At Saint Louis University, we are using graphing calculators as the primary technology in teaching our introductory calculus courses.

However, as students advance to multivariable calculus, the need to visualize in 3 dimensions makes Maple far more effective than graphing calculators. Our Calculus III course is being taught in a computer classroom where the students have access to Maple.

The strategy I have used for bringing Maple into the classroom is to introduce it through carefully designed worksheets, which I use as:

• Lecture aids with the instructor running the worksheet with a projection system.
• Handouts for the students
• Lab assignment that the class will start together as a substitute for a lecture.
• Supplemental homework assignments.

These worksheets include a significant amount of exploratory text and exercises. The exercises ask the student to repeat the examples in the worksheets with minor modification. I do not expect them to produce the code, but rather to copy and modify a code template, focusing on the results of the problems.

Download the full set of 25 worksheets, or preview them individually.

Preliminaries: Plotting in 2D and 3D with Maple
Sec. 11.2 Visualizing Tangent Planes
Computing and graphing tangent planes to surfaces
Sec. 11.7 Multivariable Limits
The formal definition of limit for functions of two variables. To simplify graphing, square neighborhoods in the domain are used in the definition.
Sec. 12.1 Visualizing Vectors
Use Maple to visualize vectors, vector arithmatic and cross products.
Sec. 12.2 Cross and Dot Products
A fast handout explaining the syntax for dot and cross product in Maple. The intent is to show the students how to use Maple to check their work with vector computations.
Sec. 13.3 Local Linearity
Visualizing the definition that a function is differentiable at a point if the graph near the point is locally approximated by the tangent plane. The definition is used to understand the corresponding delta-epsilon definition.
Sec. 13.5 Directional Derivatives and Gradients
Demonstrates directional derivatives and connects them to the gradient for differentiable functions.
Sec. 13. 9 Bivariate Taylor Series
Steps the students through the construction of Taylor polynomials for functions of 2 variables.
Sec. 13.10 Checking Differentiability
Steps the student through the process of checking differentiability of a function at a point.
Sec. 14.2 Lagrange Multipliers
An animation approach to demonstrating the Lagrange Multiplier Theorem for extrema problems.
Sec. 14.3 Gradient Search
Shows how to mechanize a gradient search to find a solution to a minimization problem.
Sec. 14.4 Rotating Axes to Eliminate the Cross Term
Looks at the algebraic manipulation that underlies the discriminant test for extrema in two variables.
Sec. 15.01 Integration Checker
Demonstrates for the students the Maple commands needed to do integration. It seems useful in this chapter where many of the problems reduce to "and finish by evaluating the two or three integrals."
Sec. 15.02 Plotting in Other Coordinate Systems
How to plot in coordinate systems other than Cartesian. It also shows how to combine objects described in different coordinate systems on a single plot.
Sec. 15.1 Defining Double Integrals
The Riemann sum definition of double integrals. It follows the usual pattern of the course by reviewing the definitions in the one variable case, then generalizing.
Sec. 15.2 Double Integrals with dxdy
Visualizing limits of integration in Cartesian coordinates in 2 dimensions and in changing the order of integration.
Sec. 15.3 Triple Integrals with dxdydz
Similar to the double integral worksheet, but with triple integrals.
Sec. 15.4 Monte Carlo Integration
Fast in-class demonstration of the Monte Carlo technique of integration.
Sec. 15.5 Double Integrals in Polar Coordinates
This worksheet was done by the students in class. It looks at setting up integrals in polar coordinates and switching between rectangular and polar coordinates.
Sec. 16.1 Parametric Curves
Parameterizing curves in R2 and R3
Sec. 16.3 Parametric Surfaces
How to parametrize surfaces. Special attention is given to surfaces of revolution.
Sec. 16.5 Planetary Motion
Parameterizing planetary motion under gravity. This is a demonstration worksheet and was done after Chapter 17. It solves for planetary motion with a flow line solution of a vector field in 4 dimensions. The orbits of Mars and Halley's comet are studied as examples.
Sec. 17.1 Vector Fields and Gradient Fields
Plotting vector fields and gradient fields in 2 and 3 dimensions
Sec. 17.2 Plotting Flow Lines
Plotting flow lines for vector fields in 2 and 3 dimensions. It also shows how Euler's method works as a numerical method.
Sec. 18.2 Line Integrals
The procedure of setting up and evaluating a line integral along a parameterized curve. It is intended as a homework checker.
Sec. 19.3 Flux Integrals
The procedure of setting up and evaluating a flux integral through a surface. It is intended as a homework checker.