Calculus, Differential Equations and Linear Algebra course sequence for science and engineering

Each of these courses 1500-1505-2500-2705 have 2 in-class closed book "hour = 55 minute" tests, a third week-long take home open resource test and a closed book in-class 2.5 hour final exam, with about 8 or 9 weekly quizzes during non-test weeks: quiz-test archives [test rules]. Each course has a PDF handout list including some Maple worksheets, but the current complete class daily log and homework page has links to all PDF notes and Maple worksheets.

Why MAPLE?

Maple example worksheets

See the Maple Hints and examples page first and the VU Maple FAQ for how to access Maple and deal with its idiosyncrasies.

• mplweb.htm calculus worksheets [moved to my own website, links to fix, but see above]

• ../maple/index.htm many Maple examples accumulated over decades

• Maple's Explore command takes math to the next level by making it interactive

Maple tease

Here is a tease illustrating a force driven periodic undamped 2 mass 3 spring coupled mass spring system

shown in the left diagram below with the two small round masses oscillating about their equilibrium positions on the vertical axis. These oscillations are simultaenously being plotted versus time on the horizontal axis.. The right diagram decomposes those displacements plotted as a system point in the plane of the two displacements x1 and x2 into the homogeneous free motion component (blue), the response component (green), and the total motion (red) (displacement plane on right):
.

A natural extension of this example explores the reaction of a multistory building to horizontal earthquake vibrations. These are the building profiles for the 7 natural modes of vibration of a 7 story building (exaggerated of course, but with correct relative frequencies).

Here is a multivariable calculus tease: a point traces out uniformly a circle in a vertical plane which is itself rotating about the vertical axis. This is a toy model of the GP-B satellite experiment to test Einstein's test of general relativity. [For explanation, see this web page.]

For spin precession on precessing conical section planar GR orbits, see:
http://www34.homepage.villanova.edu/robert.jantzen/maple/misc/grprecession/

The square wheel problem [statement to challenge math problem solver (pdf), Maple solution and graphics] analyzes a structure anchored in the Serret-Frenet TNB frame of a plane curve (Calc 3!), although one does not need to introduce this language to solve the problem, which only requires single variable calculus. [dr bob visits the Museum of Math square wheel tricycle ride!]

Cavatappo 2.0: geodesics on a corkscrew symmetric helical tube surface