MATLAB Numerical Calculations by Cesar Perez Lopez

Introduction

MATLAB is the tool of the modern day mathematician or engineer. Te incredible deep functionality of MATLAB makes what would have taken hours 40 years ago, often less than a minute with MATLAB built in functions. MATLAB enables you to explore multiple approaches and reach a solution faster often more accurately than with other tools or traditional programming languages, such as C/C++ or Java. More importantly, it has changed the way we learn and made getting solutions immensely simpler. So, you can now focus on the application, instead of the math. And with that easily available power, you can explore and fnd more and more functions, test hypotheses and become a signifcantly more powerful worker.

Tis book is designed for use, in part, as a tool to enable you to use MATLAB as a scientifc/business calculator so that you can get numerical solutions to problems involving a wide array of mathematics using MATLAB. But it is broader in scope than that. Te book can be used as an independent resource for MATLAB. A background in the necessary mathematics is assumed, so this book shows you how to interpret your problems to get MATLAB to do what you want it to do. Just look up the function you want in the book and you are ready to use it in MATLAB or use the book to learn about the enormous range of options that MATLAB offers. Te book is topical, picking examples to show not only general methods in using MATLAB, but specifcs to use MATLAB for advanced mathematical computations while giving a glimpse at their application.

MATLAB Numerical Calculations focuses on MATLAB capabilities to give you numerical solutions to problems you are likely to encounter in your professional or scholastic life. It introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at basic MATLAB functionality with integers, rational numbers and real and complex numbers, and MATLAB’s relationship with Maple, you will learn how to solve equations in MATLAB, and how to simplify the results. You will see how MATLAB incorporates vector, matrix and character variables, and functions thereof. MATLAB is a powerful tool used to defned, manipulate and simplify complex algebraic expressions. With MATLAB you can also work with ease in matrix algebra, making use of commands which allow you to fnd eigenvalues, eigenvectors, determinants, norms and various matrix decompositions, among many other features. Lastly, you will see how you can write scripts and use MATLAB to explore numerical analysis, fnding approximations of integrals, derivatives and numerical solutions of differential equations.

MATLAB Numerical Calculations Contents

About the Author ……………………………………………xi
Introduction…………………………………………… xv
■Chapter 1: Introduction to MATLAB ……………………………………………1
■Chapter 2: Integers, Divisibility and Number Systems……………………………………………11
■Chapter 3: Real and Complex Numbers……………………………………………43
■Chapter 4: Numerical Variables, Vectors and Matrices……………………………………………95
■Chapter 5: Vectors and Matrices……………………………………………139
■Chapter 6: Functions ……………………………………………179
■Chapter 7: Programming and Numerical Analysis ……………………………………………211
■Chapter 8: Numerical Algorithms: Equations, Derivatives, Integrals and
Differential Equations………………………………………………279