Partial Differential Equations

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Course Unit Code714-0321/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredSummer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites
PrerequisitiesCourse Unit CodeCourse Unit Title
714-0369Mathematics IV
Name of Lecturer(s)Personal IDName
DOL30doc. 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 TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit40 20
        ExaminationExamination60 31