Mathematics applied to deterministic problems in the natural sciences [electronic resource] / C.C. Lin, L.A. Segel ; with material on elasticity by G.H. Handelman.
Saved in:
| Online Access: |
Full Text (via SIAM) |
|---|---|
| Main Author: | |
| Corporate Author: | |
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Philadelphia, Pa. :
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),
1988.
|
| Series: | Classics in applied mathematics ;
1. |
| Subjects: |
Table of Contents:
- Part A: An overview of the interaction of mathematics and natural science. Chapter 1: What is applied mathematics: On the nature of applied mathematics; Introduction to the analysis of galactic structure; Aggregation of slime mold amebae
- Chapter 2: Deterministic systems and ordinary differential equations: Planetary orbits; Elements of perturbation theory, including Poincare's method for periodic orbits; A system of ordinary differential equations
- Chapter 3: Random processes and partial differential equations: Random walk in one dimension; Langevin's equation; Asymptotic series, Laplace's method, gamma function, Stirling's formula; A difference equation and its limit; Further considerations pertinent to the relationship between probability and partial differential equations
- Chapter 4: Superposition, heat flow, and fourier analysis: Conduction of heat; Fourier's theorem; On the nature of Fourier series; Chapter 5: Further Developments in Fourier Analysis; Other aspects of heat conduction; Sturn-Liouville systems; Brief introduction to Fourier transform; Generalized harmonic analysis.
- Part B: Some fundamental procedures illustrated on ordinary differential equations. Chapter 6: Simplification, dimensional analysis, and scaling: The basic simplification procedure; Dimensional analysis; Scaling
- Chapter 7: Regular perturbation theory: The series method applied to the simple pendulum; Projectile problem solved by perturbation theory
- Chapter 8: Illustration of techniques on a physiological flow problem: Physical formulation and dimensional analysis of a model for "standing gradient" osmotically driven flow; A mathematical model and its dimensional analysis; Obtaining the final scaled dimensionless form of the mathematical model; Solution and interpretation
- Chapter 9: Introduction to singular perturbation theory: Roots of polynomial equations; Boundary value problems for ordinary differential equations
- Chapter 10: Singular perturbation theory applied to a problem in biochemical kinetics: Formulation of an initial value problem for a one enzyme-one substrate chemical reaction; Approximate solution by singular perturbation methods
- Chapter 11: Three techniques applied to the simple pendulum: Stability of normal and inverted equilibrium of the pendulum; A multiple scale expansion; The phase plane.
- Part C: Introduction to theories of continuous fields. Chapter 12: Longitudinal motion of a bar: Derivation of the governing equations; One-dimensional elastic wave propagation; Discontinuous solutions; Work, energy, and vibrations
- Chapter 13: The continuous medium: The continuum model; Kinematics of deformable media; the material derivative; The Jacobian and its material derivative
- Chapter 14: Field equations of continuum mechanics: Conservation of mass; Balance of linear momentum; Balance of angular momentum; Energy and entropy; On constitutive equations, covariance; and the continuum model
- Chapter 15: Inviscid fluid flow: Stress in motionless and inviscid fluids; Stability of a stratified fluid; Compression waves in gases; Uniform flow past a circular cylinder
- Chapter 16: Potential theory: Equations of Laplace and Poisson; Green's functions; Diffraction of acoustic waves by a hole.