Mathematica for Scientists and Engineers

About Thomas B. Bahder Thomas B. Bahder is a research scientist at Harry Dimond Labs in Adelphi, Maryland, where he uses Mathematica as a tool to solve complex problems. He also teaches popular Mathematica workshops through the Center for the Applications of Mathematics at George Mason University. Dr. Bahder holds a Ph.D. in theoretical physics from Rutgers University. 0201540908AB04062001

1. The Building Blocks. Starting Mathematica. Arithmetic Operations. Assigning Values to Symbols. Internal Representation. Programming. Patterns. Replacement Rules. Getting Information on Commands and Variables. 2. Working With Lists. The Listable Attribute of Built-In Functions. Accessing Parts of Lists. Creating Lists. 3. Graphics. Graphics Overview. Plotting Functions. Plotting Data. Graphics Programming. Animating Graphics: Mathematica Movies. Sound. 4. Scoping Constructs. Local Variables. Performance Considerations. 5. Functions. Defining Functions. Evaluation of Function Arguments. Functions that Call Other Functions. Delayed vs. Immediate Assignment. Splicing-In Function Arguments. Functions that Remember Their Values. Pure Functions. Attributes. Values Associated with Symbols. Variable Scope in Function Definitions. Complex Variables. Compiled Functions. Piecewise Continuous Functions. 6. Symbolic Calculation. Operations with Polynomials. Rational Expressions. Differentiation. Integration. Power Series. Equations. Simplifying Algebraic Expressions Using Patterns. Working with Units. 7. Numerical Calculations. Types of Numbers. Precision and Accuracy. Numerical Functions. Assigning Numerical Values to Symbols. Protecting Function Arguments From N(). 8. Vector, Matrices And Tensors. Linear Algebra. Vector Field Theory. Cartesian Tensors and Spinors. General Tensors: Math Tensor. 9. Differential Equations. Automatic Symbolic Solution. Variation of Parameters. Series Approximations. Solution by Laplace Transforms. Numerical Solution. Perturbation Solution. 10. Boundary Value Problems. Analytic Solution. Shooting Methods. Finite Difference Method. 11. Input And Output. Output Formats. Input and Output of Expressions: Path and Current Directory. Input and Output of Graphics and Large Expressions. Reading and Writing Files. Formatting Numbers. Writing Numbers to a File in "e" Format. Writing Lists to a File as Arrays. Working with Binary Files. Working with Files and Directories. Strings as Streams. Input from the Keyboard. Defining Print Formats. 12. Running Mathematica. Various Ways to Run Mathematica. Running from a Command Line. Reading Expressions from a File. Running Mathematica in Background. Logging Your Session. 13. Mathematica Packages. Using Packages. Contexts and Content Search Path. Motivation for Contexts. Writing a Package. A Context Scratch Pad. Practical Programming. 14. Introduction To Mathlink Communication. Calling C from Mathematica. Calling FORTRAN from Mathematica.