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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

MI-NON.16 Nonlinear Continuous Optimization and Numerical Methods Extent of teaching: 2P+1C
Instructor: Completion: Z,ZK
Department: 18101 Credits: 5 Semester: Z

Annotation:
Students will be introduced to nonlinear continuous optimization, principles of the most popular methods of optimization and applications of such methods to real-world problems. They will also learn the finite element method and the finite difference method used for solving ordinary and partial differential equations in engineering. They will learn to solve systems of linear algebraic equations that arise from discretization of the continuous problems by direct and iterative algorithms. They will also learn to implement these algorithms sequentially as well as in parallel.

Lecture syllabus:
1. Partial derivative, gradient, hessian.
2. Continuous optimization of the 1st and 2nd order.
3. Quasi-Newton method, conjugate gradient method.
4. Application of methods of nonlinear continuous optimization.
5. Introduction to ordinary and partial differential equations (taxonomy, the notion of the solution, physical interpretation).
6. Ordinary differential equations - boundary value problem (exact solution, finite difference method, finite differences).
7. Ordinary differential equations - boundary value problem (finite element method).
8. Partial differential equations - stationary cases (finite difference method).
9. Partial differential equations - stationary cases (finite element method).
10. Ordinary differential equations - initial value problem.
11. Partial differential equations - nonstationary problems.
12. Iterative methods (Gauss-Seidel method, conjugate gradient method).
13. Introduction to domain decomposition methods. Parallel solvers of sets of linear equations.

Seminar syllabus:
1. [4] Cvičení algoritmů spojité optimalizace.
2. [6] Cvičení metod numerického řešení diferenciálních rovnic.

Literature:
1. Kruis, J. ''Domain Decomposition Methods for Distributed Computing''. Saxe-Coburg Publications, 2007. ISBN 1874672237.
2. Petzold, L. R. ''Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations''. Society for Industrial and Applied Mathematics, 1998. ISBN 0898714125.

Requirements:
Basic knowledge of linear algebra (vectors, matrices, systems of linear algebraic equations, Gaussian elimination method), polynoms, differential calculus (derivative, integral).

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The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NI-TI.2018 Computer Science PS Není
MI-SP-TI.2016 System Programming PZ 3


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška