* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code | 714-0321/01 | |||||
---|---|---|---|---|---|---|

Number of ECTS Credits Allocated | 4 ECTS credits | |||||

Type of Course Unit * | Optional | |||||

Level of Course Unit * | Second Cycle | |||||

Year of Study * | First Year | |||||

Semester when the Course Unit is delivered | Summer Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech | |||||

Prerequisites and Co-Requisites | ||||||

Prerequisities | Course Unit Code | Course Unit Title | ||||

714-0369 | Mathematics IV | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

DOL30 | doc. RNDr. Jarmila Doležalová, CSc. | |||||

Summary | ||||||

Learning Outcomes of the Course Unit | ||||||

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. | ||||||

Course Contents | ||||||

Syllabus of lecture
1. Fourier series: periodic functions, Fourier coefficients, functions of the period 2, function of the period T, even and odd functions 2. Even and odd functions, half - range cosine and sine series, convergence of Fourier series 3. Solution of 2nd order linear differential equations with constant coefficients by Fourier series 4. Partial differential equations: general discussion 5. Methods of solutions of partial differential equations of the first order 6. Methods of solutions of partial differential equations of the second order 7. Fourier´s method of separation 8. 2nd order partial linear differential equations 9. Canonical form of 2nd order partial linear differential equations 10. Laplace equation: separated solutions, boundary conditions 11. Solution of the one-dimensional wave equation: d’Alembert solution, method of the separation of variables, 12. Solution of a boundary problem 13. Solution of the heat-conduction: one dimensional heat conduction equation, separation method. 14. Reserve | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993
| ||||||

Drábek, P.- Holubová, G.: Parciální diferenciální rovnice. http://mi21.vsb.cz
Škrášek, J.-Tichý, Z.: Základy aplikované matematiky II, SNTL Praha, 1986 | ||||||

Recommended Reading: | ||||||

James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993 | ||||||

Franců, J.: Parciální diferenciální rovnice. Akademické nakladatelství CERM, Brno 2003. ISBN 80-214-2334-X
Drábek, P. – Holubová, G.:. Parciální diferenciální rovnice: úvod do klasické teorie. Západočeská univerzita, Plzeň 2001. ISBN 80-7082-766-1 Ošťádalová, E. a kol.: Parciální diferenciální rovnice. Skriptum VŠB Ostrava, 1988 http://mdg.vsb.cz/M | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Individual consultations, Tutorials, Project work | ||||||

Assesment methods and criteria | ||||||

Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing | |||

Credit and Examination | Credit and Examination | 100 (100) | 51 | |||

Credit | Credit | 40 | 20 | |||

Examination | Examination | 60 | 31 |