Introduction , The quasi-linear equation , General equation , First-order equations , The wave equation , The general semi-linear partial differential equation in two independent variables , Three examples from fluid mechanics , Riemann invariants and simple waves , Travelling-wave solutions , The method of separation of variables , Similarity solutions , Introduction , The quasi-linear equation , General equation , First-order equations , The wave equation , The general semi-linear partial differential equation in two independent variables , Three examples from fluid mechanics , Riemann invariants and simple waves , Travelling-wave solutions , The method of separation of variables , Similarity solutions ,
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Hi friends, here Neeraj Yadav uploaded notes for Engineering Mathematics and Mathematics with title **An introduction to partial differential equations pdf notes and ebook download**. You can download this lecture notes,
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Part I 10

First-order partial differential equations 10

List of examples 11

Preface 12

1 Introduction 13

1.1 Types of equation 13

Exercises 1 14

2 The quasi-linear equation 15

2.1 Of surfaces and tangents 15

2.2 The Cauchy (or initial value) problem 18

2.3 The semi-linear and linear equations 22

2.4 The quasi-linear equation in n independent variables 23

Exercises 2 24

3 The general equation 25

3.1 Geometry again 25

3.2 The method of solution 27

3.3 The general PDE with Cauchy data 34

3.4 The complete integral and the singular solution 36

Exercises 3 47

Answers 48

Part II 49

Partial differential equations: classification and canonical forms 49

List of Equations 50

Preface 52

1 Introduction 53

1.1 Types of equation 53

2 First-order equations 55

2.1 The linear equation 56

2.2 The Cauchy problem 58

2.3 The quasi-linear equation 59

Exercises 2 62

3 The wave equation 63

3.1 Connection with first-order equations 63

3.2 Initial data 65

Exercises 3 70

4 The general semi-linear partial differential equation in two independent variables 71

4.1 Transformation of variables 71

4.2 Characteristic lines and the classification 73

4.3 Canonical form 76

4.4 Initial and boundary conditions 81

Exercises 4 83

5 Three examples from fluid mechanics 84

5.1 The Tricomi equation 84

5.2 General compressible flow 85

5.3 The shallow-water equations 88

5.4 Appendix: The hodograph transformation 90

Exercise 5 93

6 Riemann invariants and simple waves 94

6.1 Shallow-water equations: Riemann invariants 95

6.2 Shallow-water equations: simple waves 96

Part III 99

Partial differential equations: method of separation of variables and

similarity & travelling-wave solutions 99

List of Equations 100

Preface 102

1 Introduction 103

1.1 The Laplacian and coordinate systems 103

1.2 Overview of the methods 106

2 The method of separation of variables 107

2.1 Introducing the method 107

2.2 Two independent variables: other coordinate systems 110

2.3 Linear equations in more than two independent variables 114

2.4 Nonlinear equations 118

Exercises 2 121

3 Travelling-wave solutions 122

3.1 The classical, elementary partial differential equations 123

3.2 Equations in higher dimensions 125

3.3 Nonlinear equations 127

Exercises 3 131

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