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Partial differential equations for engineers

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Course Unit Code310-3146/01
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
KUC14prof. RNDr. Radek Kučera, Ph.D.
Summary
The aim of the course is to provide an overview of mathematical modeling using partial differential equations. The subject is adapted to the use of models of equations of mathematical physics in practical engineering tasks. Students will acquire skills and competences that will enable them to understand the description of selected physical phenomena using partial differential equations and in reasonably simple situations solve these equations using classical methods.
Learning Outcomes of the Course Unit
The course deals with mathematical modeling based on equations of mathematical physics. Students will acquire advanced knowledge and skills of given parts of mathematics adapted to the needs of practical modeling in engineering practice. The course focuses on classical methods of solving problems expressed by partial differential equations.
Course Contents
1. Introduction, terminology, motivational examples.
2. Equations of the first order, method of characteristics.
3. Classification of second order equations.
4. Derivation of heat conduction equation in rod and body.
5. Derivation of equation of diffusion and vibration of string.
6. Derivation of equations using the variational principle.
7. Method of characteristics for hyperbolic equations.
8. Fourier series.
9. Fourier series method.
10. Method of integral transformation.
11. Green function method.
12. Principle of maximum and uniqueness of tasks.
13. Potential method.
14. Final summary, evaluation of results, reserve.
Recommended or Required Reading
Required Reading:
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6
Drábek, P., Holubová, G.: Parciální diferenciální rovnice. http://mi21.vsb.cz.
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6
Recommended Reading:
Ka Kit Tung: Methods for Partial Differential Equations. https://amath.washington.edu/courses/2019/spring/amath/503/a.
Franců, J.: Parciální diferenciální rovnice. Akademické nakladatelství CERM, 2018 (5. vydání).
Drábek, P., Holubová, G.: Parciální diferenciální rovnice: úvod do klasické teorie. Západočeská univerzita, Plzeň, 2001.
Ka Kit Tung: Methods for Partial Differential Equations. https://amath.washington.edu/courses/2019/spring/amath/503/a.
Planned learning activities and teaching methods
Lectures, Tutorials
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
        CreditCredit20 5
        ExaminationExamination80 51