Mathcad-based Explorations of

Linear Algebra Applications

http://ist.uwaterloo.ca/ic/syde114

These explorations were originally created for:


Systems Design 114 - Linear Algebra

which uses the text:

Elementary Linear Algebra - Applications Version 8E

But they are intended to be of use by any Linear Algebra course using any text,
and therefore have been registered with www.merlot.org.

Support is gratefully acknowledged from

The Centre for Learning & Teaching Through Technology (LT3)
at the University of Waterloo


Application for LT3 Project in Spring 2001


                                                         The following table of contents is based on
                     Anton and Rorres's Elementary Linear Algebra - Applications Version 8E, Wiley, 2000.
 

1. Systems of Linear Equations and Matrices

1.1. Introduction to Systems of Linear Equations
Nutrition - nutrition-1.mcd
1.2. Gaussian Elimination (including Gauss-Jordan Elimination)
Circuit Simulation - circuit-1.mcd
1.4. Inverses; Rules of Matrix Arithmetic
Enciphering - cipher-1.mcd
2. Determinants
2.4. Cofactor Expansion; Cramer's Rule
Programming (cofactors) - programming-1.mcd
3. Vectors in 2-space and 3-space
3.4. Cross Productor
Area of 3-D Triangle - area-1.mcd
4. Euclidean Vector Spaces
4.2. Linear Transformations from Rn to Rm
Computer Graphics - pyramid-1.mcd
6. Inner Product Spaces
6.3. Orthonormal Bases; Gram-Schmidt Process; QR-Decomposition
Orthonormal Bases; Orthogonal Matrices - bases-1.mcd

Orthogonal Projection - orthogonal-projection-demo-1.mcd

6.4. Best Approximation; Least Squares
Polynomial Curve Fit - polynomial-1.mcd (using Least Squares)
(See also: demo.mcd - computes SSE)

Computed Tomography -  tomography-1.mcd

6.5. Orthogonal Matrices; Change of Basis
Change of Basis - change_of_basis_1.mcd
7. Eigenvalues, Eigenvectors
7.1 Eigenvalues and Eigenvectors
9. Additional Topics
9.3. Least Squres Fitting to Data
Polynomial Curve Fit - polynomial-1.mcd (using Least Squares)
(See also: demo.mcd - computes SSE)
9.4. Approximation Problems; Fourier Series
Signal Processing - signal-1_template.mcd and noisy.txt


11. Applications of Linear Algebra

11.2. Electrical Networks
Circuit Simulation - circuit-1.mcd
11.11. Computer Graphics
Computer Graphics - pyramid-1.mcd
11.13. Computed Tomography
Computed Tomography -  tomography-1.mcd
11.16. Cryptography
Enciphering - cipher-1.mcd
11.18. Age-Specific Population Growth
Population Growth -  population-1.mcd


                  The Mathcad files of all the above applicable examples contain hyperlinks to the on-line version of
                                     Carl D. Meyer's Matrix Analysis and Applied Linear Algebra, SIAM, 2000

Last updated September 6, 2001 by Wu (Kevin) Li, Systems Design and Colin Campbell, IST