Introduction to Technical Mathematics, 5th edition

Published by Pearson (February 5, 2007) © 2008

  • Allyn J. Washington Dutchess Community College
  • Mario F. Triola Dutchess Community College
  • Ellena E. Reda Dutchess Community College
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Introduction to Technical Mathematics, Fifth Edition, has been thoroughly revised and modernized with up-to-date applications, an expanded art program, and new pedagogy to help today’s students relate to the mathematics they are learning. The new edition continues to provide a thorough review of arithmetic and a solid foundation in algebra, geometry, and trigonometry. In addition to thousands of exercises, the examples in this text include a wealth of applications from various technological fields: electronics, mechanics, civil engineering, forestry, architecture, industrial engineering and design, physics, chemistry, and computer science.  To enhance your course, the fifth edition is now available with Addison-Wesley’s MathXL® and MyMathLab® technologies.

  • Over 6,500 exercises allow students to practice and master the material.
  • A comprehensive set of diagrammed examples is reinforced by problem-solving strategies to guide students through the material.
  • Real-life applications from different technical fields illustrate the exercises and examples. Fields include electronics, mechanics, civil engineering, forestry, architecture, industrial engineering and design, physics, chemistry, and computer science.
  • A thorough review of arithmetic skills and a solid introduction to algebra, geometry, and trigonometry prepares students for the future.
  • Chapter opening applications, along with new and updated applications throughout the text, keep students interested and engaged in the reading.
  • Section objectives give clear learning objectives so that students remain focused.
  • Chapter 5, “Graphs,” previously Chapter 13, is moved up to include functions earlier in the text and to allow for graphical solutions throughout the remainder of the textbook.
  • Chapter 17, “Introduction to Data Analysis,” has been added to include introductory material on data analysis. This chapter is not meant to be a comprehensive unit on statistics but rather introduces students to some basic concepts they are likely to encounter in other courses.
  • Now Try It! margin exercises give students the opportunity to practice newly learned skills and check their work immediately.
  • Caution boxes in the margin remind students where common mistakes happen and offer advice on how to avoid these common pitfalls.
  • Using Technology boxes offer graphing calculator instruction and examples where appropriate. This text also includes new screenshots to assist students who use the graphing calculator.
  • Updated and revised art illustrates for students the greater emphasis on real data and applications.
  • End-of-chapter material summarizes the concepts and helps students find important information to assist with homework or study for the test. The end-of-chapter material includes: Key Terms, Key Concepts (including equations and formulas from the chapter), Review Exercises, and a Chapter Test.
  • Addison-Wesley MathXL® and MyMathLab® technologies are now available for your courses.
1. Signed Numbers

1.1 Signed Numbers

1.2 Addition and Subtraction of Signed Numbers

1.3 Multiplication and Division of Signed Numbers

1.4 Powers and Roots

1.5 Order of Operation

1.6 Scientific Notation

1.7 Problem-Solving Strategies

Summary

Review Exercises

Test

 

2. Units of Measurement and Approximate Numbers

2.1 Working with Units of Measure

2.2 Units of Measurement: The Metric System

2.3 Reduction and Conversion of Units

2.4 Approximate Numbers and Significant Digits

Summary

Review Exercises

Test

 

3. Introduction to Algebra

3.1 Working with Formulas

3.2 Basic Algebraic Expressions

3.3 Addition and Subtraction of Algebraic Expressions

3.4 Multiplication of Algebraic Expressions

3.5 Division of Algebraic Expressions

Summary

Review Exercises

Test

 

4. Simple Equations and Inequalities

4.1 Solving a Simple Equation

4.2 Simple Formulas and Literal Equations

4.3 Simple Inequalities

4.4 Problem-Solving Strategies and Word Problems

4.5 Ratio, Proportion, and Variation

Summary

Review Exercises

Test

 

5. Graphs

5.1 Functions and Function Notation

5.2 The Rectangular Coordinate System

5.3 The Graph of a Function

5.4 Graphs of a Linear Function

5.5 Graphs of Other Functions

5.6 Graphical Solutions

5.7 Graphing Inequalities

Summary

Review Exercises

Test

 

6. Introduction to Geometry

6.1 Basic Geometric Figures

6.2 Perimeter

6.3 Area

6.4 Volume

Summary

Review Exercises

Test

 

7. Simultaneous Linear Equations

7.1 Graphical Solution of Two Simultaneous Equations

7.2 Substitution Method

7.3 Addition-Subtraction Method for Solving Simultaneous Equations

7.4 Determinants in Two Equations

7.5 Problem Solving Using Systems of Linear Equations

Summary

Review Exercises

Test

 

8. Factoring

8.1 The Distributive Property and Common Factors

8.2 Factoring Trinomials

8.3 Factoring General Trinomials

8.4 The Difference Between Two Squares

8.5 The Sum and Difference of Cubes

Summary

Review Exercises

Test

 

9. Algebraic Fractions

9.1 Equivalent Algebraic Fractions

9.2 Multiplication and Division of Algebraic Fractions

9.3 The Lowest Common Denominator

9.4 Addition and Subtraction of Algebraic Fractions

9.5 Solving Fractional Equations

Summary

Review Exercises

Test

 

10. Exponents, Roots, and Radicals

10.1 Integral Exponents

10.2 Fractional Exponents

10.3 Imaginary Roots

10.4 Simplifying Radicals

10.5 Operations with Radicals

10.6 Working with Radical Equations

Summary

Review Exercises

Test

 

11. Quadratic Equations

11.1 The Quadratic Equation

11.2 Solving Quadratic Equations by Factoring

11.3 Completing the Square

11.4 Solving Quadratic Equations Using the Quadratic Formula

11.5 Graphing the Quadratic Function

Summary

Review Exercises

Test

 

12. Exponential and Logarithmic Functions

12.1 Exponential Functions

12.2 Logarithms

12.3 Properties of Logarithms

12.4 Natural Logarithms

12.5 Exponential and Logarithm Equations

12.6 Log-log and Semi-log Graphs

Summary

Review Exercises

Test

 

13. Geometry and Right Triangle Trigonometry

13.1 Angles and Their Measure

13.2 Other Geometric Figures

13.3 Right Triangles and the Pythagorean Theorem

13.4 Similar Triangles

13.5 The Trigonometric Ratios

13.6 Values of the Trigonometric Ratios

13.7 Right Triangle Applications

Summary

Review Exercises

Test

 

14. Oblique Triangles and Vectors

14.1 Trigonometric Functions of Any Angle

14.2 The Law of Sines

14.3 The Law of Cosines

14.4 Introduction to Vectors

14.5 Vector Components

14.6 Vector Addition

Summary

Review Exercises

Test

 

15. Graphs of Trigonometric Functions

15.1 Radian Measure

15.2 Applications of Radian Measure

15.3 Graphs of y = a sin x and y = a cos x

15.4 Graphs of y = a sin bx and y = a cos bx

15.5 Graphs of y = a sin (bx + c) and y = a cos (bx + c)

15.6 The Sine Function as a Function of Time

Summary

Review Exercises

Test

 

16. Complex Numbers

16.1 Introduction to Complex Numbers

16.2 Basic Operations with Complex Numbers

16.3 Graphical Representation of Complex Numbers

16.4 Polar Form of Complex Numbers

Summary

Review Exercises

Test

 

17. Introduction to Data Analysis

17.1 Creating Pie Charts and Bar Graphs

17.2 Frequency Tables and Histograms

17.3 Measures of Central Tendency

17.4 Measures of Spread and Variation

17.5 Probability

Summary

Review Exercises

Test

 

Appendix Review of Arithmetic

A.1 Addition and Subtraction of Whole Numbers

A.2 Multiplication and Division of Whole Numbers

A.3 Fractions

A.4 Equivalent Fractions

A.5 Addition and Subtraction of Fractions

A.6 Multiplication and Division of Fractions

A.7 Decimals

A.8 Percent

 

Answers to Selected Exercises

Index
Allyn Washington was born and educated in Connecticut, where he also began teaching at Trinity College, his alma mater. He taught at Boise Junior College (now Boise State University) before joining the newly forming Dutchess Community College, in Poughkeepsie, New York, where he began writing Basic Technical Mathematics.

At the time, technical mathematics did not have a text that gave students the math they needed to successfully achieve their goals in the technical mathematics program. Al decided to write a book that specifically aligned itself with the technical programs these students were taking. He wanted his text to be flexible, allowing instructors to teach in ways that would most benefit their students. Through his vision and determination, Allyn Washington created the Technical Mathematics series.


Mario F. Triola is a Professor Emeritus of Mathematics at Dutchess Community College, where he has taught statistics for over 30 years. Marty is the author of Elementary Statistics, 10th Edition, Elementary Statistics Using Excel, Elementary Statistics Using the TI-83 84 Plus Calculator, and he is a co-author of Biostatistics for the Biological and Health Sciences, Statistical Reasoning for Everyday Life, and Business Statistics. He has written several manuals and workbooks for technology supporting statistics education. Outside of the classroom, Marty has been a speaker at many conferences and colleges. His consulting work includes the design of casino slot machines and fishing rods, and he has worked with attorneys in determining probabilities in paternity lawsuits, identifying salary inequities based on gender, analyzing disputed election results, analyzing medical data, and analyzing medical school surveys. Marty has testified as an expert witness in New York State Supreme Court. The Text and Academic Authors Association has awarded Mario F. Triola a "Texty" for Excellence for his work on Elementary Statistics.


Ellena Reda is the Department Head of the Mathematics, Physical and Computer Sciences Department at Dutchess Community College in Poughkeepsie, NY. She began her career at DCC in 1988 as an adjunct instructor. Ellena received her Bachelor’s degree in Mathematics at Marist College, her Master’s degree in Mathematics/Education from the State University of New York at New Paltz, and an advanced graduate certificate in Educational Computing from the University at Stony Brook. She is the program coordinator at DCC for the Verizon Next Step Program, has served as the program’s mathematics curriculum leader, and has taught a variety of courses in this technical program.

Ellena is a member of the American Mathematical Association of Two Year Colleges. She was a writing team member of the NSF - AMATYC Math Works Project. She was the principal investigator for a National Science Foundation Computer Science, Engineering and Mathematics Scholarship (CSEMS) Grant and a team leader/teacher leader for the State Professional Development Collaborative, an NSF/ATE Grant. In spring 2005 she was named a Regional Teacher of the Year by the New York State Technology Education Association. Ellena has co-authored the Excel Manual that accompanies Elementary Statistics, 8th, 9th and 10th editions written by Mario Triola.

In her spare time Ellena enjoys golfing, running, and reading. In 2003 she ran her first marathon to raise money for the American Stroke Association. Since then she has run 2 marathons and 3 half-marathons. She has three grown children and lives locally with her husband.

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