Differential Equations and Boundary Value Problems: Computing and Modeling, 6th edition
- C Henry Edwards
- , David E. Penney
- , David Calvis
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1. First-Order Differential Equations
- 1.1 Differential Equations and Mathematical Models
- 1.2 Integrals as General and Particular Solutions
- 1.3 Slope Fields and Solution Curves
- 1.4 Separable Equations and Applications
- 1.5 Linear First-Order Equations
- 1.6 Substitution Methods and Exact Equations
2. Mathematical Models and Numerical Methods
- 2.1 Population Models
- 2.2 Equilibrium Solutions and Stability
- 2.3 Acceleration - Velocity Models
- 2.4 Numerical Approximation: Euler's Method
- 2.5 A Closer Look at the Euler Method
- 2.6 The Runge - Kutta Method
3. Linear Equations of Higher Order
- 3.1 Introduction: Second-Order Linear Equations
- 3.2 General Solutions of Linear Equations
- 3.3 Homogeneous Equations with Constant Coefficients
- 3.4 Mechanical Vibrations
- 3.5 Nonhomogeneous Equations and Undetermined Coefficients
- 3.6 Forced Oscillations and Resonance
- 3.7 Electrical Circuits
- 3.8 Endpoint Problems and Eigenvalues
4. Introduction to Systems of Differential Equations
- 4.1 First-Order Systems and Applications
- 4.2 The Method of Elimination
- 4.3 Numerical Methods for Systems
5. Linear Systems of Differential Equations
- 5.1 Matrices and Linear Systems
- 5.2 The Eigenvalue Method for Homogeneous Systems
- 5.3 A Gallery of Solution Curves of Linear Systems
- 5.4 Second-Order Systems and Mechanical Applications
- 5.5 Multiple Eigenvalue Solutions
- 5.6 Matrix Exponentials and Linear Systems
- 5.7 Nonhomogeneous Linear Systems
6. Nonlinear Systems and Phenomena
- 6.1 Stability and the Phase Plane
- 6.2 Linear and Almost Linear Systems
- 6.3 Ecological Models: Predators and Competitors
- 6.4 Nonlinear Mechanical Systems
- 6.5 Chaos in Dynamical Systems
7. Laplace Transform Methods
- 7.1 Laplace Transforms and Inverse Transforms
- 7.2 Transformation of Initial Value Problems
- 7.3 Translation and Partial Fractions
- 7.4 Derivatives, Integrals, and Products of Transforms
- 7.5 Periodic and Piecewise Continuous Input Functions
- 7.6 Impulses and Delta Functions
8. Power Series Methods
- 8.1 Introduction and Review of Power Series
- 8.2 Series Solutions Near Ordinary Points
- 8.3 Regular Singular Points
- 8.4 Method of Frobenius: The Exceptional Cases
- 8.5 Bessel's Equation
- 8.6 Applications of Bessel Functions
9. Fourier Series Methods and Partial Differential Equations
- 9.1 Periodic Functions and Trigonometric Series
- 9.2 General Fourier Series and Convergence
- 9.3 Fourier Sine and Cosine Series
- 9.4 Applications of Fourier Series
- 9.5 Heat Conduction and Separation of Variables
- 9.6 Vibrating Strings and the One-Dimensional Wave Equation
- 9.7 Steady-State Temperature and Laplace's Equation
10. Eigenvalue Methods and Boundary Value Problems
- 10.1 Sturm - Liouville Problems and Eigenfunction Expansions
- 10.2 Applications of Eigenfunction Series
- 10.3 Steady Periodic Solutions and Natural Frequencies
- 10.4 Cylindrical Coordinate Problems
- 10.5 Higher-Dimensional Phenomena
References for Further Study
Appendix: Existence and Uniqueness of Solutions
Answers to Selected Problems
Index
Your questions answered
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