1st Edition

Maple Animation




ISBN 9781584883784
Published May 14, 2003 by Chapman and Hall/CRC
232 Pages - 247 B/W Illustrations

 
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Book Description

There is nothing quite like that feeling you get when you see that look of recognition and enjoyment on your students' faces. Not just the strong ones, but everyone is nodding in agreement during your first explanation of the geometry of directional derivatives.

If you have incorporated animated demonstrations into your teaching, you know how effective they can be in eliciting this kind of response. You know the value of giving students vivid moving images to tie to concepts. But learning to make animations generally requires extensive searching through a vast computer algebra system for the pertinent functions. Maple Animation brings together virtually all of the functions and procedures useful in creating sophisticated animations using Maple 7, 8, or 9 and it presents them in a logical, accessible way. The accompanying CD-ROM provides all of the Maple code used in the book, including the code for more than 30 ready-to-use demonstrations.

From Newton's method to linear transformations, the complete animations included in this book allow you to use them straight out of the box. Careful explanations of the methods teach you how to implement your own creative ideas. Whether you are a novice or an experienced Maple user, Maple Animation provides the tools and skills to enhance your teaching and your students' enjoyment of the subject through animation.

Table of Contents

Getting Started
The basic command line
A few words about Maple arithmetic
Comments
Assigning names to results
Built-in functions
Defining functions
Getting help and taking the tour
Saving, quitting, and returning to a saved worksheet

The Plot
The basics
Parametric forms
Plotting points and using the plots package
Storing and displaying plots
The plot thickens
Smoothing plots
Color
Scaling
Plotting with style
Adjusting your point of view
A limited view
Tailoring the axes
Toward leaner code
Context-sensitive menus and context bars
Further details

Non-Cartesian Coordinates and Quadric Surfaces
Polar coordinates
Cylindrical coordinates
Spherical coordinates and others
Quadrics quickly
Paraboloids
Elliptic cones
Ellipsoids
Hyperboloids
Quadric surfaces with axes other than the z-axis

Simple Animations
Animating a function of a single variable
Outline of an animation worksheet
Demonstrations: Secant lines and tangent lines
Using animated demonstrations in the classroom
Watching a curve being drawn
Demonstration: The squeeze theorem
Animating a function of two variables
Demonstrations: Hyperboloids
Demonstrations: Paraboloids
Demonstration: Level curves and contour plots

Building and Displaying a Frame Sequence
Sequences
The student and Student[Calculus1] packages
Displaying a sequence of frames
Building sequences with seq
Demonstrations: Rectangular approximation of the definite integral
Demonstration: Level surfaces
Moving points
Demonstrations: Projectiles
Demonstration: Cycloid

Loops and Derivatives
The for loop
The while loop
Derivatives
The line procedure
Demonstrations: Newton's method
Demonstrations: Solids of revolution
Demonstrations: Surfaces of revolution

Adding Text to Animations
Titles
The textplot and textplot3d procedures
Making text move
Demonstrations: Secant lines and tangent lines with labels
Including computed values in text
Demonstration: Rectangular approximation of the definite integral
with annotation
Constructing Taylor polynomials
Demonstrations: Taylor polynomials
Demonstrations: Experimenting with Taylor polynomials

Plotting Vectors
The two arrow procedures
The arrow procedure of the plots package
Dot product and cross product
The arrow options
Demonstration: The cross product vector
Demonstration: Velocity and acceleration vectors in two dimensions
Demonstration: Lines in space

Plotting Space Curves
The spacecurve procedure
Demonstration: Curves in space
Demonstration: Directional derivative and gradient vector
The tubeplot procedure
Demonstration: Velocity and acceleration vectors in three dimensions

Transformations and Morphing
The plottools package
The rotate procedure
The transform procedure
Matrix transformations
Morphing
Linear transformations

Bibliography
Index

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Reviews

"Putz designed this book for teachers of precalculus and first and second year calculus to provide a large number of animations to be used to illustrate various concepts of calculus. The accompanying CD-ROM contains all the described examples coded for use in class directly, along with suggestions for how to use these examples... This book will be very useful to faculty. Recommended."
-CHOICE, 2004