- fixed point theorems,
- integration and differentiation in Banach spaces,
- the theory of monotone operators and their applications in the study of nonlinear elliptic and parabolic partial differential equations.
Nonlinear Functional Analysis with Applications to PDE (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-70-14-M-7||Nonlinear Functional Analysis with Applications to PDE||4.5 CP (135 h)|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-SPAS] Analysis and Stochastics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Nonlinear Functional Analysis with Applications to PDE
|P||28 h||107 h||-||-||PL1||4.5||irreg.|
- About [MAT-70-14-K-7]: Title: "Nonlinear Functional Analysis with Applications to PDE"; Presence-Time: 28 h; Self-Study: 107 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 86319 ("Nonlinear Functional Analysis with Applications to PDE")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
By studying concrete examples, they have gained a precise and independent handling of the terms, propositions and methods of the lecture. They understand the proofs and are able to reproduce and explain them. In particular, they can critically assess, what conditions are necessary for the validity of the statements.
- H. W. Alt: Lineare Funktionalanalysis,
- H. Gajewski, K. Gröger, K. Zacharias: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen,
- D. Gilbert, N. S. Trudinger: Elliptic partial differential equations of second order,
- E. Hille, S. Phillips: Functional analysis and semigroups,
- M. Ruzicka: Nichtlineare Funktionalanalysis: Eine Einführung,
- R. E. Showalter: Monotone operators in Banach space and nonlinear partial differential equations,
- K. Yoshida: Functional analysis,
- E. Zeidler: Nonlinear functional analysis and its applications I: Fixed-point theorems,
- E. Zeidler: Nonlinear functional analysis and its applications II/B.
Requirements for attendance of the module (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-70-11-M-4] Functional Analysis (M, 9.0 LP)
- [MAT-80-11A-M-4] Numerics of ODE (M, 4.5 LP)
- [MAT-80-11B-M-4] Introduction to PDE (M, 4.5 LP)