470-4114/02 – Variational Methods (VM)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantorprof. RNDr. Jiří Bouchala, Ph.D.Subject version guarantorprof. RNDr. Jiří Bouchala, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year1Semestersummer
Study languageEnglish
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
BOU10 prof. RNDr. Jiří Bouchala, Ph.D.
VOD03 doc. Mgr. Petr Vodstrčil, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+10

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
Tutorials

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:

M. Renardy, R. C. Rogers: An introduction to partial differential equations, Springer-Verlag, New York, 1993. E. Zeidler: Applied Functional Analysis, Springer-Verlag, New York, 1995.

Recommended literature:

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

Way of continuous check of knowledge in the course of semester

Podmínky udělení zápočtu: Aktivní účast na cvičeních. Vyřešení zadaných problémů.

E-learning

Other requirements

There are not defined other requirements for student.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Lebesgue Integral. Lebesgue Spaces. Distributions. Sobolev Spaces. Trace Theorem. Weak Solutions of Boundary Value Problems. Lax Milgram Theorem. Existence and Uniqueness of Weak Solutions. Regularity of Weak Solution. Energy Functional. Ritz and Galerkin Methods.

Conditions for subject completion

Part-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)		Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21 3
Mandatory attendence participation: Participation at tutorials is recommended.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC AMv P English Ostrava 1 Compulsory study plan
2024/2025 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics MFA P English Ostrava 1 Compulsory study plan
2023/2024 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC AMv P English Ostrava 1 Compulsory study plan
2023/2024 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics MFA P English Ostrava 1 Compulsory study plan
2022/2023 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics MFA P English Ostrava 1 Compulsory study plan
2022/2023 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC AMv P English Ostrava 1 Compulsory study plan
2021/2022 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics MFA P English Ostrava 1 Compulsory study plan
2021/2022 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC AMv P English Ostrava 1 Compulsory study plan
2021/2022 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2020/2021 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2020/2021 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC AMv P English Ostrava 1 Compulsory study plan
2020/2021 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics MFA P English Ostrava 1 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan
2019/2020 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics MFA P English Ostrava 1 Compulsory study plan
2019/2020 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC AMv P English Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Compulsory study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2017/2018 Summer