TA workshop problems

In Introduction to Differential Equations I (Ma 341) one studies systems of differential equations. In the study one uses eigenvector-eigenvalue techniques, and in this problem you will illustrate how to find eigenvectors and eigenvalues. (a) Find the eigenvalues and eigenvectors of the following matrix, and assign them to the names eigenvector_1, eigenvector_2,eigenvector_3 and eigenvalue_1, eigenvalue_2,eigenvalue_3. A:= linalg[randmatrix](3,3);

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eigenvector_1:= put_your_answer_here; eigenvector_2:= put_your_answer_here; eigenvector_3:= put_your_answer_here; eigenvalue_1:= put_your_answer_here; eigenvalue_2:= put_your_answer_here; eigenvalue_3:= put_your_answer_here; (b) Find the eigenvalues and eigenvectors of the following matrix, and assign them to the names eigenvector_1, eigenvector_2, ... eigenvector_n and eigenvalue_1, eigenvalue_2, ... eigenvalue_n. A:= linalg[randmatrix](6,6);

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(c) Is it more difficult to find the eigenvectors and eigenvalues of a 10 x 10 matric than a 3 x 3 matrix?

Explore the help page for Maple's dsolve command and then illustrate the command with several examples. See also the Maple Basic Lesson on dsolve and also the eGrader quick help topic on dsolve.

Study the help page for Maple's solve command and illutstrate how to use solve with several examples like the problem listed below. See also Ma 141 Maple Basic Lesson #2. Example Problem: Solve the following linear system. Eqn1:= randpoly({x,y,z,w},degree=1)=0; Eqn2:= randpoly({x,y,z,w},degree=1)=0; Eqn3:= randpoly({x,y,z,w},degree=1)=0; Eqn4:= randpoly({x,y,z,w},degree=1)=0;

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LywsSSJ4RzYiIiN4SSJ5R0YlIiMmKkkiekdGJSIiIkkid0dGJUYqIiNiRioiIiE=

LywsSSJ4RzYiISNHSSJ5R0YlIiM7SSJ6R0YlIiNJSSJ3R0YlISNGISM6IiIiIiIh

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solve({Eqn1,Eqn2,Eqn3,Eqn4});

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Study the help page for Maple's plot command and then use it to illustrate how to plot one or more curves in a single plot. Show how to plot the curves in different colors and how to change the thickness of the plot. See also MA 141 Maple Basic Lesson #3 for more information.

Study the help page for Maple's plot3d command and then use it to illustrate how to plot one or more surfaces in a single plot. See MA 242 Maple Basics Lesson #3 to see how students will you plot3d in Calculus III.

See Maple's help topic on the fsolve command and then illustrate its use with several examples. See also eGrader's quick help topic on fsolve.

Use Maple's Diff and diff commands to illustrate how to compute derivatives in Maple. See also MA 141 Maple Basics Lesson #4. Study the help pages for Maple's int command to illustrate how to compute anti-derivatives and definite integrals in Maple.

Read the MA 341 Maple Basic Lesson on Laplace Transforms and then illustrate how to solve a Laplace transform problem in a Maple worksheet. (a) (b)

Read Maple Basic Lesson #5 for MA 242 and then illustrate with examples how to compute surface integrals in Maple.

See MA 241 Maple Basics Lesson #3 and/or the Quick Time Video on Euler's method, and then illustrate the method with several examples. See also EulerExample.