714-0324/03 – Matrix analysis and variational calculus (MVA)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 2 |
| Subject guarantor | prof. RNDr. Radek Kučera, Ph.D. | Subject version guarantor | prof. RNDr. Radek Kučera, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | English |
| Year of introduction | 2016/2017 | Year of cancellation | 2018/2019 |
| Intended for the faculties | FS | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods. Students should learn how to analyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.
Teaching methods
Lectures
Tutorials
Summary
The course deals with the matrix calculus and the variational calculus in the context of engineering problems. The course ends by the algorithmization of the finite element method.
Compulsory literature:
Recommended literature:
1. A. Tveito, R. Winther: Introduction to Partial Differential Equations: A Computational Approach. Springer, Berlin, 2000.
2. http://mi21.vsb.cz/
Way of continuous check of knowledge in the course of semester
Tests and credits
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Exercises
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Conditions for obtaining credit points (CP):
- participation in exercises, 20% can be to apologize
- completion of three written tests, 0-15 CP
- completion of two programs, 5 CP
Exam
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- written exam 0-60 CP, successful completion at least 25 CP
- oral exam 0-20 CP, successful completion at least 5 CP
The exam questions are analogous to the program of the lectures.
E-learning
Other requirements
Credits are awarded on submission of all properly drafted tasks and active participation in exercises.
The condition of the test are credits. Part of the test is oral with written preparation.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Week. Lecture
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1st Vector space, linear mappings and matricies.
2nd Scalar product and orthogonality, orthogonalization procedure.
3rd Eigenvalues and eigenvectors, spectral decomposition.
4th Singular values and singular decomposition. Generalized inverse.
5th Matrix factorizations. Fast solving of linear systems.
6th Gradient descent method. Preconditioning.
7th Linear, bilinear and quadratic forms. Classification.
8th Weak solutions of differential equations.
9th Theorems on existence of weak solutions.
10th Variational solving differential equations. Ritz-Galerkin method.
11th Fundamentals of the finite element method.
12th Model boundary value problems for ODEs.
13th Model boundary value problems for PDEs.
14th Comparision with the finite difference method.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.