# Governor's School for the Sciences 2006

## Math 251 - Application Labs

 Over the course of these 5 weeks you need to complete 15 Application Labs. Some we will do together as a class (like Labs 1, 2 & 3) the rest you can do on your own on Open Lab days. If there is a lab listed here, we've covered the material necessary for you to complete it. You might have to read some background information from the book or other source.

 Lab Type Topic Skills 01 All MATLAB I Basics of working with MATLAB 02 All MATLAB II Working with matrices in MATLAB 03 All Network Modeling Solving Linear Systems (rref), Section 11.2 04 Open Leontief Economic Modelling Solving Linear Systems (rref), Section 11.9 05 All Markov Chains Matrix equations and products, Section 11.6 06 Open Growth Models - Leslie Matrices Matrix equations and products, Section 11.10 07 Open Graph Theory Matrix products, Section 11.7 08 All Graphics Transformations I Vectors, Matrix products, Section 11.11 09 All Graphics Transformations II Vectors, Matrix products, Section 11.11 & Section 11.21 10 Open Markov Chains II - Absorbing States Matrix products, Partitions, Inverses 11 All MRCM & IFS (Fractals Again) Graphical Transformations 12 Open 3D Graphics Graphical Transformations; Projection 13 Open Cryptography Matrix-Vector Products; Modular Arithmetic 14 All Digital Signal Processing Inner Product; Orthogonality 15 All Least-Squares Fit Linear Systems; Normal Equations 16 Open Arnold's Cat Map Matrix Multiplication (just a 2x2); Graphics; Modular Arithmetic 17 Difference Equations Eigenvalues and Eigenvectors; Matrix Multiplication 18 Open Gould Index (Application to Geography) Eigenvalues and Eigenvectors 19 Open Matchmaking Inner product; weighted inner product 20 Open Seriation (Archaeology) Matrix Transpose & Product

ccollins@math.utk.edu