104.391 Mathematics 3 for CE
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2020W, VU, 3.0h, 4.0EC, to be held in blocked form
TUWEL

Properties

  • Semester hours: 3.0
  • Credits: 4.0
  • Type: VU Lecture and Exercise
  • Format: Distance Learning

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 Laplace 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

Laplace and Fourier transform, Complex Analysis, Fourier series, Partial Differential Equations

Teaching methods

Lecture with exercise courses; see other informationes below

Mode of examination

Immanent

Additional information

Vorlesung:

Die Vorlesung findet online statt. Weiter Informationen finden Sie auf der zugehörigen Kursseite im TUWEL.

Übung:

Die Übungen finden ebenfalls online statt. Alle Informationen finden Sie auf der Kursseite für die Übung im TUWEL.

Übungstests und mündliche Prüfung:

Wenn Sie nach dem 2. Übungstest die Mindestvoraussetzungen erfüllen, können Sie sich für die mündliche Prüfung zum Vorlesungsteil der Lehrveranstalltung anmelden. Zugangsvoraussetzung für die mündliche Prüfung sind mindestenes 40% der zusammengerechneten Testpunkte. Die Gesamtnote wird in der mündlichen Prüfung auf Basis Ihrer Test- und Übungsleistung ermittelt.

Lecturers

Institute

Examination modalities

written exam

Course registration

Begin End Deregistration end
15.09.2020 09:00 14.10.2020 12:00 14.10.2020 12:00

Curricula

Study CodeSemesterPrecon.Info
066 505 Civil Engineering Science

Literature

Ein Skriptum zur Vorlesung ist im Grafischen Zentrum erhältlich.

Previous knowledge

Calculus, ODEs, vector spaces

Miscellaneous

  • Attendance Required!

Language

German