Mathematical Methods for Scientists and Engineers: Linear and Nonlinear Systems

I.
Linear Systems
0. Miscellaneous Resources
1. Matrix Theory
2. The Gamma and Related Functions
3. Elements of Asymptotics
4. Evaluation of Sums: The Euler-MacLaurin Sum Expansion
5. Evaluation of Integrals: The Laplace Method
6. Differential Equations
II. Nonlinear Systems
7. The Simple Harmonic Oscillator and the Logistic Equation
8. Aspects of Harmonic Motion and the Concept of Secular Terms
9. Equilibrium Points and the Phase Plane
10. Conservative Systems
11. Nonconservative Systems
12. The Method of Averaging (MOA)
13. The Method of Multiple Times Scales (MMTS)
14. Higher-Order Calculations
15. Error Analysis
16. One-Dimensional Iterative Maps and the Onset of Chaos
Appendix.
Index.