Mathematics Applied to Deterministic Problems in the Natural Sciences

A. An Overview of the Interaction of Mathematics and Natural Science: 1. What is applied mathematics?; 2. Deterministic systems and ordinary differential equations; 3. Random processes and ial differential equations; 4. Superposition, heat flow, and Fourier analysis; 5. Further developments in Fourier analysis; B. Some Fundamental Procedures Illustrated on Ordinary Differential Equations: 6. Simplification, dimensional analysis, and scaling; 7. Regular perturbation theory; 8. Illustration of techniques on a physiological flow problem; 9. Introduction to singular perturbation theory; 10. Singular perturbation theory applied to a problem in biochemical kinetics; 11. Three techniques applied to the simple pendulum; C. Introduction to Theories of Continuous Fields: 12. Longitudinal motion of a bar; 13. The continuous medium; 14. Field equations of continuum mechanics; 15. Inviscid fluid flow; 16. Potential theory.