Mathematical computing: an introduction to programming using Maple/ David Betounes and Mylan Redfern.

Includes bibliographical references (p. 405-407) and index.

1 Preliminaries
1.1 Maple as a Programming Language
1.2 Analyzing Programming Tasks
1.3 Documentation and Coding . .
1.4 Maple/Calculus Notes
1.4.1 Basic Syntax
1.4.2 Derivatives in Maple
1.4.3 Integrals in Maple
1.4.4 Combining Plots .
2 Basic Aspects of Maple
2.1 Variables and Constants .
2.2 Expressions and Assignments
2.3 Notation in Mathematics and in Maple
2.4 Sequences, Lists, Sets, and Arrays
2.5 The Do Loop
2.6 Procedures: A First Glance
2.7 Evaluation Rules
2.8 Maple/Calculus Notes
2.8.1 Planes Curves Given Implicitly
2.8.2 Plane Curves Given Parametrically
3 Looping and Repetition
3.1 The Basic Loop
3.2 The Do Loop with All Its Features
3.2.1 The for-from Loop .
3.2.2 The for-in Loop .
3.3 Case Study: Iterated Maps
3.4 Maple/Calculus Notes
3.4.1 Riemann Sums and the Definite Integral
Conditioneds - Flow of Control
4.1 Logic in Mathematics
4.2 Relational and Logical Operators
4.3 Boolean Expressions .
4.4 The if-then-else Statement
4.5 The if-then-elif-then Statement
4.6 Case Study: Riemann Sums for a Double Integral
4.7 Maple/Calculus Notes
4.7.1 Interiors and Exteriors of Triangles
4.7.2 Riemann (Double) Sums and Double Integrals
4.7.3 Double Integrals in Maple
Procedures
5.1 Maple's Procedure Statement
5.1.1 Aspects of the Procedure Definition
5.1.2 Aspects of the Procedure Call .
5.2 Procedures - Some Details
5.2.1 Evaluation Within a Procedure
5.2.2 Parameters and Local Variables
5.3 Groups of Related Procedures
5.4 Case Study: Trig Integrals
5.5 Maple/Calculus Notes
5.5.1 Vector Methods in Geometry
Data Structures
6.1 Expressions and Operands
6.2 Quotes and Strings
6.3 Numbers
6.4 Lists: Vector Methods in Geometry
6.5 Arrays and Tables
6.6 Sets: The Cantor Set and Limiting Covers .
6.7 Polynomials
6.8 Case Study: Partial Itactions
Graphics Programming
7.1 Preliminary Examples
7.2 Maple's Plot Structures .
Contents
7.3 Approximating Curves and Surfaces
7.3.1 Approximating Curves
7.3.2 Approximating Surfaces
7.4 The GRID and MESH Objects
7.4.1 The GRID Object
7.4.2 The MESH Object
7.5 Animations
7.5.1 The Display and Animate Commands
7.6 Maple/Calculus Notes
7.6.1 Parametric Representations of Curves and
. Surfaces .
7.6.2 Implicit Representations of Curves and
8 Recursion
Surfaces
8.1 Recurrence Relations - Series Solutions
8.2 Reduction Formulas for Integration
8.3 Sorting.
8.3.1 Bubble Sort
8.3.2 The Quick Sort Algorithm
8.4 Numbers
8.4.1 Numbers in Mathematics
8.4.2 Base N Representations of Numbers .
8.4.3 Numbers in Programming
8.5 Maple/Calculus Notes . . .
8.5.1 Real Numbers
9 Progreiniming Projects
9.1 Projects on Crystal Growth
9.1.1 Sample Project: Squares on Squares
9.1.2 Project: Crystal Growth (Squares)
9.1.3 Project: Crystal Growth (Isosceles, Right Triangles)
9.1.4 Project: Crystal Growth (Equilateral Triangles)
9.1.5 Project: Crystal Growth (The Koch Snow"ake) .
9.1.6 Project: Crystal Growth (Squares and Triangles)
9.2 Projects on Inscribed Polygons
9.2.1 Sample Project: Sequences of Triangles
9.2.2 Project: Asymptotics of the Triangle Sequence
9.2.3 Project: Sequences of Quadrilaterals
9.2.4 Project: Sequences of Polygons
9.3 Projects on Rfindom Walks
9.3.1 Sample Project: Simulating a Basic Random
Walk .
9.3.2 Sample Project: Random Walk in a Square
9.3.3 Sample Project: Basic Random Walk in a Disk
9.3.4 Project: Random Walks Other Boundaries and Vari
ations
9.3.5 Random Walks in 3-Dimensions
9.3.6 Project: Walking in a Random Direction
9.4 Projects on Newton's Second Law
9-.4.1 Sample Project: Motion Near the Earth's Surface
9.4.2 Project: 1-Body Planar Motion
9.4.3 Project: N-Body Planar Motion
A Maple Reference
A.l Expressions and Functions
A.2 Plotting and Visualization
A.3 Programming
A.4 Packages .