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Maths.Engineering Platform Walkthrough
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Maths.Engineering Platform Walkthrough
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1. Differential Calculus - One Variable
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1.1 Representation of Functions
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1.1.1 Introduction
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1.1.2 Representation of Functions
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1.1.3 Piecewise-defined Functions
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1.1.4 Solved Problem 1
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1.1.5 Solved Problem 2
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1.1.6 Solved Problem 3
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1.1.7 Solved Problem 4
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1.1.8 Solved Problem 5
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1.1.9 Solved Problem 6
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1.1.10 Solved Problem 7
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1.1.11 Solved Problem 8
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1.1.12 Solved Problem 9
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1.1.13 Exercises
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1.2 Limit of a Functions
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1.2.1 Introduction
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1.2.2 Solved Problem 1
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1.2.3 Solved Problem 2
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1.2.4 Solved Problem 3
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1.2.5 Solved Problem 4
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1.2.6 Solved Problem 5
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1.2.7 Solved Problem 6
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1.2.8 Limit laws
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1.2.9 Standard Limits
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1.2.10 Direct Substitution property
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1.2.11 Solved Problem 7
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1.2.12 Solved Problem 8
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1.2.13 Solved Problem 9
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1.2.14 Solved Problem 10
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1.2.15 Solved Problem 11
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1.2.16 Solved Problem 12
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1.2.17 Solved Problem 13
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1.2.18 Solved Problem 14
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1.2.19 Solved Problem 15
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1.2.20 Solved Problem 16
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1.2.21 Solved Problem 17
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1.2.22 Solved Problem 18
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1.2.23 Solved Problem 19
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1.2.24 Solved Problem 20
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1.2.25 Solved Problem 21
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1.2.26 Solved Problem 22
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1.2.27 Solved Problem 23
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1.2.28 Solved Problem 24
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1.2.29 Solved Problem 25
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1.2.30 Solved Problem 26
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1.2.31 Solved Problem 27
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1.2.32 Solved Problem 28
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1.2.33 Solved Problem 29
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1.2.34 Exercises
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1.3 Continuity
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1.3.1 Introduction
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1.3.2 Solved Problem 1
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1.3.3 Solved Problem 2
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1.3.4 Solved Problem 3
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1.3.5 Solved Problem 4
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1.3.6 Solved Problem 5
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1.3.7 Solved Problem 6
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1.3.8 Solved Problem 7
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1.3.9 Solved Problem 8
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1.3.10 Solved Problem 9
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1.3.11 Solved Problem 10
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1.3.12 Solved Problem 11
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2.3.13 Solved Problem 12
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2.3.14 Solved Problem 13
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1.3.15 Solved Problem 14
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1.3.16 Exercises
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1.4 Derivatives
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1.4.1 Introduction
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1.4.2 Solved Problem 1
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1.4.3 Solved Problem 2
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1.4.4 Solved Problem 3
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1.4.5 Solved Problem 4
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1.4.6 Solved Problem 5
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1.4.7 Exercises
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1.5 Differentiation Rules
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1.5.1 Introduction
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1.5.2 Differentiation Rules
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1.5.3 Important Differentiation Rules
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1.5.4 Sum rule
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1.5.5 Solved Problem 1
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1.5.6 Solved Problem 2
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1.5.7 Solved Problem 3
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1.5.8 Solved Problem 4
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1.5.9 Solved Problem 5
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1.5.10 Product rule
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1.5.11 Solved Problem 6
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1.5.12 Solved Problem 7
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1.5.13 Solved Problem 8
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1.5.14 Solved Problem 9
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1.5.15 Quotient rule
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1.5.16 Solved Problem 10
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1.5.17 Solved Problem 11
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1.5.18 Solved Problem 12
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1.5.19 Chain rule
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1.5.20 Solved Problem 13
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1.5.21 Solved Problem 14
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1.5.22 Solved Problem 15
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1.5.23 Solved Problem 16
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1.5.24 Solved Problem 17
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1.5.25 Solved Problem 18
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1.5.26 Exercises
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1.6 Implicit Differentiation
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1.6.1 Introduction
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1.6.2 Implicit Differentiation
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1.6.3 General differentiation formulae
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1.6.4 Solved Problem 1
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1.6.5 Solved Problem 2
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1.6.6 Solved Problem 3
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1.6.7 Solved Problem 4
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1.6.8 Solved Problem 5
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1.6.9 Solved Problem 6
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1.6.10 Solved Problem 7
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1.6.11 Solved Problem 8
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1.6.12 Solved Problem 9
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1.6.13 Solved Problem 10
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1.6.14 Exercises
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1.7 Logarithmic Differentiation
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1.7.1 Introduction
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1.7.2 Logarithmic Differentiation Formula
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1.7.3 Solved Problem 1
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1.7.4 Solved Problem 2
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1.7.5 Solved Problem 3
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1.7.6 Solved Problem 4
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1.7.7 Solved Problem 5
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1.7.8 Solved Problem 6
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1.7.9 Solved Problem 7
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1.7.10 Solved Problem 8
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1.7.11 Exercises
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1.8 Maxima and Minima of functions of one variable
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1.8.1 Introduction
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1.8.2 Extreme value Theorem
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1.8.3 Increasing and Decreasing Test
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1.8.4 Solved Problem 1
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1.8.5 Solved Problem 2
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1.8.6 Solved Problem 3
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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 Solved Problem 7
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1.8.11 Solved Problem 8
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1.8.12 Solved Problem 9
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1.8.13 Solved Problem 10
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1.8.14 Solved Problem 11
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1.8.15 Exercises
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2. Integral Calculus - One Variable
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2.1 Definite Integral
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2.1.1 Introduction
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2.1.2 Introduction to Definite Integral
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2.1.3 Standard Formulae
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2.1.4 Solved Problem 1
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2.1.5 Solved Problem 2
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2.1.6 Solved Problem 3
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2.1.7 Solved Problem 4
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2.1.8 Solved Problem 5
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2.1.9 Solved Problem 6
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2.1.10 Solved Problem 7
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2.1.11 Solved Problem 8
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2.1.12 Solved Problem 9
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2.1.13 Exercises
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2.2 Definite Integral - Reimann Sum
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2.2.1 Introduction
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2.2.2 Solved Problem 1
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2.2.3 Solved Problem 2
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2.2.4 Solved Problem 3
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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 Solved Problem 8
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2.2.10 Solved Problem 9
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2.2.11 Exercises
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2.3 Indefinite Integral
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2.3.1 Introduction
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2.3.2 Solved Problem 1
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2.3.3 Solved Problem 2
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2.3.4 Solved Problem 3
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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 Solved Problem 12
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2.3.14 Solved Problem 13
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2.3.15 Solved Problem 14
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2.3.16 Exercises
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2.4 Properties of Definite Integral
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2.4.1 Introduction
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2.4.2 Solved Problem 1
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2.4.3 Solved Problem 2
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2.4.4 Solved Problem 3
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2.4.5 Solved Problem 4
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2.4.6 Solved Problem 5
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2.4.7 Solved Problem 6
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2.4.8 Solved Problem 7
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2.4.9 Solved Problem 8
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2.4.10 Solved Problem 9
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2.4.11 Solved Problem 10
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2.4.12 Exercises
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2.5 Substitution Rule
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2.5.1 Introduction
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2.5.2 Solved Problem 1
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2.5.3 Solved Problem 2
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2.5.4 Solved Problem 3
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2.5.5 Solved Problem 4
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2.5.6 Solved Problem 5
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2.5.7 Solved Problem 6
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2.5.8 Solved Problem 7
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2.5.9 Solved Problem 8
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2.5.10 Solved Problem 9
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2.5.11 Solved Problem 10
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2.5.12 Solved Problem 11
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2.5.13 Solved Problem 12
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2.5.14 Solved Problem 13
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2.5.15 Solved Problem 14
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2.5.16 Solved Problem 15
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2.5.17 Solved Problem 16
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2.5.18 Solved Problem 17
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2.5.19 Solved Problem 18
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2.5.20 Solved Problem 19
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2.5.21 Solved Problem 20
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2.5.22 Solved Problem 21
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2.5.23 Solved Problem 22
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2.5.24 Solved Problem 23
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2.5.25 Solved Problem 24
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2.5.26 Solved Problem 25
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2.5.27 Solved Problem 26
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2.5.28 Exercises
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2.6 Integration by Parts
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2.6.1 Introduction
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2.6.2 Solved Problem 1
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2.6.3 Solved Problem 2
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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 Solved Problem 6
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2.6.8 Solved Problem 7
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2.6.9 Solved Problem 8
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2.6.10 Solved Problem 9
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2.6.11 Solved Problem 10
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2.6.12 Solved Problem 11
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2.6.13 Solved Problem 12
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2.6.14 Solved Problem 13
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2.6.15 Solved Problem 14
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2.6.16 Solved Problem 15
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2.6.17 Solved Problem 16
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2.6.18 Solved Problem 17
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2.6.19 Solved Problem 18
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2.6.20 Solved Problem 19
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2.6.21 Reduction Formula
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2.6.22 Solved Problem 20
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2.6.23 Solved Problem 21
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2.6.24 Exercises
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2.7 Trigonometric Integrals
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2.7.1 Introduction
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2.7.2 Type 2
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2.7.3 Type 3
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2.7.4 Solved Problem 1
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2.7.5 Solved Problem 2
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2.7.6 Solved Problem 3
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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 Solved Problem 8
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2.7.12 Solved Problem 9
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2.7.13 Solved Problem 10
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2.7.14 Solved Problem 11
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2.7.15 Solved Problem 12
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2.7.16 Solved Problem 13
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2.7.17 Solved Problem 14
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2.7.18 Exercises
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2.8 Trigonometric Substitutions
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2.8.1 Introduction
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2.8.2 Solved Problem 1
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2.8.3 Solved Problem 2
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2.8.4 Solved Problem 3
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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 Solved Problem 7
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2.8.9 Solved Problem 8
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2.8.10 Solved Problem 9
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2.8.11 Solved Problem 10
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2.8.12 Exercises
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2.9 Integration of rational functions by partial fraction
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2.9.1 Introduction
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2.9.2 Solved Problem 1
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2.9.3 Solved Problem 2
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2.9.4 Solved Problem 3
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2.9.5 Solved Problem 4
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2.9.6 Solved Problem 5
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2.9.7 Solved Problem 6
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2.9.8 Solved Problem 7
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2.9.9 Solved Problem 8
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2.9.10 Solved Problem 9
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2.9.11 Solved Problem 10
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2.9.12 Solved Problem 11
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2.9.13 Solved Problem 12
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2.9.14 Solved Problem 13
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2.9.15 Solved Problem 14
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2.9.16 Solved Problem 15
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2.9.17 Solved Problem 16
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2.9.18 Exercises
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2.10 Improper Integrals
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2.10.1 Introduction
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2.10.2 Definition of an Improper Integral of Type I
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2.10.3 Definition of an Improper Integral of Type II
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2.10.4 Examples of Infinite limits of Integration
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2.10.5 Solved Problem 1
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2.10.6 Solved Problem 2
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2.10.7 Solved Problem 3
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2.10.8 Solved Problem 4
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2.10.9 Solved Problem 5
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2.10.10 Solved Problem 6
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2.10.11 Solved Problem 7
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2.10.12 Solved Problem 8
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2.10.13 Solved Problem 9
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2.10.14 Solved Problem 10
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2.10.15 Solved Problem 11
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2.10.16 Solved Problem 12
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2.10.17 A comparison test for improper integrals
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2.10.18 Solved Problem 13
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2.10.19 Solved Problem 14
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2.10.20 Exercises
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2.11 Beta Function
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2.11.1 Introduction
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2.11.2 Beta Function Expressed as improper Integral
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2.11.3 Solved Problem 1
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2.11.4 Solved Problem 2
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2.11.5 Solved Problem 3
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2.11.6 Solved Problem 4
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2.11.7 Solved Problem 5
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2.11.8 Solved Problem 6
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2.11.9 Exercise
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2.12 Gamma Function
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2.12.1 Introduction
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2.12.2 Value of Gamma (n) in Terms of Factorial
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2.12.3 Properties of Gamma Function
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2.12.4 Solved Problem 1
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2.12.5 Solved Problem 2
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2.12.6 Solved Problem 3
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2.12.7 Solved Problem 4
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2.12.8 Solved Problem 5
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2.12.9 Solved Problem 6
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2.12.10 Solved Problem 7
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2.12.11 Solved Problem 8
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2.12.12 Solved Problem 9
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2.12.13 Solved Problem 10
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2.12.14 Solved Problem 11
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2.12.15 Solved Problem 12
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2.12.16 Solved Problem 13
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2.12.17 Exercise
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2.13 Relation Between Gamma and Beta Function
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2.13.1 Introduction
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2.13.2 Solved Problem 1
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2.13.3 Solved Problem 2
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2.13.4 Solved Problem 3
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2.13.5 Solved Problem 4
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2.13.6 Solved Problem 5
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2.13.7 Solved Problem 6
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2.13.8 Solved Problem 7
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2.13.9 Solved Problem 8
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2.13.10 Solved Problem 9
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2.13.11 Solved Problem 10
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2.13.12 Solved Problem 11
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2.13.13 Solved Problem 12
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2.13.14 Solved Problem 13
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2.13.15 Solved Problem 14
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2.13.16 Solved Problem 15
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2.13.17 Solved Problem 16
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2.13.18 Solved Problem 17
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2.13.19 Exercise
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3. Differential Calculus - Several Variables
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3.1 Partial Differentiation
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3.1.1 Introduction
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3.1.2 Solved Problem 1
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3.1.3 Solved Problem 2
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3.1.4 Solved Problem 3
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3.1.5 Solved Problem 4
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3.1.6 Solved Problem 5
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3.1.7 Solved Problem 6
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3.1.8 Solved Problem 7
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3.1.9 Solved Problem 8
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3.1.10 Solved Problem 9
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3.1.11 Exercises
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3.2 Euler's Theorems
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3.2.1 Introduction
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3.2.2 Euler’s theorem
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3.2.3 Solved Problem 1
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3.2.4 Solved Problem 2
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3.2.5 Solved Problem 3
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3.2.6 Solved Problem 4
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3.2.7 Solved Problem 5
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3.2.8 Solved Problem 6
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3.2.9 Solved Problem 7
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3.2.10 Solved Problem 8
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3.2.11 Solved Problem 9
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3.2.12 Exercises
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3.3 Total Derivatives
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3.3.1 Introduction
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3.3.2 Solved Problem 1
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3.3.3 Solved Problem 2
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3.3.4 Solved Problem 3
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3.3.5 Solved Problem 4
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3.3.6 Exercises
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3.4 Jacobian's
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3.4.1 Introduction
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3.4.2 Two important properties of Jacobian
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3.4.3 Chain rule for Jacobian
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3.4.4 Standard Jacobian's
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3.4.5 Solved Problem 1
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3.4.6 Solved Problem 2
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3.4.7 Solved Problem 3
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3.4.8 Solved Problem 4
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3.4.9 Solved Problem 5
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3.4.10 Solved Problem 6
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3.4.11 Solved Problem 7
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3.4.12 Solved Problem 8
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3.4.13 Solved Problem 9
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3.4.14 Solved Problem 10
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3.4.15 Solved Problem 11
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3.4.16 Solved Problem 12
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3.5 Maxima & Minima
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3.5.1 Introduction
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3.5.2 Extremum and Saddle point
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3.5.3 Extremum and Saddle point
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3.5.4 Methods of finding extrema of f(x , y)
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3.5.5 Solved Problem 1
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3.5.6 Solved Problem 2
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3.5.7 Solved Problem 3
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3.5.8 Solved Problem 4
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3.5.9 Solved Problem 5
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3.5.10 Solved Problem 6
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3.5.11 Solved Problem 7
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3.5.12 Solved Problem 8
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3.5.13 Exercises
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4. Multiple Integrals - Several Variables
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4.1 Double Integral
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4.1.1 Introduction
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4.1.2 Evaluation of Double Integrals
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4.1.3 Double Integrals
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4.1.4 Solved Problem 1
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4.1.5 Solved Problem 2
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4.1.6 Solved Problem 3
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4.1.7 Solved Problem 4
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4.1.8 Solved Problem 5
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4.1.9 Solved Problem 6
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4.1.10 Solved Problem 7
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4.1.11 Solved Problem 8
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4.1.12 Solved Problem 9
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4.1.13 Solved Problem 10
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4.1.14 Solved Problem 11
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4.1.15 Solved Problem 12
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4.1.16 Solved Problem 13
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4.1.17 Solved Problem 14
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4.1.18 Solved Problem 15
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4.1.19 Solved Problem 16
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4.1.20 Solved Problem 17
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4.1.21 Solved Problem 18
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4.1.22 Solved Problem 19
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4.1.23 Solved Problem 20
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4.1.24 Solved Problem 21
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4.1.25 Solved Problem 22
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4.1.26 Solved Problem 23
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4.1.27 Solved Problem 24
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4.1.28 Exercise
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4.2 Change of Order of Integration
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4.2.1 Introduction
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4.2.2 Solved Problem 1
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4.2.3 Solved Problem 2
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4.2.4 Solved Problem 3
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4.2.5 Solved Problem 4
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4.2.6 Solved Problem 5
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4.2.7 Solved Problem 6
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4.2.8 Solved Problem 7
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4.2.9 Solved Problem 8
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4.2.10 Solved Problem 9
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4.2.11 Solved Problem 10
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4.2.12 Solved Problem 11
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4.2.13 Exercise
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4.3 Change of Variables (Double Integral)
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4.3.1 Introduction
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4.3.2 Solved Problem 1
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4.3.3 Solved Problem 2
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4.3.4 Solved Problem 3
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4.3.5 Solved Problem 4
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4.3.6 Solved Problem 5
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4.3.7 Exercise
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4.4 Application of Double Integral (Area)
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4.4.1 Introduction
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4.4.2 Solved Problem 1
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4.4.3 Solved Problem 2
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4.4.4 Solved Problem 3
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4.4.5 Solved Problem 4
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4.4.6 Solved Problem 5
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4.4.7 Solved Problem 6
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4.4.8 Solved Problem 7
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4.4.9 Solved Problem 8
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4.4.10 Solved Problem 9
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4.4.11 Solved Problem 10
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4.4.12 Solved Problem 11
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4.4.13 Solved Problem 12
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4.4.14 Exercise
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4.5 Triple Integral
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4.5.1 Solved Problem 1
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4.5.2 Solved Problem 2
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4.5.3 Solved Problem 3
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4.5.4 Solved Problem 4
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4.5.5 Solved Problem 5
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4.5.6 Solved Problem 6
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4.5.7 Solved Problem 7
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4.5.8 Solved Problem 8
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4.5.9 Solved Problem 9
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4.5.10 Solved Problem 10
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4.5.11 Solved Problem 11
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4.5.12 Solved Problem 12
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4.5.13 Solved Problem 13
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4.5.14 Solved Problem 14
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4.5.15 Exercise
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4.6 Change of Variables (Triple Integral)
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4.6.1 Introduction
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4.6.2 Change of Cartesian to Spherical Co-Ordinates
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4.6.3 Solved Problem 1
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4.6.4 Solved Problem 2
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4.6.5 Solved Problem 3
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4.6.6 Solved Problem 4
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4.6.7 Solved Problem 5
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4.6.8 Solved Problem 6
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4.6.9 Exercise
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4.7 Application of Triple Integral (Volume)
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4.7.1 Solved Problem 1
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4.7.2 Solved Problem 2
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4.7.3 Solved Problem 3
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4.7.4 Solved Problem 4
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4.7.5 Solved Problem 5
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4.7.6 Solved Problem 6
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4.7.7 Solved Problem 7
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5. Matrices
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5.1 Introduction
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5.1.1 Introduction
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5.1.2 Types of matrix
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5.1.3 Types of matrix
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5.1.4 Types of matrix
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5.1.5 Application of matrices
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5.1.6 Matrix Introduction
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5.1.7 Matrix Addition
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5.1.8 Matrix Multiplication
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5.1.9 Determinant of Matrix
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5.1.10 Inverse of a Matrix
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5.2 Characteristic Equation
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5.2.1 Introduction
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5.2.2 Solved problem 1
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5.2.3 Solved problem 2
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5.2.4 Solved problem 3
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5.2.5 Solved problem 4
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5.2.6 Exercises
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5.3 Eigen values and Eigen vectors
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5.3.1 Introduction
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5.3.2 Eigen vectors
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5.3.3 Solved problem 1
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5.3.4 Solved problem 2
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5.3.5 Solved problem 3
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5.3.6 Solved problem 4
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5.3.7 Solved problem 5
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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 Solved problem 9
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5.3.12 Solved problem 10
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5.3.13 Solved problem 11
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5.3.14 Exercises
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5.4 Properties of Eigen values and Eigen vectors
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5.4.1 Introduction
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5.4.2 Properties of Eigen values
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5.4.3 Properties of Eigen vectors
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5.4.4 Solved problem 1
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5.4.5 Solved problem 2
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5.4.6 Solved problem 3
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5.4.7 Solved problem 4
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5.4.8 Solved problem 5
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5.4.9 Solved problem 6
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5.4.10 Solved problem 7
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5.4.11 Solved problem 8
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5.4.12 Solved problem 9
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5.4.13 Solved problem 10
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5.4.14 Solved problem 11
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5.4.15 Solved problem 12
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5.4.16 Solved problem 13
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5.4.17 Solved problem 14
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5.4.18 Exercises
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5.5 Cayley Hamilton Theorem
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5.5.1 Introduction
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5.5.2 Solved problem 1
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5.5.3 Solved problem 2
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5.5.4 Solved problem 3
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5.5.5 Solved problem 4
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5.5.6 Solved problem 5
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5.5.7 Solved problem 6
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5.5.8 Solved problem 7
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5.5.9 Solved problem 8
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5.5.10 Solved problem 9
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5.5.11 Solved problem 10
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5.5.12 Exercises
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5.6 Diagonalisation of Matrix (Orthogonal Transformation)
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5.6.1 Introduction
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5.6.1 Introduction
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5.6.2 Solved problem 1
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5.6.3 Solved problem 2
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5.6.4 Solved problem 3
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5.6.5 Exercises
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5.7 Quadratic Forms and Nature of Quadratic Forms
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5.7.1 Introduction
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5.7.2 Fundamental theorem on quadratic forms
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5.7.3 Index and signature of real quadratic form
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5.7.4 Nature of quadratic form
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5.7.5 Solved problem 1
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5.7.6 Solved problem 2
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5.7.7 Solved problem 3
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5.7.8 Solved problem 4
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5.7.9 Solved problem 5
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5.7.10 Solved problem 6
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5.7.11 Exercises
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