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.

• Complex analysis (line integrals, power series, and residue theorem)
• Fourier series (orthogonal systems of functions)
• Integral transforms (Laplace- and Fourier transform)
• Linear partial differential equations (method of characteristics, heat and wave equations)

In this exercise course the examples will be presented by the lecturers and there will be two written exams during the semester. The list of examples can be found in the "Documents" category of this course.

The course consists of six exersice classes and two midterm exams. To take part, please register for one of the groups (A, B, C).

During the exercise classes, problems and their solutions will be presented to you. Attendance is not compulsory here, but use the chance to ask questions!

Your final grade is determined solely by the two exams, see below for details.

Dates

• October 31
• November 7
• November 14
• First exam: November 23, 2019 (substitute exam: December 2, 2019)
  
• November 28
• December 5
• December 12
• Second exam: January 11, 2020 (substitute exam: January 20, 2020)

Entscheidungstest: January 27, 2020

Preparation Classes for the Tests

• November 21 (FH8 15-17h and GM2 14-16h)
• January 9 (FH8 15-17h and HS8 14-16h)

If you are sick or elsewise hindered to take the exams, please contact your tutor (including a medical certificate in the first case). There will be a substitute exam for you about a week later.

 If any questions arise, do not hesitate to contact your tutor, either via mail (firstname.lastname@tuwien.ac.at) or personally during his office hours!

There are two midterm exams (23. November 2019 and 11. January 2020) each of which lasts 90 minutes. There will be problems concerning the topics of the exercise classes. The maximum score on each exam is 20 points. Your final grade is determined by the sum of the two exam scores in the following way:

• Excellent:                40 - 35 points
• Good:                      34,9 - 30 points
• Satisfactory:            29,9 - 25 points
• Adequate:               24,9 - 20 points
• Unsatisfactory:        less than 20 points

The way in which this sum is put together does not matter, e.g. first exam 0 points, second exam 20 point, yields the same grade ('Adequate') as first exam 10 points, seconds exam 10 points.

Entscheidungstest:

If your total score is less than 20 points, but on one of the exams you have gotten at least 10 points, your are allowed to take part in a 'last chance'-exam at the end of the semester. If you pass there, your final grade will be 'Adequate' (regardless of your actual exam score).

Notes of the accompanying lecture Mathematik 3 für MB, WIMB und VT are available at Grafisches Zentrum. These notes also contain the problems we are going to discuss.

Multivariate Calculus, ODEs, vector spaces and linear algebra - all this was thoroughly covered in the Math 1 and 2 courses.