Hands on Mathematics for CS - News

• Sebastian Germesin, Stefan Nesbigall
• Dominik Jednoralski, Michael Dietrich
• Christian Hümbert, Steffen Knapp
• Suleman Parvez Butt, M Kamran Azam

• Hideo Sato, Björn Gehl
• Noreen Nasar, Sarmad Hussain
• Suleman Parvez Butt, M Kamran Azam

Function discussion

• Solve the following exercises presented in the section on Derivation rules - Rules of differentiation
  
  • Computing the derivative of triple products
  • Proof of the sum rule (only in German available)
  
  

  Use screenshots for your presentation. Make suggestions how to improve the exercises. (*)
  

• Suppose you are coaching someone in 'Derivation rules', who claims to know all the derivation rule patterns, but who does not understand how to derive the derivation rules themselves. How would you explain? Provide a general schema. Have a look at chapter on 'Derivation Rules'. (*)
  

• The Mean value theorem of differential calculus is described very(!) briefly. What does the theorem say and what is it useful for? Examine the theorem's conceptual dependency, and present its proof graphically as much as possible! Include also Rolle's theorem. You have gathered some techniques by now, try to employ them. (**)
  

• Write an applet, that given an input function, plots the function's first and second derivative (***).
  (due to the seminar end you have only 2 weeks time)
  

Numerical Integration

• Explain the rectangle aproach of the computer-based numerical integration. Compare it to the trapezoid approach. (*)
  

• What other computer-based techniques do exist? Compare to the common integration techniques learned at school. (**)
  

• Write an applet, that calculates and presents the upper and lower sum of a monotone increasing/decreasing function. Employ the rectangle technique. The stair width(?) should be variable (***).
  (due to the seminar end you have only 2 weeks time)