Asymptotic Methods in Mechanics

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

1. Demonstrate an understanding of the meaning of asymptotic solutions in the appropriate context and how to interpret these;
2. Solve simple linear and nonlinear ordinary and partial differential equations by asymptotic methods;
3. Illustrate with suitable examples the occurrence of asymptotic phenomena in mechanics.

Many mathematical problems arising in mechanics, may be formulated in terms of differential equations. However, as a rule, such problems pose new challenges from the mathematical point of view. Therefore, the simplest limit cases, which allow analytical solutions, are of particular importance. The aim of the asymptotic approach is to simplify the mathematical problem under consideration.

1. Fundamentals: main ideas and techniques, definitions of Landau symbols, asymptotic sequences and series.
2. Regular perturbation methods: polynomials, ordinary differential equations.
3. Singular perturbation methods: dominant balance, Kruskal-Newton graphs.
4. Asymptotic approximation of integrals: Taylor series, Laplace's method.
5. Non-linear oscillations: physical motivation, Duffing equation, secular terms, Linstedt-Poincare method.
6. Damped oscillations: physical motivation, two-scale method.
7. Method of matched asymptotics: techniques and application.
8. Heat conduction in thin domains.

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 6