Mathematica for Scientists and Engineers

Transcription

1 Mathematica for Scientists and Engineers Thomas B. Bahder Addison-Wesley Publishing Company Reading, Massachusetts Menlo Park, California New York Don Mills, Ontario Wokingham, England Amsterdam Bonn Paris Milan Madrid Sydney Singapore Tokyo San Juan

2 Contents Chapter 1 The Building Blocks Starting Mathematica Arithmetic Operations Arithmetic Operations Complex Numbers Assigning Values to Symbols Assigning Values to Variables Defining Functions Storing Expressions in Lists Internal Representation The Expression The Atomic Types Changing Heads and Evaluation Compound Expressions Position (or Part) and Level Specifications Programming Programming Constructs Pure Functions Iteration Functions Patterns Patterns in Function Definitions Common Patterns Conditions on Patterns Strings Functions With a Variable Number of Arguments Replacement Rules Immediate versus Delayed Replacements Repeated Rule Application 70

3 xü Contents What Parts Do Rules Transform? When Does a Pattern Match? Getting Information on Commands and Variables 78 Chapter 2 Working with Lists The Listable Attribute of Built-in Functions Accessing Parts of Lists Creating Lists 95 Chapter 3 Graphics Graphics Overview Graphics Functions and Objects Plotting Functions X-Y Plots Evaluation in Function Plotting Functions Multiple Plots in One Graphic Using Options to Adjust the Plot Density Plots Contour Plots D Surface Plots Parametric Plots Plotting Data Plotting a List of Data Points Three Dimensional Data Plots Conversion of Graphics Objects D Pixel Graphics Graphics Programming Creating Graphics Objects from Graphics Primitives Writing Your Own 3-D Data Graphing Function Graphics Programming Using Packages Animating Graphics: Mathematica Movies Sound 185 Chapter 4 Scoping Constructs Local Variables Scoping of Symbols Scoping of Values of Symbols Scoping of Patterns Performance Considerations 201 Chapter 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 263

4 Contents xiii 5.10 Variable Scope in Function Definitions Complex Variables Compiled Functions Piecewise Continuous Functions 294 Chapter 6 Symbolic Calculation Operations with Polynomials Rational Expressions Differentiation Partial Derivative Total Derivative Integration Indefinite Integration Definite Integration Line Integrals Contour Integration Multiple Integrals Power Series Equations Solving Equations Solving Matrix Equations Converting Linear Equations to a Matrix Equation Simplifying Algebraic Expressions Using Patterns Working with Units 355 Chapter 7 Numerical Calculations Types of Numbers Precision and Accuracy Numerical Functions Root Finding Finding the Minimum of a Function Numerical Integration Line Integration Contour Integration Sums and Products Interpolation Functions Assigning Numerical Values to Symbols Protecting Function Arguments from N [] 407 Chapter 8 Vectors, Matrices, and Tensors Linear Algebra Vector and Matrix Algebra Creating Vectors and Matrices Operations on Vectors and Matrices Symbolic Versus Numerical Computation Solution of Linear Systems of Equations Case Study: Eigenvalues of Hermitian Matrix Vector Field Theory Vector Analysis 455

5 xiv Contents Electromagnetic Waves in an Anisotropic Medium Cartesian Tensors and Spinors Built-in Functions for Cartesian Tensors Elastic Waves in a Piezoelectric Crystal Spinors General Tensors: MathTensor Introduction to MathTensor Schwarzschild Metric: Riemann Squared Curvature Invariant 533 Chapter 9 Differential Equations Automatic Symbolic Solution Variation of Parameters Series Approximations 562 Transforming a Differential Equation Solution by Laplace Transforms Numerical Solution Perturbation Solution 594 Chapter 10 Boundary Value Problems Analytic Solution Inhomogeneous Boundary Value Problem Sturm-Liouville Eigenvalue Problem: Schrodinger Equation of a Particle in a Box Shooting Methods Simple Shooting Method Shooting to a Fitting Point Finite Difference Method A Mathematica Tutorial Inhomogeneous Boundary Value Problems Eigenvalue Problems 650 Chapter 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 Low-level Output to Files Low-level Input from Files Using Options with Read and ReadList Formatting Numbers Writing Numbers to a File in "e" Format Writing Lists to a File as Arrays Working with Binary Files Communicating with FORTRAN Communicating with С Working with Files and Directories Manipulating Files and Directories Converting a DOS Text File to UNIX Format 732

6 Contents xv Strings as Streams Input from the Keyboard Defining Print Formats 739 Chapter 12 Running Mathematica Various Ways to Run Mathematica Running from a Command Line Reading Expressions from a File Running Mathematica in Background Input from a File Running a Notebook in Background Logging Your Session 754 Chapter 13 Mathematica Packages Using Packages Contexts and Context Search Path Motivation for Contexts Writing a Package A Context Scratch Pad Practical Programming 784 Chapter 14 Introduction to MathLink Communication Calling С from Mathematica Installing an External С Function Lists as Arguments and Return Values Matrices as Arguments and Return Values Calling FORTRAN from Mathematica Calling a FORTRAN Subroutine from С Installing a Simple FORTRAN Subroutine Installing FORTRAN Matrix Multiplication Subroutine 820 Appendix: The Mathematica System 831 A.l Kernel and Front End 831 A.2 Mathematica Input 833 Index 835