470-4114/03 – Variational Methods (VM)
Gurantor department | Department of Applied Mathematics | Credits | 4 |
Subject guarantor | prof. RNDr. Jiří Bouchala, Ph.D. | Subject version guarantor | prof. RNDr. Jiří Bouchala, Ph.D. |
Study level | undergraduate or graduate | Requirement | Choice-compulsory |
Year | 1 | Semester | summer |
| | Study language | Czech |
Year of introduction | 2016/2017 | Year of cancellation | 2020/2021 |
Intended for the faculties | USP | Intended for study types | Follow-up Master |
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.