102.114 Revision course for Mathematics III

2019W, RE, 1.0h, 1.0EC

Properties

  • Semester hours: 1.0
  • Credits: 1.0
  • Type: RE Revision Course

Learning outcomes

After successful completion of the course, students are able to...

  • ... in the theory of complex functions ...
    • ... investigate the complex differentiability of a given function via the Cauchy--Riemann differential equations and calculate conjugate harmonic functions. 
    • ... calculate complex integrals over a parametrized curve or via the antiderivative.
    • ... identify and classify the pols of a complex function and calculate the residuum at a pole.
    • ... solve complex integrals via the Residue Theorem.
  • ... in the vector space theory of a system of functions ...
    • ... calculate the orthogonal projection of a given function onto the linear span of a given system of functions. 
    • ... calculate the coefficiets of the Fourier series of a given function.
    • ... determine the limit of the Fourier series of a given function at a specified point using the Dirichlet Theorem.
  • ... in the theory of integral-transformations...
    • ... calculate the Laplace tranform of a given function, via the definition and the elementary properties (linearity, similarity, differential, integration, shift, ...) of the Laplace transform.
    • ... dertermine the inverse of the Laplace transform of a function using the complex inversion-formula and the residue theorem.
    • ... solve initial value problems using the Lapace transform.
    • ... calculate the Fourier transform and inverse Fourier transform, via the definition and the elementary properties (linearity, similarity, differential, shift, ...) of the Fourier transform.
  • ... in the theory of linear partial differential equations ...
    • ... classify a given linear partial differential equation (order, coefficients, homogen or inhomogen, type,...).
    • ... determine a general solution of a given linear partial differential equation of first order via the method of characteristics.
    • ... determine a general solution of classical homgeneous linear partial differential equations  of second order (potential equation, heat equation, wave equation,...) by method of seperation of variables and fit the general solution to a given set of boundary conditions via application of the theory of Fourierseries.

Subject of course

Complex analysis, integral transforms, PDEs

Teaching methods

Discussion of case studies

Mode of examination

Immanent

Lecturers

  • Kniefacz, Philipp

Institute

Course dates

DayTimeDateLocationDescription
Mon14:00 - 15:0021.10.2019 - 16.12.2019FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Tue15:00 - 16:0007.01.2020FH Hörsaal 5 - TPH Vorbereitungsstunde 2. Test
Revision course for Mathematics III - Single appointments
DayDateTimeLocationDescription
Mon21.10.201914:00 - 15:00FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Mon28.10.201914:00 - 15:00FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Mon04.11.201914:00 - 15:00FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Mon11.11.201914:00 - 15:00FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Mon18.11.201914:00 - 15:00FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Mon25.11.201914:00 - 15:00FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Mon09.12.201914:00 - 15:00FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Mon16.12.201914:00 - 15:00FH 8 Nöbauer HS - MATH Repetitorium Mathematik III MB/WIMB/VT
Tue07.01.202015:00 - 16:00FH Hörsaal 5 - TPH Vorbereitungsstunde 2. Test

Examination modalities

none

Course registration

Begin End Deregistration end
07.10.2019 09:00 31.01.2020 12:00

Curricula

Study CodeSemesterPrecon.Info
No records found.

Literature

No lecture notes are available.

Previous knowledge

Die Studierenden sollten die in der Inhaltsangabe genannten Vorlesungen regelmäßig besuchen und sich mit den dort vorgetragenen Inhalten beschäftigen um gezielte Fragen stellen zu können.

Language

German