## Introduction to Maple

**Calculus and the Interactive Use of Maple V. A Mini-manual for Mindful Maple Users**

By: Susan Carter, edited by Tirus Porter

## Maple Files for Calculus

**Rates of change, Slopes and Secant Lines**

In the first example an ant is walking over its mound whose height is given by a function h. On the other side of the mound there is a blade of grass that the ant doesn’t see at the original location x=9. Now let the ant walk over the mound and try to find the point at which the ant first sees the blade of grass.

**Limits, Derivatives, trigonometry, maxima/minimum, Mean Value theorem**

This maple file has 5 sections with examples related to the topics above. Under the limits section, you can find the equation of the tangent line to the parabola at a specific point. You can find out how to express the limit of various functions in maple also. Derivation of functions is the next topic. Next you will find examples using the student package followed by trigonometry examples. How to find maximum and minmum values is demonstrated next. The last section exemplifies the mean value theorem.

**Visualize objects in 3D using Geomview**

Geomview is a 3 dimensional graphing tool for maple. It can graph cuboids and dodecahedrons and provides options for displaying these structures.

**Volume of solids of revolution**

Solids of revolution are obtained by rotating the graph of a function about an axis. To approximate a smooth curve, Riemann sums can be used. By rotating the Riemann sums about an axis, we approximate the actual shape of a solid of revolution. We will build a function to rotate a Riemann sum about an axis, creating a solid of revolution.

**Methods of Integration**

Tips for integrating function by substitution or by parts. Also has examples of integrating partial fractions.

**Animation techniques and examples**

Here you will find numerous examples for rotating or moving curves and objects.

**Infinite series and Taylor polynomials**

Demonstrates how maple handles infinite series and includes a graphical example of a taylor polynomial and their convergence behaviour.

**Vector calculus: lines, planes and quadratic surfaces**

More 3 dimensional graphing techniques. Demonstrates how to define and plot vector objects in 2D and 3D using the linear algebra, plot and plottool packages.

## Maple Laboratory Files

- Lab1: Basic algebra commands
- Lab2: Hints for ant/mound problem
- Lab3: Differential commands
- Lab4: Definite Integrals
- Lab5: Parametric curves, polar coordinates
- Lab6: Space curvers and curvature

## New Maple files for Visualizing Mathematics

To download, right click and choose Save Target As.

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