Singular Perturbation Methods for Ordinary Differential Equations

1: Examples Illustrating Regular and Singular Perturbation Concepts.- A. The Harmonic Oscillator: Low Frequency Situation.- B. Introductory Definitions and Remarks.- C. A Simple First-Order Linear Initial Value Problem.- D. Some Second-Order Two-Point Problems.- E. Regular Perturbation Theory for Initial Value Problems.- 2: Singularly Perturbed Initial Value Problems.- A. A Nonlinear Problem from Enzyme Kinetics.- B. The Solution of Linear Systems Using Transformation Methods.- C. Inner and Outer Solutions of Model Problems.- D. The Nonlinear Vector Problem (Tikhonov—Levinson Theory).- E. An Outline of a Proof of Asymptotic Correctness.- F. Numerical Methods for Stiff Equations.- G. Relaxation Oscillations.- H. A Combustion Model.- I. Linear and Nonlinear Examples of Conditionally Stable Systems.- J. Singular Problems.- 3: Singularly Perturbed Boundary Value Problems.- A. Second Order Linear Equations (without Turning Points).- B. Linear Scalar Equations of Higher Order.- C. First-Order Linear Systems.- D. An Application in Control Theory.- E. Some Linear Turning Point Problems.- F. Quasilinear Second-Order Problems.- G. Existence, Uniqueness, and Numerical Computation of Solutions.- H. Quasilinear Vector Problems.- I. An Example with an Angular Solution.- J. Nonlinear Systems.- K. A Nonlinear Control Problem.- L. Semiconductor Modeling.- M. Shocks and Transition Layers.- N. Phase-Plane Solutions for Conservative Systems.- O. A Geometric Analysis for Some Autonomous Equations.- P. Semilinear Problems.- Appendix: The Historical Development of Singular Perturbations.- References.