310-3143/01 – Partial Differential Equations (PDR)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year1Semestersummer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFSIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+1

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
Individual consultations
Tutorials
Project work

Summary

Studenti se seznámí s Fourierovými řadami a s klasickými metodami řešení parciálních diferenciálních rovnic. V první kapitole jsou probírány Fourierovy řady v rozsahu potřebném pro další výuku. Ve druhé kapitole se studenti velmi stručně seznámí s parciálními diferenciálními rovnicemi prvního řádu. Teorie parciálních diferenciálních rovnic druhého řádu je zaměřena na Fourierovu metodu separace proměnných a metodu charakteristik. Jádro předmětu je v řešení lineárních parciálních diferenciálních rovnic druhého řádu (Laplaceova rovnice, vlnová rovnice, rovnice vedení tepla).

Compulsory literature:

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

Recommended literature:

Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007.

Way of continuous check of knowledge in the course of semester

Set of homework examples, credit test, oral exam.

E-learning

https://amath.washington.edu/courses/2019/spring/amath/503/a

Other requirements

Set of homework examples, credit test, oral exam.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

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

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 40  20
        Examination Examination 60  25
Mandatory attendence parzicipation: 80%

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Occurrence in study plans

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2019/2020 (N2301) Mechanical Engineering (3901T003) Applied Mechanics P Czech Ostrava 1 Optional study plan
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2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (10) Rail Transport P Czech Ostrava 1 Optional study plan
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2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (30) Transport Technology P Czech Ostrava 1 Optional study plan
2019/2020 (N2301) Mechanical Engineering (2301T003) Transport Equipment and Technology (40) Air Transport P Czech Ostrava 1 Optional study plan
2019/2020 (N2301) Mechanical Engineering (2302T043) Hydraulics and Pneumatics P Czech Ostrava 1 Optional study plan
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Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner