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

Subject Matter

 * Differential Equations

Contents

 * Preface (, 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