Related: Section 8.3

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 the 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: Lab 4, Section 8.5, Section 7.3, Section 10.3

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: Lab 3, Section 8.6

Related: Section 6.7, Section 7.2, Section 10.3

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 8.7

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

Make a 4-page paper and short presentation demonstrating the use of linear algebra in lossy audio compression, the modified discrete cosine transform (MDCT). Here's an undergraduate research project that may get you quickly into the topic, which has taken on more appeal since MP3 players have dominated the market, fueled by low-cost downloadable mp3 audio. AUDIO COMPRESSION USING MODIFIED DISCRETE COSINE TRANSFORM: THE MP3 CODING STANDARD http://www.mp3-tech.org/programmer/docs/jacaba_main.pdf

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.

Finally, you can examine what others have done for linear algebra projects. A rich collection of slides, papers, matlab codes from 1997 to 2010 can be found here: