PART-A SOLUTION

   10TH EDITION

ADVANCED ENGINEERING MATHEMATICS

ERWIN KREYSZIG
Professor of Mathematics 
Ohio State University 
Columbus, Ohio
In collaboration with
HERBERT KREYSZIG
New York, New York
EDWARD J. NORMINTON
Associate Professor of Mathematics
Carleton University
Ottawa, Ontario
JOHN WILEY & SONS, INC.

PART A

Ordinary Differential Equations (ODEs)

• CHAPTER 1 First-Order ODEs
• CHAPTER 2 Second-Order Linear ODEs 
• CHAPTER 3 Higher Order Linear ODEs
• CHAPTER 4 Systems of ODEs. Phase Plane. 
• CHAPTER 5 Series Solutions of ODEs. 
• CHAPTER 6 Laplace Transforms

CHAPTER 1 First-Order ODEs 2

1.1 Basic Concepts. Modeling 2

1.2 Geometric Meaning of y- ƒ(x, y). Direction Fields, Euler’s Method 9

1.3 Separable ODEs. Modeling 12

1.4 Exact ODEs. Integrating Factors 20

1.5 Linear ODEs. Bernoulli Equation. Population Dynamics 27

1.6 Orthogonal Trajectories. Optional 36

1.7 Existence and Uniqueness of Solutions for Initial Value Problems 38

Chapter 1 Review Questions and Problems 43

Summary of Chapter 1 44

        SOL. MANUAL          

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CHAPTER 2 Second-Order Linear ODEs 46

2.1 Homogeneous Linear ODEs of Second Order 46

2.2 Homogeneous Linear ODEs with Constant Coefficients 53

2.3 Differential Operators. Optional 60

2.4 Modeling of Free Oscillations of a Mass–Spring System 62

2.5 Euler–Cauchy Equations 71

2.6 Existence and Uniqueness of Solutions. Wronskian 74

2.7 Nonhomogeneous ODEs 79

2.8 Modeling: Forced Oscillations. Resonance 85

2.9 Modeling: Electric Circuits 93

2.10 Solution by Variation of Parameters 99

Chapter 2 Review Questions and Problems 102

Summary of Chapter 2 103

  SOL. MANUAL   

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CHAPTER 3 Higher Order Linear ODEs 105

3.1 Homogeneous Linear ODEs 105

3.2 Homogeneous Linear ODEs with Constant Coefficients 111

3.3 Nonhomogeneous Linear ODEs 116

Chapter 3 Review Questions and Problems 122

Summary of Chapter 3 123

 

                             SOL. MANUAL  

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CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods 124

4.0 For Reference: Basics of Matrices and Vectors 124

4.1 Systems of ODEs as Models in Engineering Applications 130

4.2 Basic Theory of Systems of ODEs. Wronskian 137

4.3 Constant-Coefficient Systems. Phase Plane Method 140

4.4 Criteria for Critical Points. Stability 148

4.5 Qualitative Methods for Nonlinear Systems 152

4.6 Nonhomogeneous Linear Systems of ODEs 160

Chapter 4 Review Questions and Problems 164

Summary of Chapter 4 165

  SOL. MANUAL           HANDWRITTEN SOL. 

 CHAPTER 5 Series Solutions of ODEs. Special Functions 167

5.1 Power Series Method 167

5.2 Legendre’s Equation. Legendre Polynomials Pn(x) 175

5.3 Extended Power Series Method: Frobenius Method 180

5.4 Bessel’s Equation. Bessel Functions J(x) 187

5.5 Bessel Functions of the Y(x). General Solution 196

Chapter 5 Review Questions and Problems 200

Summary of Chapter 5 201

 

  SOL. MANUAL           HANDWRITTEN SOL. 

CHAPTER 6 Laplace Transforms 203

6.1 Laplace Transform. Linearity. First Shifting Theorem (s-Shifting) 204

6.2 Transforms of Derivatives and Integrals. ODEs 211

6.3 Unit Step Function (Heaviside Function). 

Second Shifting Theorem (t-Shifting) 217

6.4 Short Impulses. Dirac’s Delta Function. Partial Fractions 225

6.5 Convolution. Integral Equations 232

6.6 Differentiation and Integration of Transforms. 

ODEs with Variable Coefficients 238

6.7 Systems of ODEs 242

6.8 Laplace Transform: General Formulas 248

6.9 Table of Laplace Transforms 249

Chapter 6 Review Questions and Problems 251 

Summary of Chapter 6 253

                             SOL. MANUAL      

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