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 2012Directory Link 2012Aldous, 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 2012Directory Link 2012Azad 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

Directory of 2270 Projects Spring 2016Presented Projects 2016 Tyler Adams, David Moody, Haysun Choi:Cryptography and the Enigma MachineadamsTyler-moodyDavid-choiHaysun-CryptographyTheEnigmaMachine.pdf Veronica Dean-Perry and Marie Novozenya:Least squares fitting of weight datadeanPerryVeronica-novozenyaMarie-least-squares.pdf David Ethan Hamilton, Daniel Merrell, Aaron Kramer, Marty Simmons, and Carlos Guerra:Economics Stochastic ModelsDirectory hamiltonEthan Daniel Mattheiss:Fractals generated by iteration of affine mappingsDirectory mattheissDaniel Barrett Williams:Predicting Financial Security Prices using the FFTDirectory williamsBarrett Jie Zhang and Pratusha Bopanna:Markov Chains and Music CompositionDirectory zhang-bopanna Submitted Projects 2016 Christian Butler:Inheritance and Population Geneticsbutler-Christian-inheritance-population-genetics.pdf John Chambers:Spectral differences of sound and harmonics using Fourier TransformationschambersJohn-Spectral-Differences-Sounds-and-Harmonics.pdf William Garnes:Fractal generation using linear and affine transformationsDirectory garnesWilliam-fractals Benson HaglundLeontief Consumption Matrices and Economics ModelsDirectory haglundBenson Conner KuhnA Comparison of SVD and DCT Image Compression MethodsDirectory kuhnConnor Nicholas LloydOpenGL Matrix/Vector Manipulation using SFML: Applications of Linear and Affine TransformationslloydNick-open-GL-computer-graphics.pdf Jessica MurdockImage Manipulation Using Mathematica: Matrix Representations of Images and Linear TransformationsmurdockJessica-Image-Manipulation-Mathematica.pdf Nathan Romriell:Fractals, Julia Sets and Mandlebrot Sets: Linear and Affine TransformationsDirectory romriellNathan Dario Sanchez:Balancing Chemical Equations using Systems of Linear Algebraic EquationssanchezDario-chemistry-balancing-chemical-equations.pdf Christopher Sannar:Representation of Musical Scores by Vectors and MatricessannarChristopher-Music-scores-and-matrices.pdf Kyle Heaton and Braden Scothern:scothernBraden-heatonKyle-hamming-codes.pdf Orenda Williams: Manipulation of Digital Images using MatriceswilliamsOrenda-matrix-operations-digital-images.pdf Incomplete Projects 2016 Mahalia Lotz:Spectral properties of musicLotzMahalia-music-spectral-properties-fourier-analysis.pdf Jiwon Nam:Image CompressionnamJiwon-image-compression.pdf Seth Reelitz:Hill CipherreelitzSeth-hill-cipher.pdf

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**Cryptography: Matrices and Encryption**Directory - Alex Hawks and Matthew Westberg

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**Fractals: Starting From The Base**Directory - Dylan Johnson

**Graph Theory and Linear Algebra**Directory - Joe Narus

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**Discrete Dynamic Systems That Approximate Motion Through Velocity and Acceleration Vector Fields**Directory - Joshua Rosen and Alexandra Bertagnolli

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