Introduction

1.1. Introduction

1.2. Functions in Mathematics

1.3. Functions in Maple

1.4. Expressions vs. functions: Some puzzles

1.5. Working with expressions and Maple functions (review)

1.6. Anonymous functions and expressions (review)

1.7. Functions that return a function (optional)

2.1. Introduction

2.2. Full evaluation

2.3. Levels of evaluation

2.4. Delayed evaluation

2.5. A no evaluation rule

2.6. Last name evaluation

2.7. Evaluating function calls

2.8. Evaluating function definitions

2.9. Evaluating concatenated names (optional)

2.10. Evaluating indexed names (optional)

2.11. Online help for evaluation rules

3.1. Introduction

3.2. Basic data structures in Maple

3.2.1. Expression sequences

3.2.2. Lists

3.2.3. Sets

3.2.4. Some numeric data types

3.2.5. Names (or symbols)

3.2.6. Strings

3.2.7. Equations and inequalities

3.2.8. Ranges

3.2.9. Function calls

3.3. Data vs. data structure vs. data type

3.4. Data types in Mathematics

3.5. Nested data structures

3.6. Expressions as data structures

3.7. Expression trees

3.8. Why are expression trees important?

3.9. Some other basic data types (optional)

3.9.1. Logical data types

3.9.2. Dotted names

3.9.3. Indexed names

3.9.4. Series

3.9.5. Unevaluated expressions

3.9.6. `::`

3.10. Tables and arrays (optional)

3.10.1. Tables

3.10.2. Arrays

3.10.3. Vectors and matrices

3.10.4. Last name evaluation and the copy command

3.10.5. Names, data structures, and garbage collection

3.10.6. Index functions

3.10.7. Comparing tables with functions

3.11. Structured data types (optional)

3.11.1. Data types in general

3.11.2. Structured data types

3.11.3. Surface and nested data types

3.11.4. Defining data types

3.12. Online help for data structures and data types

4.1. Introduction

4.2. From execution group to procedure

4.3. Some definitions

4.4. Parameter, local, and global variables

4.5. Another example

4.6. Maple functions are procedures

4.7. How a mathematical function is like a procedure

4.8. Anonymous procedures

4.9. Procedures and data structures

4.10. Procedure data structure

4.11. Remember tables

4.12. The args expression sequence (optional)

4.13. Recursive procedures (optional)

4.14. Working with execution groups and procedures

4.15. Online help for procedures

5.1. Introduction

5.2. Repetition statements

5.3. More loop examples

5.3.1. Example 1: Riemann sums

5.3.2. Example 2: Pascal's triangle

5.3.3. Example 3: Periodic extensions

5.3.4. Example 4: Drawing graphs

5.3.5. Example 5: Butterfly curve

5.3.6. Example 6: Animations

5.4. Conditional statements

5.5. Boolean expressions

5.6. For-loop like commands

5.7. Statements vs. expressions (optional)

5.8. Print levels, printlevel, and print commands (optional)

5.9. Procedures that return unevaluated or return NULL (optional)

5.10. Online help for control statements

6.1. Introduction

6.2. Differentiating a monomial

6.3. Differentiating a polynomial: the map command

6.4. Some real Maple procedures

6.5. "Reversing" a polynomial

6.6. Teaching Maple new tricks

6.7. Differentiating functions

6.8. Differentiating almost anything (optional)

6.9. Online help for Maple programming