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

Subject Matter

 * Differential Equations

Contents

 * Preface ( and, 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



Source work progress
* : Chapter $1$: Introduction