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.

Laplace and Fourier transform, complex analysis, fourier series, partial differential equations

Lecture (an excercise course on the subjects of the lecture is offered as a sperate course)

Hybrid Teaching

As long as the situation allows, the lecture will take place in person/in the lecture hall. Lectures are both broadcase live and recorded and can be reviewed online by participants. Access is via TUWEL. Please also register here in TISS under Course registration.

Attention: Starting from November 22nd, only distance learning via Zoom meetings.

Blocking

Attention, this lecture will be held in blocked form until Christmas (i.e. no lectures in January).
Regular lectures will be held every Monday and Tuesday from 16:10 to 16:55.
In addition, there will be lectures on 4.10, 18.10., 25.10., 29.11. and 6.12. (Mondays each) from 17:00 to 17:45 as well as on Wednesday, 10.11., from 15:10 to 16:10.

written exam

The lecture notes are available at Grafisches Zentrum. Lecture notes from the winter semester 2020 can still be used.

Calculus, ODEs, vector spaces