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Engineering

Interactive Methods and Programs

with FORTRAN, QuickBASIC, MATLAB,

and Mathematica

Y. C. Pao

CRC Press

Boca Raton London New York Washington, D.C.

Analysis

Acquiring Editor:

Cindy Renee Carelli

Project Editor:

Albert W. Starkweather, Jr.

Cover design:

Dawn Boyd

Library of Congress Cataloging-in-Publication Data

Catalog record is available from the Library of Congress

This book contains information obtained from authentic and highly regarded sources. Reprinted

material is quoted with permission, and sources are indicated. A wide variety of references are listed.

Reasonable efforts have been made to publish reliable data and information, but the author and the

publisher cannot assume responsibility for the validity of all materials or for the consequences of their use.

Neither this book nor any part may be reproduced or transmitted in any form or by any means,

electronic or mechanical, including photocopying, microlming, and recording, or by any information

storage or retrieval system, without prior permission in writing from the publisher.

The consent of CRC Press LLC does not extend to copying for general distribution, for promotion,

for creating new works, or for resale. Specic permission must be obtained in writing from CRC Press

LLC for such copying.

Direct all inquiries to CRC Press LLC, 2000 Corporate Blvd., N.W., Boca Raton, Florida 33431.

Product or corporate names may be trademarks or registered trademarks, and are

only used for identication and explanation, without intent to infringe.

Mathematica

is developed by Wolfram Research, Inc., Champaign, IL.

Windows

is developed by Microsoft Corp., Redmond, WA.

No claim to original U.S. Government works

International Standard Book Number 0-8493-2016-X

Printed in the United States of America 1 2 3 4 5 6 7 8 9 0

Printed on acid-free paper

Trademark Notice:

Files Available from CRC Press

, and Mathematic les, which contain the

source and executable programs associated with this book are available from CRC

Press’ website — http://www.crcpress.com .

Before downloading, prepare two 3.5-inch, high-density disks — one for the

les and one for a backup. Also create a temporary directory named <interactive>

on your hard drive, which will expedite downloading. To download these les, type:

QuickBASIC

MATLAB

http://www.crcpress.com/us/ElectronicProducts/downandup.asp.

When prompted, enter

under password. Then store the les in the

<interactive> folder. If you encounter a problem, call 1-800-CRC-PRES (272-7737).

The dowloaded les may be copied to a 3.5-inch disk. The temporary <interactive>

folder then may be deleted. Don’t forget to make a backup copy of your 3.5-inch disk.

There are four subdirectories

under name and

crcpress

<QB>

, and

<Math-

tica>

which contain the

FORTRAN

source and executable programs,

QuickBASIC

source and executable programs,

les of

MATLAB

, and input and output state-

ments of for the

Mathematica

operations depicted in this textbook, respectively:

has the following les:

Bairstow.FOR CharacEquationFOR CubeSpln.FOR DiffTabl.FOR

EditFOR.EXE EigenVec.FOR

EigenvIt.FOR ExactFit.FOR

FindRoot.FOR FOR1.EXE

FOR2.EXE

FORTRAN.LIB

Gauss.FOR GauJor.FOR

LagrangI.FOR LeastSq1.FOR

LeastSqG.FOR LINK.EXE

MatxInvD.FOR NewRaphG.FOR

NuIntgra.FOR OdeBvpFD.FOR

OdeBvpRK.FOR ParabPDE.FOR

Relaxatn.FOR RungeKut.FOR

Volume.FOR WavePDE.FOR

programs index) to

include supplementary subprograms describing the problem which need to be solved

interactively. To re-edit, insert the 3.5-inch disk into Drive A and when the a:\ prompt

shows, type cd fortran to switch to the

FORTRAN

subdirectory. For example,

to solve a polynomial by the Bairstow’s method one needs to dene the polynomial,

for which the roots are to be computed. To reedit Bairstow.FOR, the user enters

a:\editfor Bairstow.for to add new

statements or change them. Notice

that both upper and lower case characters are acceptable. While creating a new

version of Bairstow.FOR, the old version will be saved in Bairstow.BAK.

To create an object le, FOR1 lename such as Bairstow.FOR and FOR2 need

to be implemented. A BAISTOW.OBJ will then be generated. For linking with the

FORTRAN

.LIB, one enters, for example, LINK

Bairstow to create an executable le Bairstow.EXE. To

library functions,

FORTRAN

, the user simply types

Bairstow after the prompt A:\ and then answers questions interactively.

run

FORTRAN

2016

EDITFOR.EXE is provided for re-editing the *.FOR source programs such as

Bairstow.FOR, CubeSpln.FOR, etc. (refer to the

FORTRAN

has the following les:

Select.BAS Select.EXE

Bairstow.EXE BRUN40.EXE

CharacEq.EXE

CubeSpln.EXE

EigenStb.EXE EigenVec.EXE

EigenVib.EXE

EigenvIt.EXE

ExactFit.EXE FindRoot.EXE

Gauss.EXE

LagrangI.EXE

LeastSq1.EXE LeastSqG.EXE

MatxInvD.EXE

NuIntgra.EXE

OdeBvpFD.EXE OdeBvpRK.EXE

ParabPDE.EXE

QB.EXE

Relaxatn.EXE RungeKut.EXE

Volume.EXE

Bairstow.QB CharacEq.QB

CubeSpln.QB

DiffTabl.QB

EigenStb.QB EigenVec.QB

EigenVib.QB

EigenvIt.QB

ExactFit.QB FindRoot.QB

GauJor.QB

Gauss.QB

LagrangI.QB LeastSq1.QB

LeastSqG.QB

MatxAlgb.QB

MatxMtpy.QB NewRaphG.QB

NuIntgra.QB

OdeBvpFD.QB

OdeBvpRK.QB ParabPDE.QB

Relaxatn.QB

RungeKut.QB

Volume.QB WavePDE.QB

, when a:\ is prompted on screen, the user enters

QB. QB.EXE and BRUN40.EXE therefore are included in

To commence

QuickBASIC

. The program

program in this textbook.

After user responds with C:\Select, the screen shows a menu as shown in Figure 1

and user then follow the screen help-messages to run a desired program.

enables user to select the available

QuickBASIC

is a subdirectory associated with

MATLAB

and has the following

les:

BVPF.m DerivatF.m DiffTabl.m EigenvIt.m

F.m FindRoot.m FP.m Functns.m

FuncZ.m FuncZnew.m FunF.m GauJor.m

integrnd.m LagrangI.m LeastSqG.m NewRaphG.m

ParabPDE.m Relaxatn.m Volume.m Warping.m

WavePDE.m

les is in Drive A, any of these

les can be accessed by enclosing the lename inside a pair of parentheses as

illustrated in

When the 3.5-inch disk containing all of these

Section 3.2

where F.m and FP.m are required for FindRoot.m and in

Section 5.2

where an integrand function

integrnd.m

is dened for numerical inte-

library m les, then no reference

to the Drive A is necessary and the pair of parentheses can also be dropped.

MATLAB

is a subdirectory associated with

Mathematica

and has the les of:

Bairstow.MTK CubeSpln.MTK DiffTabl.MTK EigenVec.MTK

ExactFit.MTK FindRoot.MTK FUNCTNS.MTK EigenvIt.MTK

Gauss.MTK GauJor.MTK LagrangI.MTK LeastSq1.MTK

LeastSqG.MTK MatxAlgb.MTK NewRaphG.MTK NuIntgra.MTK

OdeBvpFD.MTK OdeBvpRK.MTK ParabPDE.MTK Rexalatn.MTK

RungeKut.MTK Volume.MTK WavePDE.MTK

<QB>

Select

gration. If all les have been added into

Any of the above programs can be executed by

Mathematica

via mouse oper-

ation. First, by clicking the

File

option and when the pull-down menu appears, select

and then enter the lename such as a:\Mathtica\MatxAlgb.MTK (assuming

the 3.5-inch disk containing

key.

When all lines of this le is displayed on screen, move cursor to any input line such

is in Drive A) and press the

Enter

In[1]

: A = {{1,2},{3,4}}; MatrixForm[A] and hit the

Enter

key.

Mathematica

. Hence, user can reproduce all of

the output lines by sequentially running the input lines [1] through [9]. However, if

user rst run In[1] and then In[3],

Out[1]

cannot perform the addition of [A]

because [B] is not dened. If after having run In[1], user selects In[5], or, In[6],

Mathematica

then has no problem of giving out results.

FIGURE 1.

The Select screen.

Open

will respond by repeating those lines for

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