Basic Technical Mathematics with Calculus

Allyn J. Washington  
Total pages
August 2013
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Basic Technical Mathematics with Calculus
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For courses in Introductory Technical Math.  


This tried-and-true text from Allyn Washington preserves the author's highly regarded approach to technical math, while enhancing the integration of technology. Appropriate for a one- to two-semester course, BASIC TECHNICAL MATHEMATICS shows how algebra and trigonometry are used on the job. It addresses a vast number of technologies including aeronautics, construction, energy, environmental, electronics, computer design, automotive, fire science and more! Known for its exceptional problem sets and applied material, the book offers practice exercises, writing exercises, word problems, and practice tests. This edition features more technical applications, over 1300 new exercises, additional graphing calculator screens, and a robust MyMathLab online homework course.


Offers flexible coverage that easily adapts to fit several courses—the order of chapters can be changed in many places and sections may be included or omitted based  on the course length and student major.


Shows how technical math is used on the job—examples and exercises illustrate application of mathematics in all fields of technology, including aeronautics, architecture, civil, construction, energy, wastewater, environmental and more!


Uses a student-friendly layout—with over 1,000 fully-solved examples, example descriptions, chapter introductions, 1170 figures, and 420 margin notes,  material is more meaningful.


Reinforces problem-solving techniques before problem sets—authors present important formulas, special cautions, and valuable problem solving techniques in visible boxes that are easy to find.


Offers exceptional problem sets—assignment material totals over 9,000 exercises that span from practice exercises, to writing exercises, to word problems, to practice tests. This edition features:

  • 240 practice exercises with answers
  • One writing exercise per chapter and 400 additional writing exercises throughout the book
  • 700 word problems
  • Hundreds of review exercises
  • One practice test per chapter with solutions in the back of the book

Also available: MyMathLab online homework website — since 2001, these websites have helped over 9 million students succeed at more than 1,900 colleges and universities. MyMathLab engages students in active learning—it is modular, self-paced, and adaptable to each student’s learning style—and instructors can easily customize MyMathLab to better meet their students’ needs.

New to this Edition

This tenth edition features revised explanatory material, new examples, and technical applications to the hottest careers. New exercises have been included in nearly all sections.

  • More technical applications show how algebra and trigonometry are used in technical fields such as computer design, electronics, solar energy, automotive, refrigeration, fire science, policing, and more!
  • New Quick Chapter Reviews appear before the Review Exercises and include brief true or false questions.
  • Earlier coverage of changing units  (introduced in Chapter 1 and Chapter 2) provide students with a timely refresher on this basic math skill.
  • 230 graphing calculator screens reinforce how to use the TI-89 graphing calculator for computations, charting and 14 other graphing calculator programs (see Section 1.3, 3.5, and Appendix C).   
  • Over 1300 new exercises give students ample opportunity for practice and homework.
  • Over 330 applied exercises reinforce why math matters in technical and science fields.
  • 150  new word problems encourage students to develop higher level thinking skills.
  • 90 new figures, 60 new margin notes, and 90 new note indicators keep explanatory material, and your course, current.

Table of Contents

Each chapter contains:  Equations, Quick Chapter Review, Review Exercises, Practice Test


1.  Basic Algebraic Operations

1.1 Numbers

1.2 Fundamental Operations of Algebra

1.3 Calculators and Approximate Numbers

1.4 Exponents

1.5 Scientific Notation

1.6 Roots and Radicals

1.7 Addition and Subtraction of Algebraic Expressions

1.8 Multiplication of Algebraic Expressions

1.9 Division of Algebraic Expressions

1.10 Solving Equations

1.11 Formulas and Literal Equations

1.12 Applied Word Problems

2.   Geometry

2.1 Lines and Angles

2.2 Triangles

2.3 Quadrilaterals

2.4 Circles

2.5 Measurement of Irregular Areas

2.6 Solid Geometric Figures

3.  Functions and Graphs

3.1 Introduction to Functions

3.2 More about Functions

3.3 Rectangular Coordinates

3.4 The Graph of a Function

3.5 Graphs on the Graphing Calculator

3.6 Graphs of Functions Defined by Tables of Data

4.  The Trigonometric Functions

4.1 Angles

4.2 Defining the Trigonometric Functions

4.3 Values of the Trigonometric Functions

4.4 The Right Triangle

4.5 Applications of Right Triangles

5.  Systems of Linear Equations; Determinants

5.1 Linear Equations

5.2 Graphs of Linear Functions

5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

6.  Factoring and Fractions

6.1 Special Products

6.2 Factoring: Common Factor and Difference of Squares

6.3 Factoring Trinomials

6.4 The Sum and Difference of Cubes

6.5 Equivalent Fractions

6.6 Multiplication and Division of Fractions

6.7 Addition and Subtraction of Fractions

6.8 Equations Involving Fractions

7.  Quadratic Equations

7.1 Quadratic Equations; Solution by Factoring

7.2 Completing the Square

7.3 The Quadratic Formula

7.4 The Graph of the Quadratic Function

8.  Trigonometric Functions of Any Angle

8.1 Signs of the Trigonometric Functions

8.2 Trigonometric Functions of Any Angle

8.3 Radians

8.4 Applications of Radian Measure

9.  Vectors and Oblique Triangles

9.1 Introduction to Vectors

9.2 Components of Vectors

9.3 Vector Addition by Components

9.4 Applications of Vectors

9.5 Oblique Triangles, the Law of Sines

9.6 The Law of Cosines

10.  Graphs of the Trigonometric Functions

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

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

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

10.4 Graphs of y = tan x,y = cot x, y = sec x, y = csc x

10.5 Applications of the Trigonometric Graphs

10.6 Composite Trignometric Curves

11.  Exponents and Radicals

11.1 Simplifying Expressions with Integral Exponents

11.2 Fractional Exponents

11.3 Simplest Radical Form

11.3 Addition and Subtraction of Radicals

11.5 Multiplication and Division of Radicals

12.  Complex Numbers

12.1 Basic Definitions

12.2 Basic Operations with Complex Numbers

12.3 Graphical Representation of Complex Numbers

12.4 Polar Form of a Complex Number

12.5 Exponential Form of a Complex Number

12.6 Products, Quotients, Powers, and Roots of Complex Numbers

12.7 An Application to Alternating-current (ac) Circuits

13.  Exponential and Logarithmic Functions

13.1 Exponential Functions

13.2 Logarithmic Functions

13.3 Properties of Logarithms

13.4 Logarithms to the Base 10

13.5 Natural Logarithms

13.6 Exponential and Logarithmic Equations

13.7 Graphs on Logarithmic and Semilogarithmic Paper

14.  Additional Types of Equations and Systems of Equations

14.1 Graphical Solution of Systems of Equations

14.2 Algebraic Solution of Systems of Equations

14.3 Equations in Quadratic Form

14.4 Equations with Radicals

15.  Equations of Higher Degree

15.1 The Remainder and Factor Theorems; Synthetic Division

15.2 The Roots of an Equation

15.3 Rational and Irrational Roots

16.  Matrices; Systems of Linear Equations

16.1 Matrices: Definitions and Basic Operations

16.2 Multiplication of Matrices

16.3 Finding the Inverse of a Matrix

16.4 Matrices and Linear Equations

16.5 Gaussian Elimination

16.6 Higher-order Determinants

17.  Inequalities

17.1 Properties of Inequalities

17.2 Solving Linear Inequalities

17.3 Solving Nonlinear Inequalities

17.4 Inequalities Involving Absolute Values

17.5 Graphical Solution of Inequalities with Two Variables

17.6 Linear Programming

18.  Variation

18.1 Ratio and Proportion

18.2 Variation

19.  Sequences and the Binomial Theorem

19.1 Arithmetic Sequences

19.2 Geometric Sequences

19.3 Infinite Geometric Series

19.4 The Binomial Theorem

20.  Additional Topics in Trigonometry

20.1 Fundamental Trigonometric Identities

20.2 The Sum and Difference Formulas

20.3 Double-Angle Formulas

20.4 Half-Angle Formulas

20.5 Solving Trigonometric Equations

20.6 The Inverse Trigonometric Functions

21.  Plane Analytic Geometry

21. 1 Basic Definitions

21.2 The Straight Line

21.3 The Circle

21.4 The Parabola

21.5 The Ellipse

21.6 The Hyperbola

21.7 Translation of Axes

21.8 The Second-degree Equation

21.9 Rotation of Axes

21.10 Polar Coordinates

21.11 Curves in Polar Coordinates

22.  Introduction to Statistics

22.1 Frequency Distributions

22.2 Measures of Central Tendency

22.3 Standard Deviation

22.4 Normal Distributions

22.5 Statistical Process Control

22.6 Linear Regression

22.7 Nonlinear Regression

23. The Derivative

23.1 Limits

23.2 The Slope of a Tangent to a Curve

23.3 Standard Deviation

23.4 The Derivative as an Instantaneous Rate of Change

23.5 Derivatives of Polynomials

23.6 Derivatives of Products and Quotients of Functions

23.7 The Derivative of a Power of a Function

23.8 Differentiation of Implicit Funtions

23.9 Higher Derivatives

24. Applications of the Derivative

24.1 Tangents and Normals

24.2 Newton's Method for Solving Equations

24.3 Curvilinear Motion

24.4 Related Rates

24.5 Using Derivatives in Curve Sketching

24.6 More on Curve Sketching

24.7 Applied Maximum and Minimum Problems

24.8 Differentials and Linear Approximations

25. Integration

25.1 Antiderivatives

25.2 The Indefinite Integral

25.3 The Area Under a Curve

25.4 The Definite Integral

25.5 Numerical Integration: The Trapezoidal Rule

25.6 Simpson's Rule

26. Applications of Integration

26.1 Applications of the Indefinite Integral

26.2 Areas by Integration

26.3 Volumes by Integration

26.4 Centroids

26.5 Moments of Inertia

26.6 Other Appilcations

27. Differentiation of Transcendental Functions

27.1 Derivatives of the Sine and Cosine Functions

27.2 Derivatives of the Other Trigonometric Functions

27.3 Derivatives of the Inverse Trigonometric Functions

27.4 Applications

27.5 Derivative of the Logarithmic Function

27.6 Derivative of the Exponential Function

27.7 L'Hospital's Rule

27.8 Applications

28. Methods of Integration

28.1 The General Power Formula

28.2 The Basic Logarithmic Form

28.3 The Exponential Form

28.4 Basic Trigonometric Forms

28.5 Other Trigonometric Forms

28.6 Inverse Trigonometric Forms

28.7 Integration by Parts

28.8 Integration by Trigonometric Substitution

28.9 Integration by Partial Fractions: Nonrepeated Linear Factors

28.10 Integration by Partial Fractions: Other Cases

28.11 Integration by Use of Tables



Appendix A: Solving Word Problems

Appendix B: Units of Measurement: The Metric System

B.1 Introduction

B.2 Reductions and Conversions

Appendix C: The Graphing Calculator

C.1 Introduction

C.2 The Graphing Calculator

C.3 Graphing Calculator Programs

C.4 The Advanced Graphing Calculator

Appendix D: Newton's Method

Appendix E: A Table of Integrals

Answers to Odd-Numbered Exercises and Quick Chapter Reviews

Solutions to Practice Test Problems

Index of Applications

Index of Writing Exercises