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.
Introductory Material:
- For Calculus 3, Introduction to Maple (video 35 mins) and a Maple intro summary sheet (.pdf) [Source: (.tex)]
Here is the corresponding Maple worksheet: Calc. 3 Intro. to Maple (.mw) - A random Introduction to Maple (for Calc. 2) worksheet and Maple intro summary sheet (.pdf) [Source: (.tex)].
- A random Maple Introduction for some geology people (you know who you are).
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 I:
- Taylor Polynomial Demo: HTML Export [Basic_Taylor_demo.mw]
- Newton's Method (root finding): HTML Export [math1110-summer2014-newtons_method.mw]
- Riemann Sums: HTML Export [math1110-summer2014-riemann_sums.mw]
Calculus II:
- My random Introduction to Maple (for Calc II): Introduction_to_Maple_calc2.mw
Multivariable Calculus:
- My random Introduction to Maple (for Calc III): Introduction_to_Maple_calc3.mw
- Parametric Playground [parametric_curves (.mw)]
- Vectors, Lines, & Planes [vectors.mw]
- Arc Length, Curvature, & TNB-Frames [curvature.mw]
- An exploration of how bad computing curvature can get: The Scribble Curve [scribble_curve.mw]
- Osculating Circles [osculating_circles.mw]
- TNB-Frame: A curve wrapped around a torus with its TNB frame and osculating circles. This is the worksheet (.mw) (.html) used to create the picture above.
- Visualizing Line Integrals (with respect to arc length) [visualizing_line_integrals.mw] This worksheet plots a surface, curve in the xy-plane, and the sheet between those two. It also computes the area of this bent sheet using a line integral (with respect to arc length).
- Plotting in 3D [3dplots.mw] This worksheet includes examples of the 6 types of quadric surfaces.
- Multivariate Limit Weirdness [Source: (.mw)] This sheet plots a surface where approaching the origin along lines yields 0, but approaching along a parabola yields 1/2.
- Seeing signs of partial derivatives [math2130-fall2016-traces.mw] This shows a few traces on a paraboloid and attempts to help one understand the signs of the partial derivatives.
- Partial Derivatives, Gradients, & Contour Plots [contours.mw]
- Classifying Critical Points & The Method of Lagrange Multipliers [minmax.mw]
- Double Riemann Sums [double_Riemann.mw]
- Multiple Integrals [multiple_integrals.mw]
- Vector Calculus [vector_calculus.mw]
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)