## Maple Examples: A curve wrapped around a torus with its TNB-frame and osculating circles.

### Please let me know if you find any errors

NOTE: Maple 2020 changed the way its menus were organized. Some old sheets say "Edit->Execute->Worksheet" to show answers. In Maple 2020, choose "Evaluate->Entire Worksheet" (select the "Evaluate" menu and choose "Entire Worksheet") to run the computations.

### Linear Algebra:

• A few helpful tips for doing linear algebra in Maple: (.mw) and (.pdf)
• Gaussian Elimination "Graphically" -- we graph each step of Gaussian elimination for a system of 2 equations in 2 unknowns (.mw) (.html) -- this is problem 1.1.79 in Elementary Linear Algebra by Larson et. al. (5th ed.).
• Modeling a Ski Jump (.mw) and (.html).

### Calculus II:

→ Old Math 1120 homeworks and answer keys

### Multivariable Calculus:

→ Old Math 2130 homeworks and answer keys

### Differential Equations:

In the following worksheets, problem numbers refer to William E. Boyce and Richard C. DiPrima's "Elementary Differential Equations" (8th ed.) ISBN 0-471-43339-X.
• Initial Value Problems and Slope Fields: (.mws) and (.html)
• Modeling a Ball thrown into the air with air resistance (Problem 22 in Section 2.3): (.mws) and (.html)
• Modeling a sky diver with air resistance (Problem 23 in Section 2.3): (.mw) and (.html)
• Euler's Method and Backwards Euler's Method for approximating solutions of first order ODEs: (.mw) and (.html)
• Euler's and Backwards Euler's Methods (Problem 2 in Section 8.1): (.mw) and (.html)
• Plots of direction fields in phase planes: (.mw) and (.html)

### Topology:

• Unit circles/spheres in different metrics: (.mw) and (.html)