Mathematics applied to deterministic problems in the natural sciences

Abstract

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.