470-8341/02 – Selected Chapters from Mathematics (VKM)
| Gurantor department | Department of Applied Mathematics | Credits | 5 |
| Subject guarantor | prof. RNDr. Zdeněk Dostál, DSc. | Subject version guarantor | prof. RNDr. Zdeněk Dostál, DSc. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | English |
| Year of introduction | 2010/2011 | Year of cancellation | |
| Intended for the faculties | FS | Intended for study types | Master, Follow-up Master |
Subject aims expressed by acquired skills and competences
Student will understand model partial differential equations, basic methods of approximation of the solution of the boundary value problems, variational equalities and inequalities, their abstract structure and methods of solution. He/she will understand the role of these conceps in applications.
Teaching methods
Lectures
Tutorials
Summary
Successful solution of the problems arising in engineering requires anunderstanding of relevant mathematics. The students will learn about basic tools and their applications for the solution of such problems.
Compulsory literature:
K. Rektorys, Variational Methods in Mathematics, Science and Engineering. Reidel, Dordrecht, 1980
Recommended literature:
G. Strang, Introduction to Applied Mathematics. Wellesley-Cambridge Press, 1986.
ISBN-13: 9780961408800
Way of continuous check of knowledge in the course of semester
Test
Written and oral exam
E-learning
Other requirements
Additional requirements for students are not.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Boundary value problems for ordinary differential equations of the 2nd order.
Finite difference discretization and boundary conditions.
Problems with non-smooth soefficients and/or right hand side.
Variational formulation of the boundary value problems.
Discretization based on variational formulation. Collocation, Ritz method, Galerkin method, finite element method.
Propertis and direct methods of solution of the discretized systems.
Conjugate gradient method with preconditioning.
Domain decomposition and multilevel methods.
Variational inequalities and their discretization.
Numerical solution of variational inequalities.
Boundary integral equations.
Bouhary element method for a model problem.
Software.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction