Page 5 - Numerical Analysis Using MATLAB and Excel

Preface

Numerical analysis is the branch of mathematics that is used to find approximations to difficult
problems such as finding the roots of non−linear equations, integration involving complex
expressions and solving differential equations for which analytical solutions do not exist. It is
applied to a wide variety of disciplines such as business, all fields of engineering, computer science,
education, geology, meteorology, and others.
Years ago, high−speed computers did not exist, and if they did, the largest corporations could only
afford them; consequently, the manual computation required lots of time and hard work. But now
that computers have become indispensable for research work in science, engineering and other
fields, numerical analysis has become a much easier and more pleasant task.

This book is written primarily for students/readers who have a good background of high−school
*
algebra, geometry, trigonometry, and the fundamentals of differential and integral calculus. A
prior knowledge of differential equations is desirable but not necessary; this topic is reviewed in
Chapter 5.
One can use Fortran, Pascal, C, or Visual Basic or even a spreadsheet to solve a difficult problem.
It is the opinion of this author that the best applications programs for solving engineering
problems are 1) MATLAB which is capable of performing advanced mathematical and
engineering computations, and 2) the Microsoft Excel spreadsheet since the versatility offered by
spreadsheets have revolutionized the personal computer industry. We will assume that the reader
has no prior knowledge of MATLAB and limited familiarity with Excel.

We intend to teach the student/reader how to use MATLAB via practical examples and for
detailed explanations he/she will be referred to an Excel reference book or the MATLAB User’s
Guide. The MATLAB commands, functions, and statements used in this text can be executed
with either MATLAB Student Version 12 or later. Our discussions are based on a PC with
Windows XP platforms but if you have another platform such as Macintosh, please refer to the
appropriate sections of the MATLAB’s User Guide that also contains instructions for installation.

MATLAB is an acronym for MATrix LABoratory and it is a very large computer application
which is divided to several special application fields referred to as toolboxes. In this book we will
be using the toolboxes furnished with the Student Edition of MATLAB. As of this writing, the
latest release is MATLAB Student Version Release 14 and includes SIMULINK which is a

* These topics are discussed in Mathematics for Business, Science, and Technology, Third Edition, ISBN 0−9709511−
0−8. This text includes probability and other advanced topics which are supplemented by many practical applications using
Microsoft Excel and MATLAB.