Page 18 - Excel for Scientists and Engineers: Numerical Methods

Preface

The solutions to mathematical problems in science and engineering can be
obtained by using either analytical or numerical methods. Analytical (or direct)
methods involve the use of closed-form equations to obtain an exact solution, in a
nonrepetitive fashion; obtaining the roots of a quadratic equation by application
of the quadratic formula is an example of an analytical solution. Numerical (or
indirect) methods involve the use of an algorithm to obtain an approximate
solution; results of a high level of accuracy can usually be obtained by applying
the algorithm in a series of successive approximations.
As the complexity of a scientific problem increases, it may no longer be
possible to obtain an exact mathematical expression as a solution to the problem.
Such problems can usually be solved by numerical methods.

The Objective of This Book
Numerical methods require extensive calculation, which is easily
accomplished using today's desktop computers. A number of books have been
written in which numerical methods are implemented using a specific
programming language, such as FORTRAN or C++. Most scientists and
engineers received some training in computer programming in their college days,
but they (or their computer) may no longer have the capability to write or run
programs in, for example, FORTRAN. This book shows how to implement
numerical methods using Microsoft Excel@, the most widely used spreadsheet
software package. Excel@ provides at least three ways for the scientist or
engineer to apply numerical methods to problems:
by implementing the methods on a worksheet, using worksheet formulas

by using the built-in tools that are provided within Excel
by writing programs, sometimes loosely referred to as macros, in Excel's
Visual Basic for Applications (VBA) programming language.
All of these approaches are illustrated in this book.
This is a book about numerical methods. I have emphasized the methods and
have kept the mathematical theory behind the methods to a minimum. In many
cases, formulas are introduced with little or no description of the underlying
theory. (I assume that the reader will be familiar with linear interpolation, simple
calculus, regression, etc.) Other topics, such as cubic interpolation, methods for
solving differential equations, and so on, are covered in more detail, and a few

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