Mathematica by Example (eBook)
670 Seiten
Elsevier Science (Verlag)
978-1-4832-5928-4 (ISBN)
Mathematica by Example presents the commands and applications of Mathematica, a system for doing mathematics on a computer. This text serves as a guide to beginning users of Mathematica and users who do not intend to take advantage of the more specialized applications of Mathematica. The book combines symbolic manipulation, numerical mathematics, outstanding graphics, and a sophisticated programming language. It is comprised of 10 chapters. Chapter 1 gives a brief background of the software and how to install it in the computer. Chapter 2 introduces the essential commands of Mathematica. Basic operations on numbers, expressions, and functions are introduced and discussed. Chapter 3 provides Mathematica's built-in calculus commands. The fourth chapter presents elementary operations on lists and tables. This chapter is a prerequisite for Chapter 5 which discusses nested lists and tables in detail. The purpose of Chapter 6 is to illustrate various computations Mathematica can perform when solving differential equations. Chapters 7, 8, and 9 introduce Mathematica Packages that are not found in most Mathematica reference book. The final chapter covers the Mathematica Help feature. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.
Front Cover 1
Mathematica by Example 4
Copyright Page 5
Table of Contents 6
PREFACE 16
Chapter 1. Getting Started 18
1.1 Macintosh Basics 19
1.2 Introduction to the Basic Types of Cells, Cursor Shapes, and Evaluating Commands 23
1.3 Introduction to the Mathematica Menu 28
Preview 30
Chapter 2. Mathematical Operations on Numbers, Expressions and Functions in Mathematica 31
2.1 Numerical Calculations and Built-in Functions 33
2.2 Expressions and Functions 43
2.3 Mod Math 61
2.4 Graphing Functions and Expressions 65
2.5 Exact and Approximate Solutions of Equations 88
Chapter 3. Calculus 101
3.1 Computing Limits 103
3.2 Differential Calculus 109
3.3 Implicit Differentiation 131
3.4 Integral Calculus 140
3.5 Series 154
3.6 Multi-Variable Calculus 164
Chapter 4. Introduction to Lists and Tables 207
4.1 Defining Lists 209
4.2 Operations on Lists 214
4.3 Applications 227
Chapter 5. Introduction to Nested Lists: Matrices and Vectors 278
5.1 Nested Lists: Introduction to Matrices, Vectors and Matrix Operations 279
5.2 Linear Systems of Equations 294
5.3 Vector Calculus 320
5.4 Saving Results for Future Mathematica Sessions 339
Chapter 6. Applications Related to Ordinary and Partial Differential Equations 352
6.1 Linear Equations 353
6.2 Exact Differential Equations 362
6.3 Undetermined Coefficients 372
6.4 Linear n-th Order Differential Equations with Constant Coefficients 380
6.5 The Cauchy-Euler Equation 386
6.6 Variation of Parameters 389
6.7 Capabilities of DSolve 394
6.8 Systems of Linear Differential Equations 397
6.9 Series Solutions to Ordinary Differential Equations 409
6.10 Series Solutions to Partial Differential Equations 419
6.11 Numerical Solutions of Differential Equations 431
6.12 Numerical Solutions of Systems of Differential Equations 434
Chapter 7. Introduction to Mathematica Packages 439
7.1 Algebra 440
7.2 Linear Algebra 452
7.3 Version 2.0 Calculus 487
7.4 Discrete Math 498
Chapter 8. Some Graphics Packages 514
8.1 Graphics.m 514
8.2 Polyhedra.m 526
8.3 Shapes.m 530
8.4 ParametricPlot3D.m 540
8.5 ImpIicitPlot.m 546
8.6 PlotField.m 550
8.7 PlotField3D.m 552
8.8 ComplexMap.m 556
Chapter 9. Some Special Packages 560
9.1 Approximations.m 561
9.2 GaussianQuadrature.m 566
9.3 NLimit.m 570
9.4 PolynomialFit.m 576
9.5 RungeKutta.m 582
9.7 HypothesisTests.m 597
9.8 Confidencelntervals.m 603
9.9 LinearRegression.m 606
Chapter 10. Getting Help from Mathematica and Making Mathematica Do What You Want 611
10.1 Getting Help from Mathematica 611
10.2 The init.m file 626
10.3 Explanation of the Mathematica Menu 629
10.4 Some Common Errors and Their Remedies 645
10.5 Additional References 651
Appendix: Introduction to Programming in Mathematica 652
Index 664
| Erscheint lt. Verlag | 9.5.2014 |
|---|---|
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Technik | |
| ISBN-10 | 1-4832-5928-5 / 1483259285 |
| ISBN-13 | 978-1-4832-5928-4 / 9781483259284 |
| Haben Sie eine Frage zum Produkt? |
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