Variational Methods with Applications in Science and Engineering
Cambridge University Press, 7/22/2013
EAN 9781107022584, ISBN10: 1107022584
Hardcover, 432 pages, 25.7 x 17.8 x 3 cm
Language: English
There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.
1. Preliminaries
2. Calculus of variations
3. Rayleigh-Ritz, Galerkin, and finite-element methods
4. Hamilton's principle
5. Classical mechanics
6. Stability of dynamical systems
7. Optics and electromagnetics
8. Modern physics
9. Fluid mechanics
10. Optimization and control
11. Image processing and data analysis
12. Numerical grid generation.