Advanced Mathematics for Engineers with Applications

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

This course will be devoted to the various topics of mathematics including the following chapters: numerical methods for solving (partial) differential equations, elements of numerical optimization, a posteriori error estimates of numerical solution of partial differential equations, elements of qualitative theory of differential equations.

Requirements:

For doctoral students who have good knowledge of mathematical calculus.

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

References:

[1] K. Rektorys: Variational Methods in Mathematics, Science and Engineering,

2nd Edition, D. Reidel Publishing Company (Dordrecht) and SNTL (Prague), 1980.

[2] C. Grossmann; H.-G. Roos; M. Stynes: Numerical treatment of partial differential equations.

Springer, Heidelberg-Berlin, 2007.

[3] A. Quarteroni, A. Valli: Numerical Approximation of Partial Differential Equations,

Springer, Berlin, 1994.

[4] J. Nocedal, S. J. Wright: Numerical Optimization, Springer, Berlin, 1999, 2006.

[5] G. Lord, C. Powell, T. Shardlow, An Introduction to Computational Stochastic PDEs, Cambridge Texts in Applied Mathematics, 2014.

[6] M. Ainsworth, J. T. Oden, A Posteriori Error Estimation in Finite Element Analysis, Wiley, 2000.

[7] T. Kapitaniak, Chaos for Engineers, Theory, Applications, and Control Theory, Springer-Verlag Berlin Heidelberg 2000.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: