Book:William E. Boyce/Elementary Differential Equations and Boundary Value Problems/Ninth Edition
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William E. Boyce and Richard C. DiPrima: Elementary Differential Equations and Boundary Value Problems (9th Edition)
Published $\text {2009}$, 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 Separation of Variables; Heat Conduction in a Rod
- 10.6 Other Heat 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
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.)
- 1992: William E. Boyce and Richard C. DiPrima: Elementary Differential Equations and Boundary Value Problems (5th ed.)