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Ordinary differential equations : a brief eclectic tour /

Covers important topics like stability, resonance, existence of periodic solutions, and the essential role of continuation of solutions.

Bibliographic Details
Main Author: Sánchez, David A (Author)
Format: Book
Language:English
Published: Washington, DC : Mathematical Association of America, [2002]
Series:Classroom resource materials.
Subjects:
Differential equations.
Équations différentielles.
Gewöhnliche Differentialgleichung
Online Access:Table of contents
Publisher description
Table of Contents:
  • [pt]. 1. Solutions
  • 1. Polynomials
  • 2. More general equations
  • 3. Implicit equations
  • 4. Ordinary differential equations
  • 5. Existence and uniqueness : preliminaries
  • 6. Continuation
  • [pt]. 2. First order equations
  • 1. The separable equation : expanded
  • 2. Equilibria : a first look at stability
  • 3. Multiple equilibria
  • 4. The linear equation
  • 5. The Riccati equation
  • 6. Comparison sometimes helps
  • 7. Periodic solutions
  • 8. Differentiation in search of a solution
  • 9. Dependence on initial conditions
  • 10. Continuing continuation
  • [pt]. 3. Insight not numbers
  • 1. Introduction
  • 2. Two simple schemes
  • 3. Key stuff
  • 4. RKF methods
  • 5. A few examples
  • [pt]. 4. Second order equations
  • 1. What is the initial value problem
  • 2. The linear equation
  • 3. Approach 1 : dealing directly
  • 4. Approach 2 : the linear system
  • 5. Comments on the two approaches
  • 6. Constant coefficient equations : the homogeneous case
  • 7. What to do with solutions
  • 8. The nonhomogeneous equation or the variation of parameters formula untangled
  • 9. Cosines and convolutions
  • 10. Second thoughts
  • [pt]. 5. Linear and nonlinear systems
  • 1. Constant coefficient linear systems
  • 2. The phase plane
  • 3. The linear system and the phase plane
  • 4. Competition and predator-prey systems
  • 5. Harvesting
  • 6. A conservative detour
  • 7. Stability and Gronwall-ing.