Mathematical models in applied mechanics Book

1	Problem Formulation
1.1	Introduction	1
1.2	Normalization of the problem	2
1.3	Perturbation procedures	5
1.4	Analytical methods for ordinary differential equations	9
1.5	Classical analogies	21
2	Wave Motion
2.1	Transverse waves on a stretched string	37
2.2	Second-order hyperbolic equations and weak solutions	45
2.3	Linear hyperbolic systems in two independent variables	53
2.4	Multiple reflections and use of transforms	59
2.5	Wave motion with two or more space variables	65
2.6	Waveguides and dispersion	74
2.7	Quasi-linear systems	81
3	Elliptic Problems
3.1	Potential theory	95
3.2	Variational methods and variational inequalities	102
3.3	Free-boundary problems	107
3.4	Application of complex variable methods	116
3.5	Quasi-static continuum models	128
4	Diffusion
4.1	The diffusion equation	145
4.2	Stefan problems	154
4.3	Weak solutions	164
4.4	Diffusion and convection	175
4.5	Non-linear diffusion	186
5	Asymptotic Methods for Non-Linear Problems
5.1	Non-linear ordinary differential equations	203
5.2	Thin layers and lubrication theory	219
5.3	Boundary layers	233
5.4	Far-field solutions	249
	Bibliography	269
	Index	273