Teaching: Mathematische Methoden

Current issues:

• The repeat exam takes place on the 12.10.16 in PHY 9.2.01, 10:00-12:00 st.
• Results of exam see below. View into exam: Mo, 25.07, 13:00-13:30, my office. The date of the repeat exam has to be shifted to either the 10.10. or 12.10. Please contact me until the 26.07 if this causes an overlap with other exams for you.
• The registration deadline has been prolonged, see [Flexnow] for more details.

Class data:

exercises No. 52101,

credits: 10,

4SWS.

Lecture:

Exercises:

Exam

Question time

Literature

• Christian Lang, Norbert Pucker: Mathematische Methoden in der Physik, Springer 2005
  
• Jänich: Mathematik 1, Springer
• H. Schulz: Physik mit Bleistift, Verlag Harri Deutsch, 2006
• Königsberger: Analysis 1,2, Springer
• Otto Forster: Analysis 1, Vieweg
• Gerd Fischer: Lineare Algebra, Vieweg

Exercise sheets

• Sheet 1
• Sheet 2
• Sheet 3
• Sheet 4
• Sheet 5
• Sheet 6
• Sheet 7
• Sheet 8
• Sheet 9
• Sheet 10 (V2)
• Sheet 11 (V2)
• Sheet 12
• Sheet 13
• Testklausur, Testklausur+Lösungen

Add-on

• Complex numbers multiplication <--->

  From the Taylor expansion of the $\exp$-function at $x=1$ we know that $\exp(x)=\lim\limits_{n \rightarrow \infty}{\left(1+ \frac{x}{n} \right)^n}$. This gives us a nice graphical interpretation of the relation $\exp(i\pi)=-1$ since $\exp(i\pi)=\lim\limits_{n \rightarrow \infty}{\left(1+ i\frac{\pi}{n} \right)^n}$. Doing a finite ($n_{\text{max}}$ is finite) multiplication of numbers $\left(1+ i\frac{\pi}{n} \right)$ looks as follows: complex_mult.cdf
  [To open the cdf file download the player by clicking on the pic below or open it in Mathematica]. We see how $\left(1+ i\frac{\pi}{n} \right)^n$ is approaching -1.
• Taylor expansion <--->

  Taylor expansion of
  • $\sin(x)$
  • $1/(1-x)$
  [To open the cdf file download the player by clicking on the pic below or open it in Mathematica].
• Historical notes on trigonometric functions: wiki
• Example of a product of two Levi-Civita tensors with contractions: demonstrations.wolfram.com
• Curvature and torsion of different curves: demonstrations.wolfram.com

Exam results and solutions

• results
• solutions
• View into exam: Mo, 25.07, 13:00-13:30, my office.