470-6102/02 – Variational Methods for Engineers (VM)

Gurantor departmentDepartment of Applied MathematicsCredits10
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 2+0
Combined Examination 10+0

Subject aims expressed by acquired skills and competences

Students, who pases the course, will be able to define a weak solution for various kinds of elliptic boundary value problems, to prove the existence of a unique solution and master a couple of approaches to solve it numerically.

Teaching methods

Lectures
Project work

Summary

The course is offered throughout the university. Within the course the students are introduced into weak formulations of various kinds of elliptic boundary value problems, solvability conditions as well as fundamental properties of the weak solutions. The correct understanding of these notions is necessary to succeed with solution of various engineering problems.

Compulsory literature:

E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995.

Recommended literature:

M. Renardy, R. C. Rogers: An introduction to partial differential equations, Springer-Verlag, New York, 1993.

Way of continuous check of knowledge in the course of semester

Individual work.

E-learning

Další požadavky na studenta

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Lebesgue integral. 2. Lebesgue spaces L^p(Omega). 3. Lipschitz domains. 4. Distributions. 5. Sobolev spaces. 6. The Trace Theorem. 7. Weak solutions of BVP. 8. Existence and uniqueness of weak solutions. 9. Regularity. 10. Energy functional. 11. Spectrum. 12. Methods od discretisation.

Conditions for subject completion

Full-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (P0613D140006) Computer Science P English Ostrava Choice-compulsory type B study plan
2019/2020 (P0541D170006) Computational and Applied Mathematics P English Ostrava Choice-compulsory type B study plan
2019/2020 (P0541D170006) Computational and Applied Mathematics K English Ostrava Choice-compulsory type B study plan
2019/2020 (P0613D140006) Computer Science K English Ostrava Choice-compulsory type B study plan
2019/2020 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P English Ostrava Choice-compulsory study plan
2019/2020 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K English Ostrava Choice-compulsory study plan
2019/2020 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P English Ostrava Choice-compulsory study plan
2019/2020 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2018/2019 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P English Ostrava Choice-compulsory study plan
2018/2019 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P English Ostrava Choice-compulsory study plan
2018/2019 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K English Ostrava Choice-compulsory study plan
2018/2019 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P English Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P English Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K English Ostrava Choice-compulsory study plan
2017/2018 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P English Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P English Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K English Ostrava Choice-compulsory study plan
2016/2017 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics P English Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1103V036) Computational and Applied Mathematics K English Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics P English Ostrava Choice-compulsory study plan
2015/2016 (P1807) Computer Science, Communication Technology and Applied Mathematics (1801V001) Informatics K English Ostrava Choice-compulsory study plan

Occurrence in special blocks

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