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Exercises at Introduction to differentiation lead participants through calculations of compound interest that introduce e (2.7182818284590...) and derivatives of functions.

Solutions of the Bessel differential equation.

Bessel functions arise in many mathematical models such as those for vibrating surfaces.

When mathematically analyzing a vibrating drum the boundary conditions lead to solutions that are harmonic functions. When using cylindrical coordinates, the solutions are sines, cosines or Bessel functions (in the radial direction).

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Marin Mersenne's name is widely known because of his interest in prime numbers that are one less than a power of two. Mersenne also did research in the area of the theory of music and musical instruments (see Wikipedia). Participants at Mersenne primes are encouraged to join the distributed computing project that allows the computing power of personal computers to help search for Mersenne prime numbers.

The Euler-Lagrange equation of classical mechanics was discovered during attempts to find a curve for which the time taken by a frictionless particle sliding down it under uniform gravity to its lowest point is independent of its starting point.

Did you know that Wikiversity can never have enough examples and solved problems? Wikiversity does not always have to re-create the wheel. Do you know a good website with mathematics example problems? Wikiversity needs branches of the Hunter-gatherers project for each academic subject area. Please make note of good online mathematics resources at Hunter-gatherers/Mathematics and link to these resources from the appropriate mathematics pages of Wikiversity.

**Example**. Did you know that there is a wiki for mathematics example problems? See www.exampleproblems.com. How do participants in the mathematics area of Wikipedia feel about linking to .com websites?

Graphical representation of a dynamical system.

"Stephen Smale awarded Wolf Prize in mathematics" by Robert Sanders

Stephen Smale, known for his work on Topology, the study of dynamical systems and a list of 18 problems in mathematics to be solved in the 21st century, known as Smale's problems.

"A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal Turing Machine." -Alan Turing