Differentiation Quizzes  

How to use this topic lion

Step 1:  

Complete Quiz 1.
Step 2:   If successful move on to the next topic.
If unsuccessful investigate the topic using the websites below.
Step 3:   Complete Quiz 2.
Step 4:   If successful move on to the next topic.
If unsuccessful investigate the topic further using the websites below.
Step 5:   Complete Quiz 3.
Step 6:   If successful move on to the next topic.
If unsuccessful investigate the Further Resources below.
Useful Websites lion

There are probably two distinct areas that need attention in differentiation, understanding the concept of derivative functions and the mechanics of differentiation. The http://www.univie.ac.at/future.media/moe/galerie/ has quite a lot of interactive material but some theoretical introduction would be worthwhile. The site http://cow.math.temple.edu/ is a calculus on the web (cow) site. It must be navigated through carefully. It has a series of interactive problems and the help button explains the theory. To consider differentiation go to Calculus Book 1 and then the derivative. Before attempting the problems push the help button to get the theory. The section on limits is probably more technical than you need but the sections on differentiation of polynomials and using the product, chain and quotient rules is very good. There are very few other sites that are reliably available.

The calculus booklet from the Maths Learning Centre at http://www.usyd.edu.au/stuserv/academic_support/maths_learning_centre/publications.shtml. is a good source of explanations and exercises.

An introduction to the concept of slope as a derivative can be found at http://www.univie.ac.at/future.media/moe/galerie/geom1/geom1.html. It looks at the relationship between slope and angles as well as introducing the concept of dx and dy.

The next site at http://www.univie.ac.at/future.media/moe/galerie/diff1/diff1.html has 5 applets, the first looks at the definition of derivative and shows the tangent to a curve as you move along the curve, stating the slope as it goes, the next 3 are useful puzzles that investigate the relationship between a function and its derivative. It also links to http://www.univie.ac.at/future.media/moe/tests/diff1/ablerkennen.html a larger derivative puzzle of the same form as the 3 previous applets. The site finishes with an applet on 1st and 2nd derivatives. It looks at a cubic polynomial and shows what happens to the function, its 1st derivative and 2nd derivative as you change the coefficients of the polynomial.

Further Resources lion

The Mathematics Learning Centre holds workshops at the beginning of each semester. Keep an eye out for dates.

There is a Massey Universtiy Site that covers most topics well and is worth having a good look at. There are also some quizzes at http://webct-ce.massey.ac.nz/SCRIPT/tsamith1/scripts/serve_home that can help you identify problem areas.