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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-Fri 10:00-12:00, Tue+Thu 14:00-16:00

Tel.: +49 721 608 42064

Fax.: +49 721 608 46530

Classical Methods for Partial Differential Equations (Winter Semester 2015/16)

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


Schedule
Lecture: Monday 11:30-13:00 SR 1.066 / 1.067
Wednesday 11:30-13:00 SR 1.066 / 1.067
Problem class: Wednesday 14:00-15:30 Redt.
Lecturers
Lecturer Prof. Dr. Michael Plum
Office hours: Thu 13:30 - 14:30 and by appointment.
Room 3.028 Kollegiengebäude Mathematik (20.30)
Email: michael.plum@kit.edu
Problem classes M.Sc. Piotr Idzik
Office hours: by appointment
Room 3.038 Kollegiengebäude Mathematik (20.30)
Email: vil02@o2.pl

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.

Exercise sheets:

Exercise Sheet 1
Exercise Sheet 2
Exercise Sheet 3
Exercise Sheet 4
Exercise Sheet 5
Exercise Sheet 6
Exercise Sheet 7
Exercise Sheet 8
Exercise Sheet 9
Exercise Sheet 10
Exercise Sheet 11
Exercise Sheet 12
Exercise Sheet 13
Exercise Sheet 14

Exam sheet:

Exam sheet

Script:

Preliminary unofficial and uncorrected version: script

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.