Mathematics for Business, Science, and Technology: With MATLAB and Excel Computations

628 Pages·2007·5.5 MB·english

by  Steven Karris

AH
MT
Mathematics
for Business, Science, and Technology
® ®
with MATLAB and Excel Computations
Third Edition
Steven T. Karris
y
14,000
Includes a
12,000
Profit Comprehensive
10,000
Treatment of Probability
Revenue
8,000 and Statistics Illustrated
$
Cost with Numerous
6,000
Examples
4,000
Break-Even Point
2,000
0 x
100 200 300 400 500
Units Sold
Orchard Publications
www.orchardpublications.com
Mathematics Students and working professionals will find Mathematics
for Business, Science, and Technology with MATLAB®
ffoorr BBuussiinneessss,, SScciieennccee,, aanndd TTeecchhnnoollooggyy and Excel® Computations to be a concise and easy-to-
learn text. It provides complete, clear, and detailed expla-
with MATLAB® and Excel® Computations nations of the principal mathematical concepts including
probability and statistics, and these are illustrated with
Third Edition
numerous practical examples.
This text includes the following chapters and appendices:
• Numbers and Arithmetic Operations • Elementary Algebra • Intermediate Algebra
• Fundamentals of Geometry • Fundamentals of Plane Trigonometry • Fundamentals of
Calculus • Introduction to Probability and Statistics • Random Variables • Common Probability
Distributions and Tests • Curve Fitting, Regression, and Correlation • Analysis of Variance
(ANOVA) • Introduction to MATLAB • The Gamma and Beta Functions and their Distributions
• Introduction to Markov Chains • The Lambda Index • The Black-Scholes Stock Options Model
• The Alltman Bankuptcy Z-Score
Each chapter contains numerous practical applications supplemented with detailed instructions
for using MATLAB and Excel to obtain quick answers.
Steven T. Karris is the president and founder of Orchard Publications, has undergraduate and
graduate degrees in electrical engineering, and is a registered professional engineer in California
and Florida. He has more than 35 years of professional engineering experience and more than 30
years of teaching experience as an adjunct professor, most recently at UC Berkeley, California.
Orchard Publications
Visit us on the Internet
www.orchardpublications.com or email us:
[email protected]
ISBN-13: 978-11-9934404-002-77
ISBN-10: 1-9934404-002-00 $60.00 U.S.A.
Mathematics

for Business, Science, and Technology
Third Edition
With MATLAB®and Excel®Computations
Steven T. Karris
Orchard Publications
www.orchardpublications.com
Mathematics for Business, Science, and Technology with MATLAB® and Excel® Computations, Third Edition
Copyright © 2007 Orchard Publications. All rights reserved. Printed in the United States of America. No part of this
publication may be reproduced or distributed in any form or by any means, or stored in a data base or retrieval
system, without the prior written permission of the publisher.
Direct all inquiries to Orchard Publications, 39510 Paseo Padre Parkway, Fremont, California 94538, U.S.A.
URL: http://www.orchardpublications.com, e-mail: [email protected].
Product and corporate names are trademarks or registered trademarks of the MathWorks™, Inc., and Microsoft™
Corporation. They are used only for identification and explanation, without intent to infringe.
Library of Congress Cataloging-in-Publication Data
Library of Congress Control Number: 2007922089
Copyright Number: TX-5-471-563
ISBN-13: 978-1-934404-02-7
ISBN-10: 1-934404-02-0
Disclaimer
The publisher has used his best effort to prepare this text. However, the publisher and author makes no warranty of any
kind, expressed or implied with regard to the accuracy, completeness, and computer codes contained in this book, and
shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the
performance or use of these programs.
Preface
This text is written for
a. high school graduates preparing to take business or science courses at community colleges or
universities
b. working professionals who feel that they need a math review from the very beginning
c. young students and working professionals who are enrolled in continued education
institutions, and majoring in business related topics, such as business administration and
accounting, and those pursuing a career in science, electronics, and computer technology.
Chapter 1 is an introduction to the basics of algebra.
Chapter 2 is a continuation of Chapter 1 and presents some practical examples with systems of
two and three equations.
Chapters 3 and 4 discuss the fundamentals of geometry and trigonometry respectively. These
treatments are not exhaustive; these chapters contain basic concepts that are used in science and
technology.
Chapter 5 is an abbreviated, yet a practical introduction to calculus.
Chapters 6 and 7 serve as an introduction to the mathematics of finance and economics and the
concepts are illustrated with numerous real−world applications and examples.
Chapters 8 through 12 are devoted to probability and statistics. Many practical examples are
given to illustrate the importance of this branch of mathematics. The topics that are discussed,
are especially important in management decisions and in reliability. Some readers may find
certain topics hard to follow; these may be skipped without loss of continuity.
In all chapters, numerous examples are given to teach the reader how to obtain quick answers to
some complicated problems using computer tools such as MATLAB®and Microsoft Excel.®
Appendix A contains a review of the basic arithmetic operations, introduces the SI system of
units, and discusses different types of graphs. It is written for the reader who needs a review of the
very basics of arithmetic.
Appendix B is intended to teach the interested reader how to use MATLAB. Many practical
examples are presented. The Student Edition of MATLAB is an inexpensive software package; it
can be found in many college bookstores, or can be obtained directly from
The MathWorks™ Inc., 3 Apple Hill Drive, Natick, MA 01760−2098
Phone: 508 647−7000, Fax: 508 647−7001
http://www.mathworks.com
e−mail: [email protected]
Appendix C introduces the gamma and beta functions. These appear in the gamma and beta
distributions and find many applications in business, science, and engineering. For instance, the
Erlang distributions, which are a special case of the gamma distribution, form the basis of queuing
theory.
Appendix D is an introduction to Markov chains. A few practical examples illustrate their
application in making management decisions.
Appendices E, F, and G are introductions to the Lambda Index, Black−Scholes stock options
pricing, and the Altman Z−score bankruptcy prediction respectively.
Every chapter and appendix in this text is supplemented with Excel and / or MATLAB scripts to
verify the computations and to construct relevant plots. The pages where the Excel and
MATLAB scripts appear are listed in the Table of Contents.
New to the Second Edition
This is an refined revision of the first edition. The most notable changes are the addition of the
new Chapters 6 and 7, chapter−end summaries, and detailed solutions to all exercises. The latter
is in response to many students and working professionals who expressed a desire to obtain the
author’s solutions for comparison with their own.
New to the Third Edition
This is an refined revision of the second edition. The most notable is the addition of Appendices
E, F, and G. All chapters and Appendices A through D have been rewritten, and graphs have
been redrawn with the latest MATLAB® Student Version, Release 14.
All feedback for typographical errors and comments will be most welcomed and greatly
appreciated.
Orchard Publications
www.orchardpublications.com
[email protected]
Table of Contents
1
Elementary Algebra 1−1
1.1 Introduction..................................................................................................1−1
1.2 Algebraic Equations......................................................................................1−2
1.3 Laws of Exponents........................................................................................1−5
1.4 Laws of Logarithms.....................................................................................1−10
1.5 Quadratic Equations...................................................................................1−13
1.6 Cubic and Higher Degree Equations..........................................................1−15
1.7 Measures of Central Tendency...................................................................1−15
1.8 Interpolation and Extrapolation.................................................................1−20
1.9 Infinite Sequences and Series.....................................................................1−23
1.10 Arithmetic Series........................................................................................1−23
1.11 Geometric Series.........................................................................................1−24
1.12 Harmonic Series.........................................................................................1−26
1.13 Proportions .................................................................................................1−27
1.14 Summary.....................................................................................................1−29
1.15 Exercises .....................................................................................................1−33
1.16 Solutions to End−of−Chapter Exercises.....................................................1−35
Excel Computations: Pages 1−7, 1−11, 1−16, 1−17, 1−33, 1−36
MATLAB Computations: Pages 1−7, 1−11
2
Intermediate Algebra 2−1
2.1 Systems of Two Equations........................................................................................2−1
2.2 Systems of Three Equations......................................................................................2−6
2.3 Matrices and Simultaneous Solution of Equations...................................................2−7
2.4 Summary.................................................................................................................2−26
2.5 Exercises..................................................................................................................2−30
2.6 Solutions to End−of−Chapter Exercises..................................................................2−32
Excel Computations: Pages 2−23, 2−24, 2−30, 2−31
MATLAB Computations: Pages 2−15, 2−16, 2−24, 2−25, 2−32, 2−36
3
Fundamentals of Geometry 3−1
3.1 Introduction...............................................................................................................3−1
3.2 Plane Geometry Figures.............................................................................................3−1
3.3 Solid Geometry Figures............................................................................................3−16
3.4 Using Spreadsheets to Find Areas of Irregular Polygons.........................................3−20
3.5 Summary..................................................................................................................3−23
Mathematics for Business, Science, and Technology, Third Edition i
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3.6 Exercises..................................................................................................................3−27
3.7 Solutions to End−of−Chapter Exercises..................................................................3−29
Excel Computations: Pages 3−20, 3−30
4
Fundamentals of Plane Geometry 4−1
4.1 Introduction.............................................................................................................4−1
4.2 Trigonometric Functions.........................................................................................4−2
4.3 Trigonometric Functions of an Acute Angle..........................................................4−2
4.4 Trigonometric Functions of an Any Angle.............................................................4−3
4.5 Fundamental Relations and Identities....................................................................4−6
4.6 Triangle Formulas..................................................................................................4−12
4.7 Inverse Trigonometric Functions..........................................................................4−13
4.8 Area of Polygons in Terms of Trigonometric Functions.......................................4−14
4.9 Summary................................................................................................................4−16
4.10 Exercises................................................................................................................4−18
4.11 Solutions to End−of−Chapter Exercises................................................................4−19
Excel Computations: Pages 4−9 through 4−11, 4−13, 4−19 through 4−21
MATLAB Computations: Page 4−15
5
Fundamentals of Calculus 5−1
5.1 Introduction............................................................................................................5−1
5.2 Differential Calculus...............................................................................................5−1
5.3 The Derivative of a Function.................................................................................5−3
5.4 Maxima and Minima.............................................................................................5−11
5.5 Integral Calculus...................................................................................................5−15
5.6 Indefinite Integrals................................................................................................5−16
5.7 Definite Integrals..................................................................................................5−16
5.8 Summary...............................................................................................................5−21
5.9 Exercises................................................................................................................5−23
5.10 Solutions to End−of−Chapter Exercises...............................................................5−24
Excel Computations: Pages 5−8, 5−11, 5−18
MATLAB Computations: Pages 5−24 through 5−26
6
Mathematics of Finance and Economics 6−1
6.1 Common Terms........................................................................................................6−1
6.1.1 Bond...............................................................................................................6−1
6.1.2 Corporate Bond.............................................................................................6−1
6.1.3 Municipal Bond.............................................................................................6−1
ii Mathematics for Business, Science, and Technology, Third Edition
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6.1.4 Treasury Bond...............................................................................................6−1
6.1.5 Perpetuity......................................................................................................6−1
6.1.6 Perpetual Bond..............................................................................................6−1
6.1.7 Convertible Bond..........................................................................................6−2
6.1.8 Treasury Note...............................................................................................6−2
6.1.9 Treasury Bill..................................................................................................6−2
6.1.10 Face Value...................................................................................................6−2
6.1.11 Par Value......................................................................................................6−2
6.1.12 Book Value...................................................................................................6−3
6.1.13 Coupon Bond...............................................................................................6−3
6.1.14 Zero Coupon Bond......................................................................................6−3
6.1.15 Junk Bond....................................................................................................6−3
6.1.16 Bond Rating Systems...................................................................................6−3
6.1.17 Promissory Note..........................................................................................6−4
6.1.18 Discount Rate..............................................................................................6−4
6.1.19 Prime Rate...................................................................................................6−4
6.1.20 Mortgage Loan............................................................................................6−4
6.1.21 Predatory Lending Practices........................................................................6−5
6.1.22 Annuity.......................................................................................................6−5
6.1.23 Ordinary Annuity........................................................................................6−5
6.1.24 Sinking Fund...............................................................................................6−6
6.2 Interest....................................................................................................................6−6
6.2.1 Simple Interest.............................................................................................6−6
6.2.2 Compound Interest......................................................................................6−8
6.2.3 Effective Interest Rate...............................................................................6−22
6.3 Sinking Funds........................................................................................................6−24
6.4 Annuities...............................................................................................................6−29
6.5 Amortization.........................................................................................................6−34
6.6 Perpetuities............................................................................................................6−36
6.7 Valuation of Bonds................................................................................................6−39
6.7.1 Calculating the Purchase Price of a Bond...................................................6−40
6.7.2 Total Periodic Bond Disbursement.............................................................6−42
6.7.3 Calculation of Interest Rate of Bond..........................................................6−44
6.8 Spreadsheet Financial Functions.........................................................................6−45
6.8.1 PV Function..............................................................................................6−46
6.8.2 FV Function..............................................................................................6−48
6.8.3 PMT Function...........................................................................................6−49
6.8.4 RATE Function.........................................................................................6−50
6.8.5 NPER Function..........................................................................................6−51
6.8.6 NPV Function...........................................................................................6−52
6.8.7 IIR Function..............................................................................................6−54
Mathematics for Business, Science, and Technology, Third Edition iii
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6.8.8 MIIR Function...........................................................................................6−56
6.8.9 IPMT Function..........................................................................................6−58
6.8.10 PPMT Function........................................................................................6−59
6.8.11 ISPMT Function........................................................................................6−60
6.9 The MATLAB Financial Toolbox.......................................................................6−61
6.9.1 irr MATLAB Function...............................................................................6−61
6.9.2 effrr MATLAB Function............................................................................6−62
6.9.3 pvfix MATLAB Function..........................................................................6−62
6.9.4 pvvar MATLAB Function.........................................................................6−63
6.9.5 fvfix MATLAB Function...........................................................................6−64
6.9.6 fvvar MATLAB Function..........................................................................6−65
6.9.7 annurate MATLAB Function.....................................................................6−66
6.9.8 amortize MATLAB Function.....................................................................6−67
6.10 Comparison of Alternate Proposals.......................................................................6−68
6.11 Kelvin’s Law...........................................................................................................6−71
6.12 Summary................................................................................................................6−75
6.13 Exercises.................................................................................................................6−78
6.14 Solutions to End−of−Chapter Exercises................................................................6−81
Excel Computations: Pages 6−10 through 6−14, 6−28, 6−29, 6−33, 6−35,
6−45 through 6−52, 6−54, 6−56, 6−58 through 6−61, 6−81
MATLAB Computations: Pages 6−61, 6−68
7
Depreciation, Impairment, and Depletion 7−1
7.1 Depreciation Defined................................................................................................7−1
7.1.1 Items that Can Be Depreciated......................................................................7−2
7.1.2 Items that Cannot Be Depreciated.................................................................7−2
7.1.3 Depreciation Rules..........................................................................................7−2
7.1.4 When Depreciation Begins and Ends.............................................................7−3
7.1.5 Methods of Depreciation................................................................................7−3
7.1.5.1 Straight−Line (SL) Depreciation Method..........................................7−4
7.1.5.2 Sum of the Years Digits (SYD) Method.............................................7−5
7.1.5.3 Fixed-Declining Balance (FDB) Method...........................................7−6
7.1.5.4 The 125%, 150%, and 200% General Declining Balance Methods...7−8
7.1.5.5 The Variable Declining Balance Method...........................................7−9
7.1.5.6 The Units of Production Method.....................................................7−10
7.1.5.7 Depreciation Methods for Income Tax Reporting...........................7−11
7.2 Impairments............................................................................................................7−18
7.3 Depletion................................................................................................................7−19
7.4 Valuation of a Depleting Asset..............................................................................7−20
7.5 Summary.................................................................................................................7−25
iv Mathematics for Business, Science, and Technology, Third Edition
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