Book:J. David Logan/A First Course in Differential Equations

Subject Matter

 * Differential Equations

Contents

 * Preface
 * To the Student


 * 1. Differential Equations and Models
 * 1.1 Differential Equations
 * 1.1.1 Equations and Solutions
 * 1.1.2 Geometrical Interpretation
 * 1.2 Pure Time Equations
 * 1.3 Mathematical Models
 * 1.3.1 Particle Dynamics
 * 1.3.2 Autonomous Differential Equations
 * 1.3.3 Stability and Bifurcations
 * 1.3.4 Heat Transfer
 * 1.3.5 Chemical Reactors
 * 1.3.6 Electric Circuits


 * 2. Analytic Solutions and Approximations
 * 2.1 Separation of Variables
 * 2.2 First-Order Linear Equations
 * 2.3 Approximation
 * 2.3.1 Picard Iteration
 * 2.3.2 Numerical Methods
 * 2.3.3 Error Analysis


 * 3. Second-Order Differential Equations
 * 3.1 Particle Mechanics
 * 3.2 Linear Equations with Constant Coefficients
 * 3.3 The Nonhomogeneous Equation
 * 3.3.1 Undetermined Coefficients
 * 3.3.2 Resonance
 * 3.4 Variable Coefficients
 * 3.4.1 Cauchy–Euler Equation
 * 3.4.2 Power Series Solutions
 * 3.4.3 Reduction of Order
 * 3.4.4 Variation of Parameters
 * 3.5 Higher-Order Equations
 * 3.6 Summary and Review


 * 4. Laplace Transformations
 * 4.1 Definition and Basic Properties
 * 4.2 Initial Value Problems
 * 4.3 The Convolution Property
 * 4.4 Discontinuous Sources
 * 4.5 Point Sources
 * 4.6 Table of Laplace Transformations


 * 5. Linear Systems
 * 5.1 Introduction
 * 5.2 Matrices
 * 5.3 Two-Dimensional Systems
 * 5.3.1 Solutions and Linear Orbits
 * 5.3.2 The Eigenvalue Problems
 * 5.3.3 Real Unequal Eigenvalues
 * 5.3.4 Complex Eigenvalues
 * 5.3.5 Real, Repeated Eigenvalues
 * 5.3.6 Stability
 * 5.4 Nonhomogeneous Systems
 * 5.5 Three-Dimensional Systems


 * 6. Nonlinear Systems
 * 6.1 Nonlinear Models
 * 6.1.1 Phase Plane Phenomena
 * 6.1.2 The Lotka-Volterra Model
 * 6.1.3 Holling Functional Responses
 * 6.1.4 An Epidemic Model
 * 6.2 Numerical Methods
 * 6.3 Linearization and Stability
 * 6.4 Periodic Solutions
 * 6.4.1 The Poincaré-Bendixson Theorem


 * Appendix A. References
 * Appendix B. Computer Algebra Systems
 * B.1 Maple
 * B.2 MATLAB
 * Appendix C. Sample Examinations
 * Appendix D. Solutions and Hints to Selected Exercises


 * Index