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

## William E. Boyce and Richard C. DiPrima: *Elementary Differential Equations and Boundary Value Problems (9th Edition)*

Published $2009$, **John Wiley & Sons**

- ISBN 978-0470039403.

### Subject Matter

### Contents

**Chapter 1. Introduction**- 1.1 Some Basic Mathematical Models; Direction Fields
- 1.2 Solutions of Some Differential Equations
- 1.3 Classification of Differential Equations
- 1.2 Historical Remarks

**Chapter 2. First Order Differential Equations**- 2.1 Linear Equations; Method of Integrating Factors
- 2.2 Separable Equations
- 2.3 Modeling with First Order Equations
- 2.4 Differences Between Linear and Nonlinear Equations
- 2.5 Autonomous Equations and Population Dynamics
- 2.6 Exact Equations and Integrating Factors
- 2.7 Numerical Approximations: Euler's Method
- 2.8 The Existence and Uniqueness Theorem
- 2.9 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; the Wronskian
- 3.3 Complex Roots of the Characteristic Equation
- 3.4 Repeated Roots; Reduction of Order
- 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
- 3.6 Variation of Parameters
- 3.7 Mechanical and Electrical Vibrations
- 3.8 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 Euler Equations; Regular Singular Points
- 5.5 Series Solutions near a Regular Singular Point, Part I
- 5.6 Series Solutions near a Regular Singular Point, Part II
- 5.7 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 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 Fundamental Matrices
- 7.8 Repeated Eigenvalues
- 7.9 Nonhomogeneous Linear Systems

**Chapter 8. Numerical Methods**- 8.1 The Euler or Tangent Line Method
- 8.2 Improvements on the Euler Method
- 8.3 The Runge-Kutta Method
- 8.4 Multistep Methods
- 8.5 More on Errors; Stability
- 8.6 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 Locally 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 Two-Point Boundary Value Problems
- 10.2 Fourier Series
- 10.3 The Fourier Convergence Theorem
- 10.4 Even and Odd Functions
- 10.5 Seperation of Variables; Head Conduction in a Rod\
- 10.6 Other Head Conduction Problems
- 10.7 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**- 11.1 The Occurrence of Two-Point Boundary Value Problems
- 11.2 Sturm-Liouville Boundary Value Problems
- 11.3 Nonhomogeneous Boundary Value Problems
- 11.4 Singular Sturm-Liouville Problems
- 11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
- 11.6 Series of Orthogonal Functions: Mean Convergence

**Answers to Problems**

**Index**