Module S2.1 - Advanced Mathematics
Lecturer
Dr. Holger Babovsky (e-mail: )
Coordinator
Prof. Dr. Christian Franke
Content
The lectures will cover content in the field of vector analysis:
- Line, surface and volume integrals
- Green’s theorem, Stokes theorem, Gauss’s law
- Flow of a vector field through a surface element
A section on partial differential equations includes the topics:
- Partial differential equations on the example of the wave-equation
- D’Alembert’s Method
- Separation of variables
- Bessel equation
Components of the module
- Lectures: Thursday, 14:00-16:00, SR Kollegiengasse 10
- Seminars: every second Friday 10:00-12:00; SR 5 (Helmholtzweg 4)
- For further information please visit the course space on moodle
- The online content will be provided via moodle
- If you are interested in the module, please enrol to it in Friedolin to get access to the moodle class
Requirements to complete the module
- regular work on the exercises
- exam
Exam
- t.b.a.
Overview of the individual lectures (Details can be found in the corresponding moodle class)
| Lectures | |
| Week | Subject and content |
|
1 |
Recap, Vector Opterators Vectors, Integrals, Spherical Polra Coordinates, Gradient, Divergence, Curl |
|
2 |
Line Integrals I Line Integrals, Evaluating line integrals |
|
3 |
Line Integrals II Differential criterium, conservative vector fields, potential |
|
4 |
Surface and volume integrals Double and triple integrals, Cavalieri's principle |
|
5 |
Volume integral and Green's theorem Spherical and cylindrical coordinates, Green's theorem |
|
6 |
Stokes' theorem |
|
7 |
Stokes' theorem II and Gauss' theorem |
|
8 |
Gauss' theorem II |
|
9 |
Gauss' theorem III |
|
10 |
Partial differential equations I |
|
11 |
Partial differential equations II |
|
12 |
Partial differential equations III |