# Book:William E. Boyce/Elementary Differential Equations and Boundary Value Problems/Fifth Edition

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## William E. Boyce and Richard C. DiPrima:

## William E. Boyce and Richard C. DiPrima: *Elementary Differential Equations and Boundary Value Problems (5th Edition)*

Published $\text {1992}$, **Wiley**

- ISBN 0-471-57019-2.

### Subject Matter

### Contents

- Preface (William E. Boyce, Troy, New York, June $1991$)

- Acknowledgments

**Chapter 1. Introduction**- 1.1 Classification of Differential Equations
- 1.2 Historical Remarks

**Chapter 2. First Order Differential Equations**- 2.1 Linear Equations
- 2.2 Further Discussion of Linear Equations
- 2.3 Separable Equations
- 2.4 Differences Between Linear and Nonlinear Equations
- 2.5 Applications of First Order Linear Equations
- 2.6 Population Dynamics and Some Related Problems
- 2.7 Some Problems in Mechanics
- 2.8 Exact Equations and Integrating Factors
- 2.9 Homogeneous Equations
- 2.10 Miscellaneous Problems and Applications
- *2.11 The Existence and Uniqueness Theorem
- 2.12 First Order Difference Equations

**Chapter 3. Second Order Linear Equations**- 3.1 Homogeneous Equations with Constant Coefficients
- 3.2 Fundamental Solutions of Linear Homogeneous Equations
- 3.3 Linear Independence and the Wronskian
- 3.4 Complex Roots of the Characteristic Equation
- 3.5 Repeated Roots; Reduction of Order
- 3.6 Nonhomogeneous Equations; Method of Undetermined Coefficients
- 3.7 Variation of Parameters
- 3.8 Mechanical and Electrical Vibrations
- 3.9 Forced Vibrations

**Chapter 4. Higher Order Linear Equations**- 4.1 General Theory of $n$th Order Linear Equations
- 4.2 Homogeneous Equations with Constant Coefficients
- 4.3 The Method of Undetermined Coefficients
- 4.4 The Method of Variation of Parameters

**Chapter 5. Series Solutions of Second Order Linear Equations**- 5.1 Review of Power Series
- 5.2 Series Solutions near an Ordinary Point, Part I
- 5.3 Series Solutions near an Ordinary Point, Part II
- 5.4 Regular Singular Points
- 5.5 Euler Equations
- 5.6 Series Solutions near a Regular Singular Point, Part I
- 5.7 Series Solutions near a Regular Singular Point, Part II
- *5.8 Series Solutions near a Regular Singular Point; $r_1 = r_2$ and $r_1 - r_2 = N$
- *5.9 Bessel's Equation

**Chapter 6. The Laplace Transform**- 6.1 Definition of the Laplace Transform
- 6.2 Solution of Initial Value Problems
- 6.3 Step Functions
- 6.4 Differential Equations with Discontinuous Forcing Functions
- 6.5 Impulse Functions
- 6.6 The Convolution Integral

**Chapter 7. Systems of First Order Linear Equations**- 7.1 Introduction
- 7.2 Review of Matrices
- 7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
- 7.4 Basic Theory of Systems of First Order Linear Equations
- 7.5 Homogeneous Linear Systems with Constant Coefficients
- 7.6 Complex Eigenvalues
- 7.7 Repeated Eigenvalues
- 7.8 Fundamental Matrices
- 7.9 Nonhomogeneous Linear Systems

**Chapter 8. Numerical Methods**- 8.1 The Euler or Tangent Line Method
- 8.2 Errors in Numerical Procedures
- 8.3 Improvements on the Euler Method
- 8.4 The Runge-Kutta Method
- 8.5 Some Difficulties with Numerical Methods
- 8.6 A Multistep Method
- 8.7 Systems of First Order Equations

**Chapter 9. Nonlinear Differential Equations and Stability**- 9.1 The Phase Plane: Linear Systems
- 9.2 Autonomous Systems and Stability
- 9.3 Almost Linear Systems
- 9.4 Competing Species
- 9.5 Predator-Prey Equations
- 9.6 Liapunov's Second Method
- 9.7 Periodic Solutions and Limit Cycles
- 9.8 Chaos and Strange Attractors: The Lorenz Equations

**Chapter 10. Partial Differential Equations and Fourier Series**- 10.1 Separation of Variables; Heat Conduction
- 10.2 Fourier Series
- 10.3 The Fourier Theorem
- 10.4 Even and Odd Functions
- 10.5 Solution of Other Heat Conduction Problems
- 10.6 The Wave Equation: Vibrations of an Elastic String
- 10.7 Laplace's Equation
- Appendix A. Derivation of the Heat Conduction Equation
- Appendix B. Derivation of the Wave Equation

**Chapter 11. Boundary Value Problems and Sturm-Liouville Theory**- 11.1 The Occurrence of Two-Point Boundary Value Problems
- 11.2 Linear Homogeneous Boundary Value Problems: Eigenvalues and Eigenfunctions
- 11.3 Sturm-Liouville Boundary Value Problems
- 11.4 Nonhomogeneous Boundary Value Problems
- *11.5 Singular Sturm-Liouville Problems
- *11.6 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
- *11.7 Series of Orthogonal Functions: Mean Convergence

**Answers to Problems**

**Index**

## Further Editions

- 1965: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems* - 1969: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(2nd ed.) - 1977: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(3rd ed.) - 1986: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(4th ed.) - 2009: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(9th ed.)

## Source work progress

- 1992: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(5th ed.) ... (next): Chapter $1$: Introduction: $1.1$ Classification of Differential Equations