Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-80-11B-K-4

PDE: An Introduction (2V+1U, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
2 V Lecture 3.0 CP 28 h 62 h
1 U Exercise class (in small groups) 1.5 CP 14 h 31 h
(2V+1U) 4.5 CP 42 h 93 h

Basedata

SWS 2V+1U
CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. in WiSe
Level [4] Bachelor (Specialization)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-TEMA] Industrial Mathematics
Livecycle-State [NORM] Active

Notice

This course is part of the course [MAT-80-11-K-4] (normally, second half of the semester).

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
  • Examination number (Study achievement): 84023 ("Exercise Class PDE: An Introduction")
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

Contents

This course gives an introduction to the classical theory of partial differential equations. In particular, the following contents are dealt with:
  • Classification and well-posed problems,
  • Quasilinear equations: Cauchy problem,
  • Wave equation: existence, uniqueness, stability, maximum principle,
  • Poisson equation: separation ansatz, fundamental solutions, Green's function, maximum principle, existence and uniqueness,
  • Heat equation: separation of variables, Fourier transformation, semigroups, maximum principle, existence and uniqueness.

Competencies / intended learning achievements

Upon completion of this module, the students have studied and understand the extension of ordinary differential equations to partial differential equations. They understand the proofs presented in the lecture and are able to comprehend and explain them.

By completing exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies.

Literature

  • L.C. Evans: Partial differential equations,
  • F. John: Partial differential equations.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Desirable is knowledge from the course [MAT-12-27-K-3].

Modules:

Courses

Requirements for attendance (formal)

None

References to Course [MAT-80-11B-K-4]

Module Name Context
[MAT-30-10L-M-5] Specialisation Module (Teachers Training Programme Mathematics) WP: Obligation to choose in Obligatory-Modulteil #A (Lectures) 2V, 3.0 LP
[MAT-80-11B-M-4] Introduction to PDE P: Obligatory 2V+1U, 4.5 LP
[MAT-80-11-M-4] Differential Equations: Numerics of ODE & Introduction to PDE P: Obligatory 2V+1U, 4.5 LP
Course-Pool Name
[MAT-70-2V-KPOOL-4] Elective Courses Analysis and Stochastics (2V, B.Sc.)
[MAT-80-2V-KPOOL-4] Elective Courses Modelling and Scientific Computing (2V, B.Sc.)