Mathlab Math 221 Support Page

The lab consists primarily of dual booting Windows 2000/Linux Pentium 4 machines. There are also 4 old Macs.

Linear algebra capable programs to support Math 221 in the lab include:

Maple

is installed on all Windows and linux machines with support notes at http://www.mathlab.cornell.edu/support/maple.html.

Some linear algebra samples for getting started include:

linalg: html format | Basiclinalg.mws (more symbolic support)

LinearAlgebra: html format | BasicLinearAlgebra.mws (faster numerical support)

Entering Matrices: html format | EnteringMatrices.mws

Matlab

is installed on all pentium 4 linux and windows 2000 machines with support notes at http://www.mathlab.cornell.edu/support/matlab/using_matlab.html.

Mathematica

is installed right now on two machines; the linux side of indian and the Windows 2000 side of tahoe.

We have a number of reference books in the lab on using Maple and Matlab within linear algebra courses. (Specific List Forthcoming)

A general listing of references in the lab is at http://mathlab.cit.cornell.edu/references/references.html.

The lab also has much support for differential equations. For the moment you might refer to our Math 420 support page http://mathlab.cit.cornell.edu/support/m420_support/m420_support.html and the differential equation ideas below.

Some Ideas for Computer Usage to Enhance a Linear Algebra Course:

• Interesting applications of matrix multiplication. (e.g. path counting via adjacency matrices, Markov chains, exchange economies.)

  An old Markov Chains assignment also using the row operations package:

  html format

  pdf format

• Geometry of linear transformations.

  A small worksheet for parallelogram images:

  html format

  parallelograms.mws

  Auxiliary text file pargrm_image.txt loaded by parallelograms and paralleopipeds worksheets.

  A small worksheet for parallelopiped images:

  html format

  parallelopipeds.mws

  An old assignment using the parallelogram image package:

  html format

  pdf format

• Fitting data to equations. (Direct and via determinants.)

  A small worksheet for a circle through 4 points by a determinant:

  html format

  curves_from_points.mws

• Explore interesting matrix groups.
• Least squares and overdetermined systems.

  Small worksheets for least squares solution:

  html format

  least_squares_2d.mws

  html format on least_squares_parabola.mws

  least_squares_parabola.mws

• Behavior of algorithms (e.g. least squares) when they nearly fail.
• Traffic flows and linear equations.
• Codes obtained via matrix multiplication.
• Roundoff error in matrix operations.
• Convergence of power series in matrices.
• Computer assistance for Gram-Schmidt either geometrically or for orthogonal polynomials.
• Powers of matrices and eigenvalues.

  A small worksheet for the power method:

  html format

  powers.mws

• Difference equations.
• Geometry of diagonalizing quadratic forms.

  A small worksheet for diagonalizing a quadratic form:

  html format

  quadratic_forms_and_eig.mws

• Interpretation of linear ODE solutions (e.g damped driven harmonic oscillators.)
• Web Resources:

  Mathlab:

  http://www.mathlab.cornell.edu/computer_and_portfolio/index.html#LINALG

  Connected Curriculum Project:

  
  http://www.math.duke.edu/education/ccp/materials/linalg/index.html

  Row Operations Applet:

  
  http://people.hofstra.edu/faculty/Stefan_Waner/tutorialsf1/javapiv.html

  Linear Transformation Applet:

  http://math.smith.edu/patela/Applets/transf_index.html

  Images of Transformations Applet:

  http://www.ies.co.jp/math/java/misc/lintra/lintra.html

Some Ideas for Computer Usage to Enhance a Differential Equations Course:

• Errors in ODE integration schemes as a function of method and step size. Empirical measures of the order of a method.
• Experiment with graphical integrators and then argue for the correctness of some of the results seen. (e.g. fences, vertical asymptotes, behavior at infinity.)
• Bifurcations of 2d homogeneous linear systems.
• Matrix exponential and applications.
• Computer assistance for variation of parameters.
• Computer assistance for change of coordinates.
• Logistic, predator-prey and generalizations as a function of parameter.
• Computer algebra systems in scratchpad mode to assist with power series and Frobenius methods solutions.
• Use computers to bring some special functions to life.
• Study some basic low codimension bifurcations (e.g. saddle node, pitchfork, hopf.)
• Sensitive dependence on initial conditions.
• Study attractive periodic points as a function of parameter in the 1d discrete logistic equation to see chaotic behavior.
• Explore the restricted 3 body problem numerically.
• Web Resources:

  Java and Matlab versions of Dfield and Pplane:

  http://math.rice.edu/polking

  Dynamics Solver Source:

  http://tp.lc.ehu.es/JMA/ds/ds.html

  Interactive Differential Equations:

  http://awlonline.com/ide/ (All labs available online in pdf format!)

  IDEA:

  http://www.sci.wsu.edu/idea

  CODEE

  http://www.math.hmc.edu/codee/main.html

  Mathlab:

  http://www.mathlab.cornell.edu/computer_and_portfolio/index.html#ODE

Mathlab Hours during the Semester

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Last Update: September 16, 2002