Applied Mathematics in Mechanics

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Technical Mathematics

Synopsis:

Annotation: Knowledge of mathematical analysis from the basic courses is considered. on a level alpha. Partial differential equations of the first order. Types of partial differential equations of the second order with constant coefficients, formulation of basic problems. Classical solution of model problems. Numerical solution of PDE by finite difference method.

Requirements:

Syllabus of lectures:

•Partial differential equations of first order

•Classification, characteristics, canonical forms of second order PDE with constant coefficients

•Wave equation, initial and mixed problem, domain of dependence, Fourier‘s method

•Green‘s identities, properties of harmonic functions, maximum principle, mean value theorem

•Boundary value problem for Laplace equation, fundamental solution

•Green’s function, Fourier’s method

•Initial and mixed problem for heat equation. Maximum principle. Fundamental solution. Fourier’s method

•Stability, convergence and consistency of finite difference scheme for PDE

•Explicit and implicit schemes for evolution equations – heat equation, wave equation, transport equation

•Solution of steady problems by iterative methods (Laplace‘s and Poisson‘s equations]

Syllabus of tutorials:

•Partial differential equations of first order

•Classification, characteristics, canonical forms of second order PDE with constant coefficients

•Wave equation, initial and mixed problem, domain of dependence, Fourier‘s method

•Green‘s identities, properties of harmonic functions, maximum principle, mean value theorem

•Boundary value problem for Laplace equation, fundamental solution

•Green’s function, Fourier’s method

•Initial and mixed problem for heat equation. Maximum principle. Fundamental solution. Fourier’s method

•Stability, convergence and consistency of finite difference scheme for PDE

•Explicit and implicit schemes for evolution equations – heat equation, wave equation, transport equation

•Solution of steady problems by iterative methods (Laplace‘s and Poisson‘s equations]

Study Objective:

Study materials:

•Barbu V. : Partial differential Equations and Boundary Value Problems. Kluwer Academics Publishers, Dordrecht 1998

•Quarteroni A. , Valli A.: Numericla Approximation of Partial Differential Equations, Springer, 1998

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: