Mathematics Applied to Deterministic Problems in the Natural Sciences

Addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences. The authors case studies approach leads to excitement in teaching realistic problems. The exercises reinforce, test and extend the readers understanding. This reprint volume may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers working on fluid mechanics, elasticity, perturbation methods, dimensional analysis, numerical analysis, continuum mechanics and differential equations.

Spis treści:
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.