# 101.803 Partial Differential Equations This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2023W 2022W 2021W 2020W 2019W

2022W, VU, 4.5h, 7.0EC

## Properties

• Semester hours: 4.5
• Credits: 7.0
• Type: VU Lecture and Exercise
• Format: Online

## Learning outcomes

After successful completion of the course, students are able to

• recognize the most important basic types of partial differential equations,
• apply approaches and the necessary mathematical foundations to solve PDEs,
• classify second order linear partial differential equations,
• to calculate generalized and fundamental solutions and thus to solve boundary and initial value problems,
• examine the existence of solutions and
• present their solutions in front of peers.

## Subject of course

Quasilinear first order equations. Linear elliptic, parabolic, and hyperbolic equations of second order. Methods: maximum principle, Sobolev spaces, variational principles, spectral analysis

## Teaching methods

Lectures, exercies and a revision course are being offered. In the lecture there will be an introduction to theory and examples will be calculated. Once a week, exercise-sheets will be calculated on the blackboard by the students.The repetition offers the possibliy to make questions relating the lecture. The repetition is a complementary and optional offer.

In the WS2020 the lectures are provided by Prof. Jüngel as videos in TUWEL. Questions can be posed in the weekly Q&A hour ("repetitorium"). The latter takes place via zoom.

## Mode of examination

Immanent

This courses is blocked until Christmas.

A first meeting will be organized in the first week of October.

## Course dates

DayTimeDateLocationDescription
Tue13:00 - 15:0004.10.2022 - 24.01.2023FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu13:00 - 15:0006.10.2022 - 26.01.2023FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Partial Differential Equations - Single appointments
DayDateTimeLocationDescription
Tue04.10.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu06.10.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue11.10.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu13.10.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue18.10.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu20.10.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue25.10.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu27.10.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu03.11.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue08.11.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu10.11.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu17.11.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue22.11.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu24.11.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue29.11.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu01.12.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue06.12.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue13.12.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Thu15.12.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen
Tue20.12.202213:00 - 15:00FH Hörsaal 3 - MATH VU Partielle Differentialgleichungen

## Examination modalities

2 written tests + exercises (on blackboard) + 1 oral exam

## Group dates

GroupDayTimeDateLocationDescription
Gruppe AThu10:00 - 12:0006.10.2022 - 26.01.2023Sem.R. DA grün 04 101.803 Partial Differential Equations Gruppe A
Gruppe BFri14:00 - 16:0007.10.2022 - 20.01.2023Sem.R. DA grün 03 A 101.803 Partial Differential Equations Gruppe B

## Course registration

Use Group Registration to register.

## Group Registration

GroupRegistration FromTo
Gruppe A01.09.2022 00:0009.10.2022 23:59
Gruppe B14.09.2022 00:0009.10.2022 00:00

## Curricula

Study CodeObligationSemesterPrecon.Info
033 201 Technical Mathematics Mandatory5. Semester
066 394 Technical Mathematics Mandatory elective
066 395 Statistics and Mathematics in Economics Mandatory elective
066 405 Financial and Actuarial Mathematics Mandatory elective

## Literature

* for the individual chapters of the course:
§1: Strauss §1.1-1.5; Evans §2.1
§2: Evans §3.2; Strauss §1.6, (14.1)
§3: Renardy-Rogers §5.1-5.3; Strauss §12.1
§4: Evans §2.2; Strauss §6.1-6.3, 7.3, 12.2
§5: Evans §5+6
§6: Straus §12.3, 2.4, 4.1; Evans §2.3.1, 2.3.3, 4.3.1, D.6, (7.1)
§7: Straus §2.1-2.2, 2.5, 3.2, 4.1, 9.1; Evans §2.4.1a, 2.4.3, 7.2

* general:
W.A. Strauss: Partial Differential Equations - An Introduction, John Wiley & Sons, 1992
L.C. Evans: Partial Differential Equations, AMS, 1998
F. John, Partial Differential Equations, Springer, New York, 1975.
M. Renardy, R.C. Rogers, An Introduction to Partial Differential Equations, Springer, New York, 1993
M.E. Taylor, Partial Differential Equations - Basic Theory, Springer, 1996

## Previous knowledge

* analysis 1-3
* differential equations 1 (solving equations of 1st and 2nd order with constant coefficients [also inhomogeneous], variation of constants, separation of variables)
* functional analysis (in particular compactness, strong/weak convergence, L^p spaces, Hilbert spaces, dual spaces, Riesz-Fischer representation theorem, linear operators, spectrum)

It is recommended to take the exams for the above mentioned lectures before attending the lecture Partial Differential equations.

German