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Solutions for Differential Equations: Theory, Technique, and Practice, 3rd Edition Krantz (All Chapters included)
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Complete Solutions Manual for Differential Equations: Theory, Technique, and Practice, 3rd Edition by Steven G. Krantz ; ISBN13: 9781032102702. (Full Chapters included Chapter 1 to 13)..... 1. What Is a Differential Equation?. 2. Solving First-Order Equations. 3. Some Applications of the First-O...

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  • December 24, 2023
  • 136
  • 2022/2023
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Instructor’s Solutions Manual
for

Differential Equations: Theory, Technique,
and Practice with Boundary Value Problems
Third Edition


by Steven G. Krantz




Complete Chapter Solutions Manual
are included (Ch 1 to 13)




** Immediate Download
** Swift Response
** All Chapters included

,Table of Contents

1 What is a Differential Equation? 5
1.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 A Taste of Ordinary Differential Equations . . . . . . . . . . . . 5
1.3 The Nature of Solutions . . . . . . . . . . . . . . . . . . . . . . . 5

2 Solving First-Order Equations 9
2.1 Separable Equations . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 First-Order Linear Equations . . . . . . . . . . . . . . . . . . . . 11
2.3 Exact Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Orthogonal Trajectories and Families of Curves . . . . . . . . . . 18
2.5 Homogeneous Equations . . . . . . . . . . . . . . . . . . . . . . . 25
2.6 Integrating Factors . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.7 Reduction of Order . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Some Applications of the First-Order Theory 33
3.1 The Hanging Chain and Pursuit Curves . . . . . . . . . . . . . . 33
3.2 Electrical Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Second-Order Linear Equations 37
4.1 Second-Order Linear Equations with Constant Coefficients . . . . 37
4.2 The Method of Undetermined Coefficients . . . . . . . . . . . . . 39
4.3 The Method of Variation of Parameters . . . . . . . . . . . . . . 43
4.4 The Use of a Known Solution to Find Another . . . . . . . . . . 47
4.5 Higher-Order Equations . . . . . . . . . . . . . . . . . . . . . . . 48

5 Applications of the Second-Order Theory 51
5.1 Vibrations and Oscillations . . . . . . . . . . . . . . . . . . . . . 51
5.2 Newton’s Law of Gravitation and Kepler’s Laws . . . . . . . . . 53

6 Power Series Solutions 55
6.1 Introduction and Review of Power Series . . . . . . . . . . . . . . 55
6.2 Series Solutions for First-Order Equations . . . . . . . . . . . . . 57
6.3 Ordinary Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.4 Regular Singular Points . . . . . . . . . . . . . . . . . . . . . . . 66

3

, 4

6.5 More on Regular Singular Points . . . . . . . . . . . . . . . . . . 69
6.6 Gauss’s Hypergeometric Equation . . . . . . . . . . . . . . . . . 74

7 Fourier Series: Basic Concepts 79
7.1 Fourier Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.2 Some Remarks about Convergence . . . . . . . . . . . . . . . . . 80
7.3 Even and Odd Functions . . . . . . . . . . . . . . . . . . . . . . . 81
7.4 Fourier Series on Arbitrary Intervals . . . . . . . . . . . . . . . . 84
7.5 Orthogonal Functions . . . . . . . . . . . . . . . . . . . . . . . . 85

8 Laplace Transforms 87
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2 Applications to Differential Equations . . . . . . . . . . . . . . . 89
8.3 Derivatives and Integrals of Laplace Transforms . . . . . . . . . . 90
8.4 Convolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
8.5 The Unit Step and Impulse Functions . . . . . . . . . . . . . . . 94

9 The Calculus of Variations 97
9.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . 97
9.2 Euler’s Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
9.3 Isoperimetric Problems and the Like . . . . . . . . . . . . . . . . 99

10 Systems of First-Order Equations 103
10.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . 103
10.2 Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
10.3 Homogeneous Systems with Constant Coefficients . . . . . . . . . 107
10.4 Nonlinear System . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

11 Partial Differential Equations 115
11.1 Introduction and Historical Remarks . . . . . . . . . . . . . . . . 115
11.2 Eigenvalues and the Vibrating String . . . . . . . . . . . . . . . . 115
11.3 The Heat Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 117
11.4 The Dirichlet Problem for a Disc . . . . . . . . . . . . . . . . . . 119

12 The Nonlinear Theory 121
12.1 Some Motivating Examples . . . . . . . . . . . . . . . . . . . . . 121
12.2 Specializing Down . . . . . . . . . . . . . . . . . . . . . . . . . . 121
12.3 Types of Critical Points: Stability . . . . . . . . . . . . . . . . . 122
12.4 Critical Points and Stability for Linear Systems . . . . . . . . . . 124
12.5 Stability by Liapunov’s Direct Method . . . . . . . . . . . . . . . 126
12.6 Simple Critical Points of Nonlinear Systems . . . . . . . . . . . . 127
12.7 Nonlinear Mechanics: Conservative Systems . . . . . . . . . . . . 129
12.8 The Poincaré-Bendixson Theorem . . . . . . . . . . . . . . . . . 130

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