Final Project Ideas

In this class, you have learned the basics of

The purpose of the final project is to put all of this together into an web-based teaching project which will present a mathematical topic (using the tools you have developed).

The following is intended to give you some ideas. Clearly, the more you put into the final project, the better you will do on it...

  1. Function transformations. The basic operations (+,-,*,/) and function composition can create new functions from a basic set of elementary functions (sin,cos,exp,x^n,log,etc).

    The user should be able to input one or more function, and then manipulate them to create new functions which are graphed. This would best be done through a GUI, but an interactive m-file can also work.

  2. Root finding. Finding the roots (ie where a function crosses the horizontal axis) can be accomplished via the bisection method (easily implemented in matlab).

    The user should be able to input a function, and then have it graphed. Entering in two starting values for the bisection method, the interval containing a root is refined till a result is given (which can be graphed).

    Gui or interactive m-file can be done.

    Secant or Newton's method can also be used...

  3. Matrix transformations. 3D vectors can be manipulated using 4x4 transformation matrices. This forms the basis of all modern computer graphics, as well as video games...

    An array of 3d points (e.g. a graph of a function, or a mesh) can be rotated, stretched, even given a change of perspective.

    Look up "4x4 transformation matrices" for further info.

  4. Conic Sections General quadratics (in two variables) can be graphed in the form z=f(x,y)=Ax^2+Bxy+Cy^2+...

    The user can input a set of coefficients, which then result in a graph of the surface (using plot3).

    If two different surfaces are generated, their intersection(s) can be examined.

  5. Differential Equations Chaotic systems can be examined by solving systems of nonlinear odes.

  6. Linear Equation Solver Step by step solution of nxn linear systems (using Gaussian Elimination/Row Reduction) can be "visualized" by printing out the augmented matrix at each step ...