Computing With Mathematica – Hartmut F. W. Höft, Margret Höft – 2nd Edition

Parte I: Learning the Basics
Mathematica Basics: An Introduction
• Introduction
• Arithmetic
• Mathematical Functions
• Symbolic Computations
• Exact and Approximate Solutions for Equations
• Graphs of Functions of One Variable
• Graphs of Parametric Equations
• Graphs of Surfaces in Three Dimensions
• Graphs of Contour Curves for Surfaces
• Matrix Algebra
• Random Numbers
• Exercises
Mathematica Basics: Help
• Introduction
• The ? and ?? Operators
• The Help Browser
• Interrupting Mathematica Computations
• Memory Management in Mathematica
• Exercises
Mathematica Basics: Notebooks
• Introduction
• Notebook Toolbars
• Format Preferences
• Page Break Preferences
• Cell Groupings
• Tag Names
• Links
• In/Out Names
• Hyperlinks to Documentation
• Exercises
• Associated Notebook: CellHierarchy.nb
Mathematica Basics: Text and Typesetting
• Introduction
• Palettes (BasicTypesetting, CompleteCharacters, Algebraic Manipulation, Basic Input, Basic Calculations)
• Exercises
Mathematica Basics: Packages
• Introduction
• Loading Standard Packages
• Forgetting to Load a Package
• Exercises
Parte II: Designing Functions
Values, Variables, and Assignments
• Introduction
• Immediate Assignment (=)
• Delayed Assignment (:=)
• Evaluation Issues
• Computational Efficiency
• Exercises
Functions
• Introduction
• Functions with Single, Multiple, Structured Arguments
• Default and Variable Number of Arguments
• Exercises
Recursive Definitions
• Introduction
• Single and Multiple Recursive Arguments
• Limitations
• Exercises
Substitution Rules and Optional Arguments
• Introduction
• Replacement Mechanism
• Options in Built-in and User Functions
• Exercises
Four Spheres Packing Problem
• Introduction
• Analysis, Solution, Graphic Rendering
• Exercises
• Associated Notebooks and Drawings
Parte III: Designing Programs
List Processing Functions
• Introduction
• Map[ ], Fold[ ], Head[ ], Apply[ ], Outer[ ], Depth[ ], Position[ ]
• Exercises
Iterations with Loops
• Do[ ], While[ ], For[ ] Loops
• Alternatives with List Processing
• The Collatz Function
• Exercises
Computations with Modules and Local Variables
• Using Module[ ] with Numbers, Lists, Graphics
• Exercises
Parte IV: Exploring Advanced Features
Advanced Mathematica: Options
• Defining Single or Multiple Options
• Graphics Options
• Shared Options Across Functions
• Exercises
Advanced Mathematica: Hyperlinks and Buttons
• Internal and External Hyperlinks
• Hyperlink Buttons
• Typesetting and Evaluation Palettes
• Exercises
• Associated Notebooks and Folders
Advanced Mathematica: Packages
• Contexts and Names
• Initialization and Package Files
• Examples: Iteration, Gram-Schmidt
• Exercises
• Associated Support Files
Advanced Mathematica: Files, Data Exchange, and Conversions
• Directories and Paths
• Import/Export
• Format Conversions
• Exercises
• Associated Data and Demo Files
Parte V: Student Projects
Student Projects
• Introduction
• Arnold’s Cat Map
• Bouncing Balls
• Collatz’s Function
• Conway’s Challenge
• Fractals, Automata, Optics, Cryptography, Rainbows, etc.
• Associated Support Notebooks and Files
Index