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Workgroup Nonlinear Partial Differential Equations

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 3.029

Address
Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe
Germany

Office hours:
Mon, Wed, Thu 10-13 and by email

Tel.: +49 721 608 42064

Fax.: +49 721 608 46530

Classical Methods for Partial Differential Equations (Winter Semester 2019/20)

Lecturer: Prof. Dr. Michael Plum
Classes: Lecture (0105300), Problem class (0105310)
Weekly hours: 4+2


Exam review

The review will take place on June 9, 2020. We have already emailed all students personally.

The grades have already been published in the campus system to prevent any disadvantages for you.

Should changes become necessary after the exam review, these can be made.

If you have any questions, please contact: marion.ewald@kit.edu


Schedule
Lecture: Tuesday 11:30-13:00 SR 2.066
Thursday 11:30-13:00 SR -1.012 (UG)
Problem class: Wednesday 14:00-15:30 Redtenbacher-Hörsaal
Lecturers
Lecturer Prof. Dr. Michael Plum
Office hours: Please get in contact by email.
Room 3.028 Kollegiengebäude Mathematik (20.30)
Email: michael.plum@kit.edu
Problem classes M.Sc. Zihui He
Office hours: by appointment
Room 3.030 Kollegiengebäude Mathematik (20.30)
Email: zihui.he@kit.edu

A differential equation is a relation between an unknown function (to be determined) and its derivatives. While for ordinary differential equations the unknown function depends on a single independent variable, it depends on several variables for partial differential equations.

A huge variety of processes in science and technology is described by partial differential equations, which therefore belong to the most important objects of investigation in Applied Mathematics.

The number of phenomena occurring in the context of partial differential equations, and the number of methods and techniques to investigate them, is by far too complex to be the content of a one semester course. The lecture course can therefore only be of an introductory type. Topics to be treated are e.g. the classical wave-, Poisson-, and heat equation, maximum principles, separation of variables, classification of quasilinear second-order equations and first-order systems, normal forms, a fixed-point approach for second-order hyperbolic equations. Strong emphasis will be put on many examples from physics and engineering.

The lecture course addresses students in their fifth semester (third year) or higher, with substantial knowledge in analysis and linear algebra. It is suitable for students of mathematics, and for students of other subjects who have strong mathematical interests.

The lectures will be accompanied by exercise lessons. Attendance of these exercises is strongly recommended to all participants.

As already mentioned, this lecture course can cover only a small portion of the overall topic of partial differential equations. Deeper knowledge can be aquired in further subsequent courses.

Script:
Preliminary unofficial and uncorrected version: script

Exercise Sheets:
The first exercise class will be on 23.10.2019!
Exercise sheet 1, to be explained on 23.10.2019
Exercise sheet 2, to be explained on 30.10.2019
Exercise sheet 3, to be explained on 06.11.2019
Exercise sheet 4, to be explained on 13.11.2019
Exercise sheet 5, to be explained on 20.11.2019
Exercise sheet 6, to be explained on 27.11.2019
Exercise sheet 7, to be explained on 04.12.2019
Exercise sheet 8, to be explained on 11.12.2019
Exercise sheet 9, to be explained on 18.12.2019, solution ex.30
Exercise sheet 10, to be explained on 08.01.2020
Exercise sheet 11, to be explained on 15.01.2020
Exercise sheet 12, to be explained on 22.01.2020
Exercise sheet 13, to be explained on 29.01.2020
Exercise sheet 14, to be explained on 05.02.2020
Holiday exercise sheet


Examination

WS2019/20:
exam sheet
solution
Exam review (Klausureinsicht): TBA.

SS2020: The examination will be in the form of a written exam, which takes place on 24.09.2020, 16:00-18:30, in the 30.22 Gaede-Hörsaal. The exam can be registered in the CAMPUS system from 01.05.2020 to 01.08.2020. The deregistration is possible until 23.09.2020. If you couldn't find the exam in your CAMPUS system, please register with the student office.

References

Textbooks:

Evans, L. C.: Partial Differential Equations; Graduate Studies in Mathematics 19, American Mathematical Society.
John, F.: Partial Differential Equations; Springer.
Copson, E. T.: Partial Differential Equations; Cambridge University Press.
Courant, R., Hilbert, D.: Methods of Mathematical Physics, Vol. I + II; Wiley Classics.
Hellwig, G.: Partial Differential Equations; Teubner.


For those who understand German (or want to learn it):

Hellwig, G.: Partielle Differentialgleichungen; Teubner.
Leis, R.: Vorlesungen über partielle Differentialgleichungen zweiter Ordnung; Bibliographisches Institut, Mannheim.