Mathematics for Applications+Numerical Methods 1

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Department of Mathematics

Synopsis:

Functional analysis and solution methods for mathematical physics problems

Requirements:

Syllabus of lectures:

1.Differential operators in Hilbert space

2.Minimal energy theorem

3.Friedrich's extension of positive definite operators

4.Generalised solutions, existence and uniquenes

5.Generalised differentiation, Sobolev's spaces

6.Weak solution of PDE with boundary values

7.Partial differential equations of eliptic, parabolic and hyperbolic type

8.Principles of Finite Element Method (FEM)

9.Space, Time and Space-Time elements

10.Algorithms of FEM

11.Solving of systems of nonlinear algebraic equations

12.Computer implementation of FEM

13.Error analysis

14.Methods of mesh generation for FEM

Syllabus of tutorials:

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Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: