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SCHAUM S OUTLINE OF,THEORY AND PROBLEMS,BASIC MATHEMATICS. with Applications to,Science and Technology,Second Edition. HAYM KRUGLAK Ph D,Professor Emeritus of Physics,Western Michigan University. JOHN T MOORE Ph D,Former Professor of Mathematics,University of Western Ontario. RAMON A MATA TOLEDO Ph D,Associate Professor of Computer Science.

James Madison University,SCHAUM S OUTLINE SERIES,McGRAW HILL. New York San Francisco Washington D C Auckland Bogotci. Caracas Lisbon London Madrid Mexico City, Milan Montreal New Delhi San Juan Singapore Sydney. Tokyo Toronto, Dedicated to the Lion of Judah for his many blessings opportunities and the. wonderful family that he has given me, Dr Haym Kruglak is a Professor Emeritus of Physics at Western Michigan University. Dr John T Moore was a former professor of Mathematics at the University of Western Ontario. Dr Ramon A Mata Toledo is a tenured Associate Professor of Computer Science at James. Madison University He holds a Ph D from Kansas State University in Computer Science He. earned his M S and M B A from the Florida Institute of Technology His bachelor degree with. a double major in Mathematics and Physics is from the Instituto Pedagogic0 de Caracas. Venezuela Dr Mata Toledo s main areas of interest are databases natural language processing. and applied mathematics He is the author of numerous papers in professional magazines national. and international congresses Dr Mata Toledo can be reached at matalra jrnu edu. Schaum s Outline of Theory and Problems of,BASIC MATHEMATICS.

Copyright 0 1998 1973 by The McGraw Hill Companies Inc All rights reserved Printed in. the United States of America Except as permitted under the Copyright Act of 1976 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. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 PRS PRS 9 0 2 1 0 9. ISBN 0 07 037 132 6,Sponsoring Editor Barbara Gilson. Production Supervisor Clara Stanley,Editing Supervisor Maureen B Walker. Library of Congress Cataloging in PublicationData,Kruglak Haym. Schaum s outline of basic mathematics with applications to science. and technology 2nd ed Haym Kruglak John T Moore Ramon A. Mata Toledo,p cm Schaum s outline series, Rev ed of Schaum s outline of theory and problems of basic. mathematics with applications to science and technology Haym. Kruglak John T Moore c1973,Includes index,ISBN 0 07 037 182 6 pbk.

1 Mathematics 1 Moore John T 11 Mata Toledo Ramon A. 111 Kruglak Haym Schaum s outline of theory and problems of. basic mathematics with applications to science and technology. QA39 2 K77 1998,51Mc21 98 I3992,McGraw Hill,A Division of 7heMcGmw Mll Contpanics. This book is designed for the many individuals who have difficulties in applying. mathematics The topics were selected primarily because of their USEFULNESS Thus the. emphasis throughout the book is on the formulation and solution of problems from the physical. It is assumed that the user of this book has been exposed to some high school mathematics The. selected principles techniques and examples were developed to aid. 1 Those who have an average background in high school mathematics but have not used this. discipline for several years Veterans and other adults returning to school frequently need. not only a review of the mathematics fundamentals but also an exposure to applications. which may be new to them, 2 Those who have a good background in mathematics but need a handy refresher as well as. a source book of unfamiliar concepts techniques and applications. 3 Those who have a poor background in high school mathematics These students need a. compact reference source of mathematical concepts immediately applicable to their. mathematics science and technology courses, Basic Mathematics may also be used successfully as a classroom text 1 in community and. technical junior colleges as a first course in mathematics 2 in colleges and universities for non. credit remedial and compensatory courses 3 in high schools for special senior year review and. preparatory courses 4 in vocational schools for technical mathematics courses 5 in adult evening. schools for refresher and terminal courses, Many concepts and applications not usually taught in high school or college courses are included. in this book it should thus become a valuable supplementary text for high school and college courses. in physical science chemistry physics astronomy and computer science. Each chapter contains a summary of basic definitions principles and techniques with illustrative. examples The accompanying Solved Problems drawn largely from the elementary sciences and. technology are provided with step by step solutions. The sets of Supplementary Problems concluding the chapters are selected to reinforce the. understanding of each concept and skill Answers are given for all the problems. If the users of this book find it helpful in increasing their mathematical mastery the authors will. feel richly rewarded,HAYMKRUGLAK,RAMONA MATA TOLEDO.

How to Use This Book, Mathematics is indispensable to the understanding and application of the basic laws of the. physical world The principles examples exercises and illustrations in this book have been. especially selected so as to be of maximum value to you in using them effectively. If you are not sure what to study ask your science instructor or curriculum adviser to point out the. topics in this book which are most essential for your needs. We believe that the following suggestions will enable you to learn more efficiently the desired. mathematical skills, 1 Get to know what topics are covered in this book by scanning the table of contents and. index Skim the pages from beginning to end, 2 Have paper and pencils handy Use standard size paper or a notebook Nothing is as. subject to error as work done on small odd scraps of paper. 3 Learn the terms and definitions, 4 Reproduce in writing all the steps of the solved examples and problems. 5 Read most carefully the statement of the problem. 6 Work out all the steps of the supplementary problems in a systematic fashion Check your. solution before looking up the answer, 7 Use the index and follow up all the cross references for a given topic.

8 Obtain if necessary additional information from high school and college textbooks. available in school and public libraries, 9 Read carefully the manual of your calculator When working out the problems understand. that there may be differences in accuracy and precision between the different models and. brands of calculators, 10 The following conventions have been adopted to explain the use of the graphing calculators. Function keys are enclosed in curly brackets in CAPS for example ENTER This. instructs the user to press the key labeled ENTER Options on screen menus are. shown underlined For example for the graphing calculator HP 38G the sequence. LIB Function ENTER will indicate that Function is an option of the screen menu. obtained after pressing the key LIB Comments about the use of function keys or. options are enclosed in double quotes For example Press the shift key the turquoise. key first and then press the PLOT key in the SETUP Menu. Chapter I DECIMAL FRACTIONS 1, 1 1 The Decimal System 1 2 Decimal Fractions 1 3 Position Diagram for Decimals. 1 4 Importance of Decimal Fractions 1 5 Reading Numbers with Decimal Fractions. 1 6 Writing Numbers with Decimal Fractions 1 7 The Basic Laws of Arithmetic. 1 8 Addition of Decimals 1 9 Subtraction of Decimals 1 10 Multiplication of Deci. mals 1 11 Division of Decimals 1 12 Rounding Off Decimals. Chapter 2 MEASUREMENT AND SCIENTIFIC NOTATION 9, 2 1 Basic Concepts 2 2 Experimental Errors or Uncertainties 2 3 Accuracy 2 4. Precision 2 5 Significant Figures Definition 2 6 Reading Significant Figures 2 7. Operations with Significant Figures 2 8 Definition Scientific Notation 2 9 Advantages. of Scientific Notation 2 10 Conversion to and from Scientific Notation 2 1 1 Operations. with Scientific Notation 2 12 Approximate Computations with Scientific Notation. 2 13 Order of Magnitude 2 14 Conversion of Units 2 15 The International System of. Units 2 16 Prefixes and Decimal Multipliers,Chapter 3 COMMON FRACTIONS 36.

3 1 Fractions and Measurement 3 2 Terms 3 3 Reading and Writing Fractions 3 4. Basic Principle 3 5 Reduction to Lowest Terms 3 6 Comparison of Fractions 3 7. Addition of Fractions 3 8 Subtraction of Fractions 3 9 Multiplication of Fractions. 3 10 Division of Fractions 3 1 1 Reciprocals 3 12 Conversion of Common Fractions into. Decimal Fractions,Chapter 4 PERCENTAGE 51, 4 1 Terms 4 2 Percent and Fractions 4 3 Percent of a Quantity 4 4 Percent from. Percentage 4 5 Quantity from Percentage and Percent 4 6 Percent Error or Uncertainty. 4 7 Percent of Difference 4 8 Uncertainties in Scale Readings. Chapter 5 ESSENTIALS OF ALGEBRA 61, 5 1 Terminology 5 2 The Number Line 5 3 Absolute Value 5 4 Operations with. Signed Numbers 5 5 Operations with Monomials 5 6 Use of Grouping Symbols. 5 7 Operations with Polynomials 5 8 Simple Products 5 9 Factoring 5 10 Cancella. tion 5 1 1 Operations with Algebraic Fractions 5 12 Equations Definitions 5 13. Solutions of Linear Equations,Chapter 6 RATIO AND PROPORTION 95. 6 1 Ratio Basic Concepts 6 2 Proportion Basic Concepts 6 3 Direct Proportion. 6 4 Inverse Proportion,vi CONTENTS,Chapter 7 LINEAR EQUATIONS 106. 7 1 Function 7 2 Variables 7 3 Linear Function 7 4 Functional Representation. 7 5 Slope 7 6 Negative Slope 7 7 Direct Proportion 7 8 Applications 7 9 Linear. Equation 7 10 Representation 7 11 Negative Slope 7 12 Zero Slope 7 13 Appli. cations 7 14 Intercepts of a Line 7 15 Empirical Equations 7 16 Good Graphing. Practices 7 17 Graphing the Special Linear Function y m 7 18 Graphing the General. Linear Function y mx b 7 19 Graphing Linear functions with a Calculator. Chapter 8 EXPONENTS AND RADICALS 131, 8 1 Exponential Form 8 2 Positive Integral Exponent 8 3 Reading Exponential Nota.

tion 8 4 Zero Exponent 8 5 Negative Integral Exponent 8 6 Roots 8 7 Principal. nth Root 8 8 Radical Radicand and Index 8 9 Fractional Exponents 8 10 Power. Function 8 1 1 Variation 8 12 Direct Variation 8 13 Inverse Variation 8 14. Graphs of Power Functions 8 15 Graphing Power Functions with a Calculator. 8 16 Determining Empirical Equations of Power Functions 8 17 Joint Variation. 8 18 Formulas,Chapter 9 LOGARITHMS 171, 9 1 Numbers as Powers 9 2 Definition of a Logarithm 9 3 Common Logarithms. 9 4 Negative Logarithms 9 5 Parts of a Logarithm 9 6 Logarithmic Tables 9 7. Antilogarithms 9 8 The First Law of Logarithms 9 9 The Second Law of Logarithms. 9 10 The Third Law of Logarithms 9 11 Conversion to a Different Base 9 12. Exponential Functions 9 13 Exponential Equations 9 14 Logarithmic Functions 9 15. Logarithmic Equations 9 16 Growth and Decay 9 17 Logarithmic Graph Paper 9 18. Semilogarithmic Paper, Chapter 10 QUADRATIC EQUATIONS AND SQUARE ROOTS 214. 10 1 Quadratic Equation 10 2 Solution 10 3 Pure Quadratic Equations 10 4 Qua. dratic Equations by Factoring 10 5 The Quadratic Formula 10 6 Using a Graphing. Calculator to Solve Quadratic Equations 10 7 Irrational Solutions 10 8 Table of Square. Roots 10 9 Iterative Method 10 10 Traditional Method 10 1 1 Logarithmic Method. 10 12 Finding Square Roots with a Calculator,Chapter I1 ESSENTIALS OF PLANE GEOMETRY 243. 11 1 Terms 11 2 Lines 11 3 Symbols 11 4 Selected Geometrical Facts 11 5. Angle Types 11 6 Theorems on Equal Angles 11 7 Theorems on Supplementary. Angles 11 8 The Degree Measure 11 9 Angle Operations with a Calculator 11 10. An Abbreviated Method to Cany Out Arithmetic Operations with Angles Using a. Calculator 1 1 11 Parts of a Triangle 11 12 Types of Triangles 11 13 Congruence. of Triangles 1 1 14 Similarity of Triangles 11 15 Other Theorems on Triangles. 1 1 16 The Pythagorean Theorem 1 1 17 Quadrilaterals Terms 1 1 18 Theorems on. Parallelograms 1 1 19 Circles and Arcs Terms 1 1 20 Theorems on Circles and. Arcs 11 21 Bisecting a Line Segment 11 22 Bisecting an Angle 11 23 Erecting a. Perpendicular to a Given Line from a Given Point Not on the Line 11 24 Erecting a. Perpendicular to a Line at a Given Point on the Line 11 25 Drawing a Parallel to a Given. Line 1 1 26 Dividing a Given Line Segment into a Given Number of Equal Parts 1 1 27. Finding the Center of a Circle from a Given Arc 1 1 28 Perimeters 11 29 Areas. CONTENTS vii,Chapter 12 SOLID FIGURES 276, 12 1 Polyhedrons 12 2 Cylinders 12 3 Cones 12 4 Spheres 12 5 Similar Solids. 12 6 Area of a Prism 12 7 Area of a Pyramid 12 8 Area of a Cylinder 12 9 Area. of a Cone 12 10 Area of a Sphere 12 1 1 Areas of Similar Solids 12 12 Volume of a. Prism 12 13 Volume of a Pyramid 12 14 Volume of a Cylinder 12 15 Volume of a. Cone 12 16 Volume of a Sphere 12 17 Volumes of Similar Solids. Chapter 13 TRIGONOMETRIC FUNCTIONS 291, 13 1 Trigonometry 13 2 Ratios in Similar Triangles 13 3 Definitions from Triangle.

Ratios 13 4 Definitions from Coordinates 13 5 Trigonometric Tables 13 6 Trigono. metric Functions of Special Angles 13 7 Calculating Trigonometric Functions with a. Calculator 13 8 Cofunctions 13 9 Signs of Trigonometric Functions 13 10 Trigono. metric Identities,Chapter 14 SOLUTION OF TRIANGLES 306. SCHAUM S OUTLINE SERIES McGRAW HILL New York San Francisco Washington D C Auckland Bogotci Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto Dedicated to the Lion of Judah for his many blessings opportunities and the wonderful family that he has given me Dr Haym Kruglak is a Professor Emeritus of Physics at Western Michigan

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