Course Details
Mathematics 2
Academic Year 2023/24
DAB040 course is part of 4 study plans
DPC-GK Winter Semester 2nd year
DPA-GK Winter Semester 2nd year
DKC-GK Winter Semester 2nd year
DKA-GK Winter Semester 2nd year
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.
Course Guarantor
Institute
Syllabus
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.
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.
Prerequisites
At the level of the course DA01.
Language of instruction
Czech
Credits
10 credits
Semester
winter
Forms and criteria of assessment
examination
Specification of controlled instruction, the form of instruction, and the form of compensation of the absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 3 hours/week, elective
Syllabus
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.