Related: Section 2.6

Use Matrix Data (csv)

Total Industry Output Vector (csv)

Sample Code (maple worksheet)

Note that the Use Matrix is not the same as the consumption matrix in Strang's book. To get the consumption matrix you must rescale column j of the Use Matrix by dividing by entry j of the Total Industry Output Vector.

Related: Section 4.8, Section 4.9

Compare the waveforms of several musical instruments playing the same note. Compare their energy spectra.

Sample Code (maple .mw)

puretone.wav

flute.wav

piano.wav

trumpet.wav

Related: Chapter 7

Sample Code (maple .mw)

knot.bmp

Consider the non-linear discrete planar dynamical system that takes a point (x_i,y_i) in the plane and moves it to the point (x_{i+1},y_{i+1}) where:

x_{i+1}=1+ y_i - a (x_i)^2

y_{i+1}=b x_i

Do a few plots for a=1.4 and b=.3 and discuss the results.

What happens for different values of a and b?

Also read this well-written 2005 master's thesis here by

Make a demonstration of computer graphics operations, to illustrate how to take a 3D image and display it in a different size, at a different location, rotated in 3D. Feel free to embellish this computer science and mechanical engineering project with your own ideas of what is interesting. Try to learn some elementary computer graphics, especially related to robotics, involving homogeneous coordinates, matrix operations, data organization and Object-Oriented programming.

Related: Section 1.9

Reference: Jennifer Kay, 2005 Computer Science document, http://elvis.rowan.edu/~kay/papers/kinematics.pdf,

case1-Linear-Models-in-Economics.mw case2-Computer-Graphics-in-Automotive-Design.mw case3-determinants-in-Analytic-Geometry.mw case4-Space-Flight-and-Control-Systems.mw case5-Dynamical-Systems-and-Spotted-Owls.mw case6-Least-Squares-Solutions.mw case7-Singular-Value-Decomposition-and-Image-Processing.mwFind these edited files in this Directory

Presented Projects Aldous, Arnold and Edwards: Waveforms and Spectrograms Down, Firestone and Reed: Fractals: Iterated Function Systems and Linear Algebra Edfrennes, Roddum and Thorsen: Cracking the Code: An Introduction to Hill Ciphers Guckert: Fast Fourier Transform and the Modified Discrete Cosine Transform in MP3 Audio Compression Kubly and Pellatt: Forecasting United States Real Gross Domestic Product McGrath: Using Linear Algebra to Determine Spatial Autocorrelation: Geography Weeks: The Vertex Adjacency Matrix: Illustrated Tales of (1) The Tortoise; (2) The Spanning Tree; (3) The Eel Yizhou Ye: Image Compression by SVD and DCT Submitted Projects and Incomplete Drafts Azad and Wiser: Image Editing: Photos, RGB and Linear Algebra Bess: Image Compression via DCT and SVD: A Matlab Investigation Boyer: Gaussian Quadrature: An Application of Gram-Schmidt Christensen: A Brief History of Linear Algebra Gautam: Markov Chains and Nepal Voting Behavior Koizumi: Sound Compression of WAV Files: Maple Investigation Boya Li: Productive Economy: A Maple Investigation Partridge: Fractals: A Maple Investigation Wang and T. Ye: Relationship between Economic GDP and Mathematics

End of project suggestions.

Please, don't hesitate to suggest an interesting topic. I left out medical topics, like the artificial heart research going on at Utah, mining applications, cloaking devices for the military, vision devices for the blind using ultrasound, solar wind research, solar panels, windmills, material science, chemical engineering, particle physics research, and an endless list of other possibilities.