Harness the power of MATLAB to analyze complex problems with matricesIntroduction to MATLAB® with Numerical Preliminaries provides thorough training for using MATLAB software with an emphasis on scientific computing. Readers learn how to apply their knowledge to a variety of fields, including linear algebra, probability, finance, ecology, and discrete mathematics. The text carefully balances its coverage among four pedagogical components: analytic concepts, geometric concepts, programs and algorithms, and applications. Detailed problem sets build the reader's understanding and competence in each of these areas.All the tools needed to master and exploit all the powerful features of MATLAB are provided:"Exercises for the Reader," used throughout the text, that test readers' understanding of key concepts, helping them to move on to more advanced topics and applications (complete solutions are given in an appendix)Illustrative examples, provided throughout the text, that demonstrate MATLAB's ability to analyze an assortment of datasetsExtensive coverage of MATLAB's graphical capabilities, enabling readers to express solutions to problems using high-quality graphicsExplanations that are rigorous, yet written in a very accessible, user-friendly styleExtensive problem sets, provided at the end of each section, that enable readers to apply their knowledgeAs one of the most popular mathematical software packages used in a wide range of fields including biology, physics, engineering, business, and finance, this is essential knowledge for anyone who may need to analyze data. Moreover, the author proves how easy MATLAB is to learn, including mastering its tremendous graphical capabilities. All that is needed is a basic understanding of single variable calculus. This is an excellent text for any course in MATLAB or scientific computing. Additionally, it serves as a supplementary text for any mathematics or science course that makes use of MATLAB.
Author(s): Alexander Stanoyevitch
Edition: 1
Publisher: Wiley-Interscience
Year: 2004
Language: English
Pages: 345
Tags: Математика;Дифференциальные уравнения;
Introduction to MATLAB® with Numerical Preliminaries......Page 6
Contents......Page 8
Preface......Page 10
1.1: What Is MATLAB?......Page 14
1.2: Starting and Ending a MATLAB Session......Page 15
1.3: A First MATLAB Tutorial......Page 16
1.4: Vectors and an Introduction to MATLAB Graphics......Page 20
1.5: A Tutorial Introduction to Recursion on MATLAB......Page 27
2.1: What Is Numerical Analysis?......Page 36
2.2: Taylor Polynomials......Page 38
2.3: Taylor's Theorem......Page 47
3.1: What Are M-files?......Page 58
3.2: Creating an M-file for a Mathematical Function......Page 62
4.1: Some Basic Logic......Page 70
4.2: Logical Control Flow in MATLAB......Page 73
4.3: Writing Good Programs......Page 86
5.1: Floating Point Numbers......Page 98
5.2: Floating Point Arithmetic: The Basics......Page 99
*5.31 Floating Point Arithmetic: Further Examples and Details......Page 109
6.1: A Brief Account of the History of Rootfinding......Page 120
6.2: The Bisection Method......Page 123
6.3: Newton's Method......Page 131
*6.4: The Secant Method......Page 141
*6.5: Error Analysis and Comparison of Rootfinding Methods......Page 145
7.1: Matrix Operations and Manipulations with MATLAB......Page 156
*7.2: Introduction to Computer Graphics and Animation......Page 198
7.3: Notations and Concepts of Linear Systems......Page 199
7.4: Solving General Linear Systems with MATLAB......Page 202
7.5: Gaussian Elimination, Pivoting, and LU Factorization......Page 216
*7.6: Vector and Matrix Norms, Error Analysis, and Eigendata......Page 237
7.7: Iterative Methods......Page 265
Appendix A: MATLAB's Symbolic Toolbox......Page 298
Appendix B: Solutions to All Exercises for the Reader......Page 306
References......Page 336
MATLAB Command Index......Page 340
Index......Page 342
