# Book:William E. Boyce/Elementary Differential Equations and Boundary Value Problems/Third 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 (3rd Edition)*

Published $\text {1977}$, **Wiley**

- ISBN 0-471-83180-8

### Subject Matter

### Contents

- Preface (William E. Boyce and William E. Boyce, Troy, New York, November $1976$)

- Acknowledgments

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

**2. FIRST ORDER DIFFERENTIAL EQUATIONS**- 2.1 Linear Equations
- 2.2 Further Discussion of Linear Equations
- 2.3 Nonlinear Equations
- 2.4 Separable Equations
- 2.5 Exact Equations
- 2.6 Integrating Factors
- 2.7 Homogeneous Equations
- 2.8 Miscellaneous Problems and Applications
- 2.9 Applications of First Order Equations
- 2.10 Elementary Mechanics
- *2.11 The Existence and Uniqueness Theorem
- Appendix. Derivation of Equation of Motion of a Body with Variable Mass

**3. SECOND ORDER LINEAR EQUATIONS**- 3.1 Introduction
- 3.2 Fundamental Solutions of the Homogeneous Equation
- 3.3 Linear Independence
- 3.4 Reduction of Order
- 3.4 Complex Roots of the Characteristic Equation
- 3.5 Homogeneous Equations with Constant Coefficients
- 3.5.1 Complex Roots

- 3.6 The Nonhomogeneous Problem
- 3.6.1 The Method of Undetermined Coefficients
- 3.6.2 The Method of Variation of Parameters

- 3.7 Mechanical Vibrations
- 3.7.1 Free Vibrations
- 3.7.2 Forced Vibrations

- 3.8 Electrical Networks

**4. SERIES SOLUTIONS OF SECOND ORDER LINEAR EQUATIONS**- 4.1 Introduction: Review of Power Series
- 4.2 Series Solutions Near an Ordinary Point, Part I
- 4.2.1 Series Solutions Near an Ordinary Point, Part II
- 4.3 Regular Singular Points
- 4.4 Euler Equations
- 4.5 Series Solutions Near a Regular Singular Point, Part I
- 4.5.1 Series Solutions Near a Regular Singular Point, Part II
- *4.6 Series Solutions near a Regular Singular Point; $r_1 = r_2$ and $r_1 - r_2 = N$
- *4.7 Bessel's Equation

**5. HIGHER ORDER LINEAR EQUATIONS**- 5.1 Introduction
- 5.2 General Theory of $n$th Order Linear Equations
- 5.3 Homogeneous Equations with Constant Coefficients
- 5.4 The Method of Undetermined Coefficients
- 5.5 The Method of Variation of Parameters

**6. THE LAPLACE TRANSFORM**- 6.1 Introduction. Definition of the Laplace Transform
- 6.2 Solution of Initial Value Problems
- 6.3 Step Functions
- 6.3.1 A Differential Equation with a Discontinuous Forcing Function
- 6.4 Impulse Functions
- 6.5 The Convolution Integral
- 6.6 General Discussion and Strategy

**7. SYSTEMS OF FIRST ORDER LINEAR EQUATIONS**- 7.1 Introduction
- 7.2 Solution of Linear Systems by Elimination
- 7.3 Review of Matrices
- 7.4 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
- 7.5 Basic Theory of Systems of First Order Linear Equations
- 7.6 Homogeneous Linear Systems with Constant Coefficients
- 7.7 Complex Eigenvalues
- 7.8 Repeated Eigenvalues
- 7.9 Fundamental Matrices
- 7.10 Nonhomogeneous Linear Systems

**8. NUMERICAL METHODS**- 8.1 Introduction
- 8.2 The Euler or Tangent Line Method
- 8.3 The Error
- 8.4 An Improved Euler Method
- 8.5 The Three-Term Taylor Series Method
- 8.6 The Runge-Kutta Method
- 8.7 Some Difficulties with Numerical Methods
- 8.8 A Multistep Method
- 8.9 Systems of First Order Equations

**9. NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY**- 9.1 Introduction
- 9.2 Solutions of Autonomous Systems
- 9.3 The Phase Plane: Linear Systems
- 9.4 Stability; Almost Linear Systems
- 9.5 Competing Species and Predator-Prey Problems
- 9.6 Liapounov's Second Method
- 9.7 Periodic Solutions and Limit Cycles

**10. PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES**- 10.1 Introduction
- 10.2 Heat Conduction and Separation of Variables
- 10.3 Fourier Series
- 10.4 The Fourier Theorem
- 10.5 Even and Odd Functions
- 10.6 Solution of Other Heat Conduction Problems
- 10.7 The Wave Equation: Vibrations of an Elastic String
- 10.8 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 Introduction
- 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.) - 1986: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(4th ed.) - 1992: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(5th ed.) - 2009: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(9th ed.)

## Source work progress

- 1977: William E. Boyce and Richard C. DiPrima:
*Elementary Differential Equations and Boundary Value Problems*(3rd ed.) ... (next): Chapter $1$: Introduction