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Basic Technical Mathematics with Calculus, 12th edition

Published by Pearson (January 23, 2022) © 2023

  • Allyn J. Washington Dutchess Community College
  • Richard Evans Corning Community College

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For courses in introductory technical math. 

The student-friendly, acclaimed best seller in technical math

Basic Technical Mathematics with Calculus continues Washington's highly regarded approach with updates that support student understanding of mathematical techniques and how they apply on the job. Its concise narrative focuses on the essentials students need, with no added theory or digressions. Intended primarily for students in technical or pre-engineering programs, it uses a vast number of applications to create a solid foundation in mathematics and demonstrate its applicability in various technical fields. The 12th Edition updates applications and data throughout for increased relevancy.

Hallmark features of this title

  • Technical applications (over 3000 application exercises and 350 applied examples) are drawn from fields such as aeronautics, construction, environmental, and more. Many involve modern technologies like solar energy and fiber optics.
  • Solved examples feature blue "help text" to explain each step of the solution.
  • Problem sets offer exercises spanning practice and writing exercises to applications and practice tests.
  • "Caution" and "Note" features point out common errors, topics that frequently challenge students, and key material.
  • Practice Exercises after key examples are provided, with answers at the end of the exercise set for the section.
  • The online Graphing Calculator Handbook is referenced throughout the text via short URLs (or direct links in the eText) that take students directly to the relevant content.

New and updated features of this title

  • Real-world data and scenarios are updated throughout the text to maintain currency and relevancy for students. For example, see the updated data on social media usage in section 22.1, Graphical Displays of Data
  • A new Appendix E covers binary and hexadecimal numbers. This appendix is available online at bit.ly/3h1t3lt and has been added at users' requests.

Features of MyLab Math for the 12th Edition

  • Approximately 260 new assignable, algorithmic exercises have been added to the course. MyLab exercises reflect the approach and learning style of the text with learning aids that include guided solutions, videos, and sample problems. About 210 of the new exercises are based on existing textbook exercises; the remainder are new applications written by the author.
  • Existing MyLab exercises have been revised to improve clarity.
  • Significantly increased video coverage includes 195 new example videos for a total of 630 instructional videos, many with author Rich Evans. All videos are now re-correlated to the exercises in MyLab; when a student chooses "Video" as a learning aid within a MyLab exercise, they can be sure that the video will be helpful.
  • A new Guide to Video-Based Assignments helps instructors create assignments containing video by showing which MyLab questions relate to each video.
  • The online Graphing Calculator Handbook is referenced throughout the text via short URLs (or direct links in the eText) that take students directly to the relevant content.
  1. Basic Algebraic Operations
    • 1.1 Numbers
    • 1.2 Fundamental Operations of Algebra
    • 1.3 Calculators and Approximate Numbers
    • 1.4 Exponents and Unit Conversions
    • 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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Review Exercises and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  5. Systems of Linear Equations;Determinants
    • 5.1 Linear Equations and Graphs of Linear Functions
    • 5.2 Systems of Equations and Graphical Solutions
    • 5.3 Solving Systems of Two Linear Equations in Two Unknowns Algebraically
    • 5.4 Solving Systems of Two Linear Equations in Two Unknowns by Determinants
    • 5.5 Solving Systems of Three Linear Equations in Three Unknowns Algebraically
    • 5.6 Solving Systems of Three Linear Equations in Three Unknowns by Determinants
    • Key Formulas and Equations, Review Exercises, and Practice Test
  6. Factoring and Fractions
    • 6.1 Factoring: Greatest Common Factor and Difference of Squares
    • 6.2 Factoring Trinomials
    • 6.3 The Sum and Difference of Cubes
    • 6.4 Equivalent Fractions
    • 6.5 Multiplication and Division of Fractions
    • 6.6 Addition and Subtraction of Fractions
    • 6.7 Equations Involving Fractions
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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 Trigonometric Curves
    • Key Formulas and Equations, Review Exercises, and Practice Test
  11. Exponents and Radicals
    • 11.1 Simplifying Expressions with Integer Exponents
    • 11.2 Fractional Exponents
    • 11.3 Simplest Radical Form
    • 11.4 Addition and Subtraction of Radicals
    • 11.5 Multiplication and Division of Radicals
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Review Exercises and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  18. Variation
    • 18.1 Ratio and Proportion
    • 18.2 Variation
    • Key Formulas and Equations, Review Exercises, and Practice Test
  19. Sequences and the Binomial Theorem
    • 19.1 Arithmetic Sequences
    • 19.2 Geometric Sequences
    • 19.3 Infinite Geometric Series
    • 19.4 The Binomial Theorem
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  22. Introduction to Statistics
    • 22.1 Graphical Displays of Data
    • 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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  23. The Derivative
    • 23.1 Limits  
    • 23.2 The Slope of a Tangent to a Curve
    • 23.3 The Derivative
    • 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 Functions
    • 23.9 Higher Derivatives
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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 
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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 Applications 
    • Key Formulas and Equations, Review Exercises, and Practice Test
  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'Hopital's Rule
    • 27.8  Applications
    • Key Formulas and Equations, Review Exercises, and Practice Test
  28. Methods of Integration
    • 28.1  The Power Rule for Integration
    • 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: Non-repeated Linear Factors
    • 28.10  Integration by Partial Fractions: Other Cases
    • 28.11  Integration by Use of Tables
    • Key Formulas and Equations, Review Exercises, and Practice Test
  29. Partial Derivatives and Double Integrals
    • 29.1 Functions of Two Variables
    • 29.2 Curves and Surfaces in Three Dimensions
    • 29.3 Partial Derivatives
    • 29.4 Double Integrals
    • Key Formulas and Equations, Review Exercises, and Practice Test
  30. Expansion of Functions in Series
    • 30.1 Infinite Series
    • 30.2 Maclaurin Series
    • 30.3 Operations with Series
    • 30.4 Computations by Use of Series Expansions
    • 30.5 Taylor Series
    • 30.6 Introduction to Fourier Series
    • 30.7 More About Fourier Series 
    • Key Formulas and Equations, Review Exercises, and Practice Test
  31. Differential Equations
    • 31.1 Solutions of Differential Equations
    • 31.2 Separation of Variables
    • 31.3 Integrating Combinations
    • 31.4 The Linear Differential Equation of the First Order
    • 31.5 Numerical Solutions of First-order Equations
    • 31.6 Elementary Applications
    • 31.7 Higher-order Homogeneous Equations
    • 31.8 Auxiliary Equation with Repeated or Complex Roots
    • 31.9 Solutions of Nonhomogeneous Equations
    • 31.10 Applications of Higher-order Equations
    • 31.11 Laplace Transforms
    • 31.12 Solving Differential Equations by Laplace Transforms

APPENDICES

  1. Solving Word Problems
  2. Units of Measurement
  3. Newton's Method
  4. A Table of Integrals
  5. Binary and Hexadecimal Numbers (online at bit.ly/3h1t3lt)

Photo Credits

Answers to Odd-Numbered Exercises and Chapter Review Exercises

Solutions to Practice Test Problems

Index of Applications

Index

About our authors

The late Allyn J. Washington received his Master's Degree from Brown University. He was Professor of Mathematics at Dutchess Community College (Poughkeepsie, New York) where he served as the Mathematics Department Head as well as Dean of the College. Allyn was a founding member of the New York State Mathematics Association of Two-Year Colleges and a founding member of the American Mathematics Association of Two-Year Colleges. He was awarded an Honorary Doctorate Degree by State University of New York. He is listed in Who's Who in America. The Allyn J. Washington Center for Science and Art Building is named in his honor at Dutchess Community College. Allyn authored several textbooks in Technical Mathematics, including Basic Technical Mathematics.

Richard Evans received a Master's Degree in mathematics from Binghamton University (Binghamton, New York). He is currently a professor of mathematics at Corning Community College, where he has taken an active role in the college's governance system, including having chaired the mathematics department as well as the College Association. He is a long-standing member of the New York Mathematics Association of Two-Year Colleges and has attended and presented at many of these annual conferences. Rich has a strong background in applied mathematics and has taken two sabbatical leaves involving real-world applications of math in business and industry. In his free time, Rich enjoys spending time with his family, playing guitar, and boating in the Finger Lakes.

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