Advanced Engineering Mathematics, International Adaptation - Erwin Kreyszig

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Résumé :
TABLE OF CONTENTS

PART A Ordinary Differential Equations (ODEs)

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CHAPTER 1 First-Order ODEs

1.1 Basic Concepts. Modeling

1.2 Geometric Meaning of y' = ?(x, y). Direction Fields, Euler's Method

1.3 Separable ODEs. Modeling

1.4 Exact ODEs. Integrating Factors

1.5 Linear ODEs. Bernoulli Equation. Population Dynamics

1.6 Orthogonal Trajectories. Optional

1.7 Existence and Uniqueness of Solutions for Initial Value Problems

?Sustainability and Ethical Considerations

?Chapter 1 Review Questions and Problems

?Summary of Chapter 1

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CHAPTER 2 Second-Order Linear ODEs

2.1 Homogeneous Linear ODEs of Second Order

2.2 Homogeneous Linear ODEs with Constant Coefficients

2.3 Differential Operators. Optional

2.4 Modeling of Free Oscillations of a Mass-Spring System

2.5 Euler-Cauchy Equations

2.6 Existence and Uniqueness of Solutions. Wronskian

2.7 Nonhomogeneous ODEs

2.8 Modeling: Forced Oscillations. Resonance

2.9 Modeling: Electric Circuits

2.10 Solution by Variation of Parameters

Sustainability and Ethical Considerations

Chapter 2 Review Questions and Problems

Summary of Chapter 2

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CHAPTER 3 Higher Order Linear ODEs

3.1 Homogeneous Linear ODEs

3.2 Homogeneous Linear ODEs with Constant Coefficients

3.3 Nonhomogeneous Linear ODEs

Sustainability and Ethical Considerations

Chapter 3 Review Questions and Problems

Summary of Chapter 3

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CHAPTER 4 Systems of ODEs. Phase Plane. Qualitative Methods

4.0 For Reference: Basics of Matrices and Vectors

4.1 Systems of ODEs as Models in Engineering Applications

4.2 Basic Theory of Systems of ODEs. Wronskian

4.3 Constant-Coefficient Systems. Phase Plane Method

4.4 Criteria for Critical Points. Stability

4.5 Qualitative Methods for Nonlinear Systems

4.6 Nonhomogeneous Linear Systems of ODEs

Sustainability and Ethical Considerations

Chapter 4 Review Questions and Problems

Summary of Chapter 4

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CHAPTER 5 Series Solutions of ODEs. Special Functions

5.1 Power Series Method

5.2 Legendre's Equation. Legendre Polynomials (x)

5.3 Extended Power Series Method: Frobenius Method

5.4 Bessel's Equation. Bessel Functions (x)

5.5 Bessel Functions of the (x). General Solution

Sustainability and Ethical Considerations

Chapter 5 Review Questions and Problems

Summary of Chapter 5

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CHAPTER 6 Laplace Transforms

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

6.2 Transforms of Derivatives and Integrals. ODEs

6.3 Unit Step Function (Heaviside Function). Second Shifting Theorem (t-Shifting)

6.4 Short Impulses. Dirac's Delta Function. Partial Fractions

6.5 Convolution. Integral Equations

6.6 Differentiation and Integration of Transforms. ODEs with Variable Coefficients

6.7 Systems of ODEs

6.8 Laplace Transform: General Formulas

6.9 Table of Laplace Transforms

Sustainability and Ethical Considerations

Chapter 6 Review Questions and Problems

Summary of Chapter 6

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PART B Linear Algebra. Vector Calculus

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CHAPTER 7 Linear Algebra: Matrices, Vectors, Determinants. Linear Systems

7.1 Matrices, Vectors: Addition and Scalar Multiplication

7.2 Matrix Multiplication

7.3 Linear Systems of Equations. Gauss Elimination

7.4 Linear Ind...

Biographie:

ERWIN KREYSZIG, Professor of Mathematics, Ohio State University, Columbus, Ohio.