Table of Contents

Brief Table of Contents

Introduction

Worksheet 1. Maple Basics (PDF version)

  • 1.1. Introduction
  • 1.2. Getting started with Maple
  • 1.3. Basic Maple commands
    • 1.3.1. Maple is a numeric calculator
    • 1.3.2. Maple is a symbolic calculator
    • 1.3.3. Maple is a graphing calculator
    • 1.3.4. Maple is a programmable calculator (optional)
  • 1.4. Getting help in Maple
  • 1.5. Working with worksheets
    • 1.5.1. Entering text into a worksheet
    • 1.5.2. Menu bar, tool bar, and context bar
    • 1.5.3. Maple Notation vs. Standard Math Notation
    • 1.5.4. Execution groups
    • 1.5.5. An important warning
    • 1.5.6. The restart command
    • 1.5.7. Working without a worksheet
    • 1.5.8. Working with multiple worksheets
    • 1.5.9. Save your work!
    • 1.5.10. More information
  • 1.6. How Maple is organized

Worksheet 2. Variables, Assignment, and Equations (PDF version)

  • 2.1. Introduction
  • 2.2. Assigned and unassigned variables
  • 2.3. Equal signs, equations, and assignments
  • 2.4. Variable names
  • 2.5. Indexed names
  • 2.6. Concatenated names
  • 2.7. Online help for variables and names

Worksheet 3. Solving Equations (PDF version)

  • 3.1. Introduction
  • 3.2. The basics of using solve and fsolve
  • 3.3. Solving a single polynomial equation
  • 3.4. Solving a single nonlinear equation
  • 3.5. Solving a system of equations
  • 3.6. Using fsolve
  • 3.7. Using fsolve with a system of equations
  • 3.8. Solving inequalities
  • 3.9. Online help for solving equations

Worksheet 4. Functions in Maple (PDF version)

  • 4.1. Introduction
  • 4.2. Functions in Mathematics
  • 4.3. Functions in Maple
  • 4.4. Working with expressions and Maple functions
  • 4.5. Converting Maple functions to expressions and back again
  • 4.6. Equations vs. functions: ambiguity
  • 4.7. Equations vs. functions: implicit functions
  • 4.8. Piecewise defined functions
  • 4.9. Plot valued functions
  • 4.10. Vector valued functions
  • 4.11. Anonymous functions
  • 4.12. Functions that return a function (optional)
  • 4.13. More examples of expressions vs. Maple functions (optional)
  • 4.14. Online information for functions and expressions

Worksheet 5. Graphs of Functions and Equations (PDF version)

  • 5.1. Introduction
  • 5.2. A review of graphs
  • 5.3. Graphs of real valued functions of one variable
  • 5.4. Graphs of parametric curves
    • 5.4.1. Parametric curves in the plane
    • 5.4.2. Animating parametric curves
    • 5.4.3. Parametric graphs of real valued functions
    • 5.4.4. Parametric polygons
    • 5.4.5. Parametric polygon spirals
    • 5.4.6. Parametric curves in space: the spacecurve command
    • 5.4.7. The tubeplot command
  • 5.5. Non Cartesian coordinate systems in the plane
    • 5.5.1. Polar coordinates and other non Cartesian coordinate systems
    • 5.5.2. Real valued functions of a single variable in polar coordinates
    • 5.5.3. Real valued functions of a single variable in non Cartesian coordinates
    • 5.5.4. Parametric curves in the plane using non Cartesian coordinates
  • 5.6. Graphs of real valued functions of two variables
    • 5.6.1. The plot3d command
    • 5.6.2. Non rectangular regions
    • 5.6.3. Level curves, level sets, and the contourplot command
    • 5.6.4. Using levels curves when drawing surfaces
    • 5.6.5. Drawing curves on surfaces
  • 5.7. Graphs of parametric surfaces
    • 5.7.1. Parametric surfaces and the plot3d command
    • 5.7.2. Parameterizing a sphere
    • 5.7.3. Parameterizing a torus
    • 5.7.4. Parameterizations as patterns
    • 5.7.5. Exercises with parametric surfaces
  • 5.8. Non Cartesian coordinate systems in space
    • 5.8.1. Real valued functions and cylindrical coordinates
    • 5.8.2. Real valued functions and spherical coordinates
    • 5.8.3. More curves on surfaces
    • 5.8.4. Parametric surfaces in non Cartesian coordinates
    • 5.8.5. Non rectangular regions: fixing a bug in Maple
  • 5.9. Graphs of equations
  • 5.10. Graphs of vector fields
  • 5.11. Online help for graphing and visualization

Worksheet 6. How Maple Draws Graphs (PDF version)

  • 6.1. Introduction
  • 6.2. The plot command
  • 6.3. The implicitplot command
  • 6.4. The plot3d command
  • 6.5. Animations
    • 6.5.1. Animating curves
    • 6.5.2. Animating surfaces
  • 6.6. Defining coordinate systems

Worksheet 7. Mathematical Identities and Maple's Assume Facility (PDF version)

  • 7.1. Introduction
  • 7.2. Mathematical identities
  • 7.3. A closer look at mathematical identities
  • 7.4. The assuming command
  • 7.5. Using Maple's assume facility
  • 7.6. The RealDomain package
  • 7.7. Online information on assume

Worksheet 8. Manipulating and Simplifying Expressions (PDF version)

  • 8.1. Introduction
  • 8.2. factor
  • 8.3. combine
  • 8.4. expand
  • 8.5. simplify
  • 8.6. convert
  • 8.7. Polynomial expressions
  • 8.8. Rational expressions
  • 8.9. Power expressions
  • 8.10. Radical expressions
  • 8.11. Exponential expressions
  • 8.12. Trigonometric expressions
  • 8.13. Logarithmic expressions
  • 8.14. Online information on manipulating expressions

Worksheet 9. Maple as a Numeric Calculator (PDF version)

  • 9.1. Introduction
  • 9.2. Symbolic vs. numeric arithmetic
  • 9.3. Decimal places, more decimal places, and correct decimal places
  • 9.4. Online help for numerical calculations

Worksheet 10. Some Grammar (PDF version)

  • 10.1. Introduction
  • 10.2. Syntax and parsing

Worksheet 11. Maple's Evaluation Rules (PDF version)

  • 11.1. Introduction
  • 11.2. Full evaluation
  • 11.3. Levels of evaluation
  • 11.4. Delayed evaluation
  • 11.5. A no evaluation rule
  • 11.6. Last name evaluation
  • 11.7. Evaluating function calls
  • 11.8. Evaluating function definitions
  • 11.9. Evaluating concatenated names (optional)
  • 11.10. Evaluating indexed names (optional)
  • 11.11. Online help for evaluation rules

Worksheet 12. Data Structures in Maple (PDF version)

  • 12.1. Introduction
  • 12.2. Basic data structures in Maple
    • 12.2.1. Expression sequences
    • 12.2.2. Lists
    • 12.2.3. Sets
    • 12.2.4. Some numeric data types
    • 12.2.5. Names (or symbols)
    • 12.2.6. Strings
    • 12.2.7. Equations and inequalities
    • 12.2.8. Ranges
    • 12.2.9. Function calls
  • 12.3. Data vs. data structure vs. data type
  • 12.4. Data types in Mathematics
  • 12.5. Nested data structures
  • 12.6. Expressions as data structures
  • 12.7. Expression trees
  • 12.8. Why are expression trees important?
  • 12.9. Some other basic data types (optional)
    • 12.9.1. Logical data types
    • 12.9.2. Unevaluated concatenated names
    • 12.9.3. Indexed names
    • 12.9.4. Series
    • 12.9.5. Unevaluated expressions
    • 12.9.6. `::`
  • 12.10. tables, arrays, vectors and matrices (optional)
    • 12.10.1. tables
    • 12.10.2. arrays
    • 12.10.3. vectors and matrices
    • 12.10.4. Last name evaluation and the copy command
    • 12.10.5. Names, data structures, and garbage collection
    • 12.10.6. Index functions
    • 12.10.7. Comparing tables with functions
  • 12.11. rtables, Arrays, Vectors and Matrices (optional)
    • 12.11.1. rtables
    • 12.11.2. Arrays
    • 12.11.3. Vectors
    • 12.11.4. Matrices
  • 12.12. Structured data types (optional)
    • 12.12.1. Data types in general
    • 12.12.2. Structured data types
    • 12.12.3. Surface and nested data types
    • 12.12.4. Defining data types
  • 12.13. Online help for data structures and data types

Worksheet 13. Procedures in Maple (PDF version)

  • 13.1. Introduction
  • 13.2. From execution group to procedure
  • 13.3. Some definitions
  • 13.4. Parameter, local, and global variables
  • 13.5. Another example
  • 13.6. Maple functions are procedures
  • 13.7. How a mathematical function is like a procedure
  • 13.8. Procedures and data structures
  • 13.9. Anonymous procedures
  • 13.10. Procedure data structure
  • 13.11. Remember tables
  • 13.12. Return values and side effects
  • 13.13. The args expression sequence (optional)
  • 13.14. Recursive procedures (optional)
  • 13.15. Evaluation rules and procedures (optional)
  • 13.16. Procedures that return procedures (optional)
  • 13.17. Working with execution groups and procedures
  • 13.18. Online help for procedures

Worksheet 14. Maple's Control Statements (PDF version)

  • 14.1. Introduction
  • 14.2. Repetition statements
  • 14.3. More loop examples
    • 14.3.1. Example 1: Riemann sums
    • 14.3.2. Example 2: Pascal's triangle
    • 14.3.3. Example 3: Periodic extensions
    • 14.3.4. Example 4: Drawing graphs
    • 14.3.5. Example 5: Butterfly curve
    • 14.3.6. Example 6: Animations
  • 14.4. Conditional statements
  • 14.5. Boolean expressions
  • 14.6. For-loop like commands
  • 14.7. Statements vs. expressions (optional)
  • 14.8. Print levels, printlevel, and print commands (optional)
  • 14.9. Procedures that return unevaluated or return NULL (optional)
  • 14.10. Online help for control statements

Worksheet 15. Manipulating Data Structures with Procedures (PDF version)

  • 15.1. Introduction
  • 15.2. Differentiating a monomial
  • 15.3. Differentiating a polynomial: the map command
  • 15.4. Some real Maple procedures
  • 15.5. "Reversing" a polynomial
  • 15.6. Teaching Maple new tricks
  • 15.7. Differentiating functions
  • 15.8. Differentiating almost anything (optional)
  • 15.9. Online help for Maple programming
Return to the Maple for Math Majors page.

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