Applied Mathematics in Mechanics

Course guarantor:

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, Fouriers method

Greens identities, properties of harmonic functions, maximum principle, mean value theorem

Boundary value problem for Laplace equation, fundamental solution

Greens function, Fouriers method

Initial and mixed problem for heat equation. Maximum principle. Fundamental solution. Fouriers 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 (Laplaces and Poissons 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, Fouriers method

Greens identities, properties of harmonic functions, maximum principle, mean value theorem

Boundary value problem for Laplace equation, fundamental solution

Greens function, Fouriers method

Initial and mixed problem for heat equation. Maximum principle. Fundamental solution. Fouriers 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 (Laplaces and Poissons 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: