FAST-DAB040Acad. year: 2020/2021
Mathematical approaches to the analysis of engineering problems, namely ordinary and partial differential equations, directed to numerical calculations - deeper knowledge than from the course DA01.
Institute of Mathematics and Descriptive Geometry (MAT)
Learning outcomes of the course unit
At the level of the course DA01.
Recommended optional programme components
Recommended or required reading
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
1. Formulation of the initial-value problem for ordinary differential equations of degree 1, basic properties, existence and uniqueness of solutions.
2. Basic numerical methods for the initial-value problems and their absolute stability.
3. Introduction to the variational calculus, basic spaces of integrable functions.
4. Classical and variational formulations of elliptic problems for ordinary differential equations of degree 2, basic physical meanings.
5. Standard finite difference method for elliptic problems for ordinary differential equations (ODE) of degree 2 and its stable modifications.
6. Approximation of boundary-value problems for ODE of degree 2 by the finite element method.
7. Classical and variational formulation of elliptic problems for ODE od degree 4 and approximation by the finite element method.
8. Classical and variational formulation of elliptic problems for partial differential equations od degree 2.
9. Finite element method for elliptic problems for partial differential equations od degree 2.
10. Finite volume method.
11. Discretization of non-stationary problems for degree 2 differential equations by the method of lines.
12. Mathematical models of flow. Nonlinear problems and problems with dominating convection.
13. Numerical methods for the models of flow.
Specification of controlled education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Classification of course in study plans
- Programme DKC-GK Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme DPA-GK Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme DKA-GK Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme DPC-GK Doctoral, 2. year of study, winter semester, 10 credits, compulsory-optional
Type of course unit
39 hours, optionally
Teacher / Lecturer