[...]... Developone or more numerical methods for solving the problem Illustrate the numerical methodswith examples In most cases, the numerical methodspresented to solve a particular problemproceed from simple methods to complex methods, which in manycases parallels the chronological development of the methods Somepoor methods and some bad methods, as well as good methods, are presented for pedagogical reasons... accuracy ,and errors, and a discussionof number representation A brief description of software packagesand libraries is presented Last, the Taylor series and the Taylor polynomial, which are indispensable in developing and understanding manynumerical algorithms, are presented and discussed 0.1 OBJECTIVE AND APPROACH The objective of this bookis to introduce the engineer and scientist to numericalmethods... PDEsare presented Numerous numerical methodsfor solving the model PDEsare presented The material presented in this book is an introduction to numerical methods Many practical problems can be solved by the methodspresented here Many other p[actical problems require other or more advanced numerical methods Mastery of the material presented in this bookwill prepare engineers and scientists to solve many... language FORTRAN one of the oldest programminglanguages Whencarefully prepared, is FORTRAN approach pseudocode Consequently, the programs presented in this book can are written in simple FORTRAN There are several vintages of FORT_RAN: FORTRAN I, FORTRAN FORTRAN 77, and 90 The programs presented in this book are II, 66, compatible with FORTRAN and 90 77 Several programs are presented in each chapter for. .. lot of computationaleffort and for algorithms that are applied many times Several programming languages are available for preparing computerprograms: FORTRAN, Basic, C, PASCAL, etc., and their variations, to namea few Pseudocode,whichis a set of instructions for implementing algorithm an expressed in conceptual form, is also quite popular Pseudocode be expressed in the can detailed form of any specific... whenother methodsare required, and give them the backgroundto study other methodsin other books and journals 0.3 EXAMPLES All of the numerical methodspresented in this book are illustrated by applying themto solve an example problem Each chapter has one or two example problems, which are solved by all of the methodspresented in the chapter This approachallows the analyst to comparevarious methodsfor the... PACKAGES AND LIBRARIES Numerous commercialsoftware packages and libraries are available for implementingthe numerical solution of engineering and scientific problems Twoof the more versatile software packages are Mathcadand Matlab These software packages, as well as several other packagesand several libraries, are listed belowwith a brief description of each one and references to sources for the software... modulescontained in some80 software packages at NIST (National Institute for Standards and Technology) and NETLIB gams.nist.gov IMSL IMSL (International Mathematicsand Statistical Library) is a comprehensive resource of more than 900 FORTRAN subroutines for use in general mathematics and statistical data analysis Also available in C and Java Visual Numerics, Inc., 1300W.Sam Houston Parkway S., Suite 150,... Polynomial approximation essential for interpolation, differentiation, and integrais tion of sets of discrete data A good understanding of polynomial approximation is a necessary requirementfor the numerical analyst 1.5 NUMERICAL DIFFERENTIATION AND DIFFERENCE FORMULAS The evaluation of derivatives, a process known differentiation, is required in many as problemsin engineering and science Differentiation... the methods presented in Chapter 4, or fit approximately by the least squares procedure described in Chapter4 Several numericaldifferentiation formulasbasedon differentiation of polynomialsare presented in Chapter 5 Numericaldifferentiation formulas also can be developedusing Taylor series This approach is quite useful for developing difference formulas for approximating exact derivatives in the numericalsolution .