7 Solved problem 6
PDF
5.7.8 Solved problem 7
PDF
5.7.9 Exercise
Exercise
5.8 Moments and Centre of Mass, Moment of Inertia
5.8.1 Moments and centres of mass, Moment of Inertia
PDF
5.8.2 Solved problem 1
Video
11:32
5.8.3 Solved problem 2
Video
12:22
5.8.4 Solved problem 3
PDF
5.8.5 Solved problem 4
PDF
5.8.6 Solved problem 5
PDF
5.8.7 Solved problem 6
PDF
5.8.8 Exercises
PDF
Important Q&A
101 Learning Materials
1. Matrices
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. Differential Calculus
Standard Differentiation Formulas
PDF
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
2.15 Part B: Q&A - 14
PDF
2.16 Part B: Q&A - 15
PDF
3. Functions of Several Variables
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
PDF
3.12 Part B: Q&A - 11
PDF
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
PDF
3.16 Part B: Q&A - 15
PDF
3.17 Part B: Q&A - 16
PDF
3.18 Part B: Q&A - 17
PDF
3.19 Part B: Q&A - 18
PDF
3.20 Part B: Q&A - 19
PDF
3.21 Part B: Q&A - 20
PDF
3.22 Part B: Q&A - 21
PDF
3.23 Part B: Q&A - 22
PDF
3.24 Part B: Q&A - 23
PDF
4. Integral Calculus
Standard Integration Formulas
PDF
4.1 Part A: Q&A
PDF
4.2 Part B: Q&A - 1
PDF
4.3 Part B: Q&A - 2
PDF
4.4 Part B: Q&A - 3
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
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4.9 Part B: Q&A - 8
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4.10 Part B: Q&A - 9
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4.11 Part B: Q&A - 10
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4.12 Part B: Q&A - 11
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4.13 Part B: Q&A - 12
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4.14 Part B: Q&A - 13
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4.15 Part B: Q&A - 14
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4.16 Part B: Q&A - 15
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4.17 Part B: Q&A - 16
PDF
4.18 Part B: Q&A - 17
PDF
5. Multiple Integrals
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
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5.10 Part B: Q&A - 9
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5.11 Part B: Q&A - 10
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5.12 Part B: Q&A - 11
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5.13 Part B: Q&A - 12
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5.14 Part B: Q&A - 13
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5.15 Part B: Q&A - 14
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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
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5.22 Part B: Q&A - 21
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5.23 Part B: Q&A - 22
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5.24 Part B: Q&A - 23
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
January 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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