Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Partial Differential Equations I
Semester
SoSe 2023

Lecturer
Richard Höfer

Type of course (Veranstaltungsart)
Vorlesung

German title
Partielle Differentialgleichungen I

Contents
The lecture series gives an introduction to the theory of partial differential equations (PDEs). In the first part we will study classical solution theories for PDEs. In particular we will discuss some fundamental equations and examples and show limitations of classical solution concepts. In the second part of the lecture series an introduction to the modern theory of PDEs is given, which is based on a weaker notion of solutions and functional analytic concepts. In particular we will study elliptic PDEs. The content of the lecture consists of the following parts:
  • nonlinear PDEs of first order, method of characteristics
  • fundamental examples for PDEs of second order
  • maximum principles for elliptic and parabolic PDEs
  • distributions and Sobolev spaces
  • linear elliptic PDEs


Literature
  • M. Renardy und R. C. Rogers, An Introduction to Partial Differential Equations, Springer, 1993
  • L.C. Evans, Partial Differential Equations, American Mathematical Society, 1998


Recommended previous knowledge
Analysis I-III, Linear Algebra I: useful, but not necessary: Functional Analysis

Time/Date
Mo. 12-14 and Thu. 8-10

Location
Mo. 12-14 in M104, Thu. 8-10 in M103

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=60022
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for the exercise classes: During the first week of the lecture time in the summer
    term 2022 via the course homepage (GRIPS).
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes: 50% of the maximal points in the
    exercise sheets, satisfactory presentation of one solution
  • For module MV (without mark, "unbenotet"): passing a short oral examination
    ("Fachgespräch", 15 min.) on the content of the lecture series
Examination (Prüfungsleistungen)
  • Oral exam: Duration: 30 minutes, Date: individual, by appointment, re-exam: Date: individual,
    by appointment
  • Combined exam in agreement with the lecturer in combination with, e.g.: Functional Analysis or
    Partial Differential Equation II, oral exam: Duration: 45 minutes, Date: individual, by
    appointment
Additional comments
The combined exam is an alternative to the oral examination of 30 minutes.

Modules
BV, MV, MAngAn, PHY-B-WE3, PHY-M-VE3, CS-B-Math4, CS-M-P1, CS-M-P2, CS-M-P3

ECTS
9