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

## 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.

### 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