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Basic Technical Mathematics with Calculus, 11th edition

Published by Pearson (January 4, 2017) © 2018

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

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For courses in technical and pre-engineering technical programs or other programs for which coverage of basic mathematics is required.

The best-seller in technical mathematics gets an “Oh, wow!” update

The 11th Edition of Basic Technical Mathematics with Calculusis a bold revision of this classic best-seller. The text now sports an engaging full-color design, and new co-author Rich Evans has introduced a wealth of relevant applications and improvements, many based on user feedback. The text is supported by an all-new online graphing calculator manual, accessible at point-of-use via short URLs. The new edition continues to feature a vast number of applications from technical and pre-engineering fields–including computer design, electronics, solar energy, lasers fiber optics, and the environment–and aims to develop students’ understanding of mathematical methods without simply providing a collection of formulas. The authors start the text by establishing a solid background in algebra and trigonometry, recognizing the importance of these topics for success in solving applied problems.

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About the Book                                                                        

  • Flexible coverage that easily adapts to fit several courses allows for the chapter order to be changed. Additionally, sections may be included or omitted based on the course length and student major.
  • Relevant technical applications – including 250 applied examples and 2,500 applied exercises--relate to traditional fields such as aeronautics, architecture, automotive, business, chemical, civil, construction, energy, fire science, machine, refrigeration, as well as more up-and-coming fields such as computer design, solar energy, lasers, fiber optics, and the environment.
  • UPDATED! A student-friendly layout now features a full-color design to bring the content to life for students. The layout makes the material easier to understand, as the authors specifically avoid breaking examples or important discussions across pages. Also, all figures are shown immediately adjacent to the material in which they are discussed. Finally, the authors avoid referring to equations or formulas by number when the referent is not on the same page spread.
  • The over 1400 fully-solved examples feature blue “help text” that explains each step of the solution.
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  • End of Chapter material helps students review and prepare for tests:
    • Key Formulas and Equations provide a handy reference for the chapter.
    • Chapter Review Exercises consist of (a) Concept Check Exercises (a set of true/false questions) and (b) Practice and Applications.
    • Chapter Test mirrors what students might see on an actual test. Complete step-by-step solutions are given at the end of the text.

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MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. The MyLab Math course features hundreds of new algorithmic exercises, tutorial videos, and PowerPoint slides.

  • Improved results with MyLab Math: A fully developed MyLab Math program is available with this text, providing students with guided instruction, unlimited practice, and worked video examples for every section of the text.
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  • UPDATED! The 446 instructional videos (including 223 new videos) in the 11th edition MyLab Math course provide help for students outside of the classroom. These videos are also available as learning aids within the homework exercises, for students to refer to at point-of-use.
  • NEW! Graphing Calculator Manual, created specifically for this text, features instructions for the TI-84 and TI-89 family of calculators. This graphing manual is available online, and can easily be accessed at point-of-use via links in the eText, or short URLs in the printed text.
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  • The complete eText is available to students through their MyLab Math courses for the lifetime of the edition, giving students unlimited access to the eText within any course using that edition of the textbook. The eText includes links to videos.
  • NEW! Study skills modules help foster strong study skills in collegiate courses and prepare students for future professions and with the life skills that can make the difference between passing and failing. Topics include “Time Management” and “Stress Management.”
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About the Book

  • REVISED! Refreshed design, in full color, helps students better use the text and motivates them to learn the mathematics.
  • UPDATED! TI-84 Plus-C Graphing Calculator Screens now replace the older TI-84 screens with updated, color versions. Additionally, graphing calculator help for students is accessible online via short URLs in the margins.
  • Over 350 new applications feature in the examples and exercises, including:
    • Power of a wind turbine (Section 3.4)
    • Height of One World Trade Center (Section 4.4)
    • GPS satellite velocity (Section 8.4)
    • Google’s self-driving car laser distance (Section 9.6)
    • Phase angle for current/voltage lead and lag (Section 10.3)
    • Growth of computer processor transistor counts (Section 13.7)
    • Bezier curve roof design (Section 15.3)
    • Cardioid microphone polar pattern (Section 21.7)
    • Social networks usage (Section 22.1)
    • Video game system market share (Section 22.1)
    • Bluetooth headphone maximum revenue (Section 24.7)
    • Saddledome roof slopes (Section 29.3)
    • Weight loss differential equation (Section 31.6)
  • Over 1000 new and updated exercises give students ample opportunity for practice and application. The authors analyzed aggregated student usage and performance data from MyLab™ Math to create better quality exercises that are more relevant to instructors and students.
  • REVISED! Chapter End-matter exercises, formerly called “Quick Chapter Review,” are now labeled “Concept Check Exercises” to better communicate their function within the chapter end-matter.
  • REVISED! Rewritten examples and explanatory material make the content more valuable to students.

Content updates for the eleventh edition were informed by the extensive reviews of the text completed for this revision. These include:

  • Unit analysis, including operations with units and unit conversions, has been moved from Appendix B to Section 1.4. Appendix B has been streamlined, but still contains the essential reference materials on units.
  • In Section 1.3, more specific instructions have been provided for rounding combined operations with approximate numbers.
  • Engineering notation has been added to Section 1.5.
  • Finding the domain and range of a function graphically has been added to Section 3.4.
  • The terms input, output, piecewise defined functions, and practical domain and range have been added to Chapter 3.
  • In response to reviewer feedback, the beginning of Chapter 5 has been reorganized so that systems of equations has a strong introduction in Section 5.2.  The prerequisite material needed for systems of equations (linear equations and graphs of linear functions) has been consolidated into Section 5.1.  An example involving linear regression has also been added to Section 5.1.
  • Solving systems using reduced row echelon form (rref) on a calculator has been added to Chapter 5.
  • Several reviewers made the excellent suggestion to strengthen the focus on factoring in Chapter 6 by taking the contents of 6.1 (Special Products) and spreading it throughout the chapter. This change has been implemented. The terminology greatest common factor (GCF) has also been added to this chapter.
  • In Chapter 7, the square root property is explicitly stated and illustrated.
  • In Chapter 8, the unit circle definition of the trigonometric functions has been added.
  • In Chapter 9, more emphasis had been given to solving equilibrium problems, including those that have more than one unknown.
  • In Chapter 10, an example was added to show how the phase angle can be interpreted, and how it is different from the phase shift.
  • In Chapter 16, the terminology row echelon form is used.  Also, solving a system using rref is again illustrated.  The material on using properties to evaluate determinants was deleted.
  • The terminology binomial coefficients was added to Chapter 19.
  • Chapter 22 (Introduction to Statistics) has undergone significant changes.
    • Section 22.1 now discusses common graphs used for both qualitative data (bar graphs and pie charts) and quantitative data (histograms, stem-and-leaf plots, and time series plots).
    • In Section 22.2, what was previously called the arithmetic mean is now referred to as simply the mean.
    • The empirical rule had been added to Section 22.4.
    • The sampling distribution of x has been formalized including the statement of the central limit theorem.
    • A discussion of interpolation and extrapolation has been added in the context of regression, as well an information on how to interpret the values of r and r2.
    • The emphasis of Section 22.7 on nonlinear regression has been changed.  Information on how to choose an appropriate type of model depending on the shape of the data has been added. However, a calculator is now used to obtain the actual regression equation.
  • In Chapter 23, the terminology direct substitution has been introduced in the context of limits.
  • Throughout the calculus chapters, many of the differentiation and integration rules have been given names so they can be easily referred to. These include, the constant rule, power rule, constant multiple rule, product rule, quotient rule, general power rule, power rule for integration, etc.
  • In Chapter 30, the proof of the Fourier coefficients has been moved online.
Also available with MyLab Math

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. The MyLab Math course features hundreds of new algorithmic exercises, tutorial videos, and PowerPoint slides.

  • MyLab Math content features new additions, including:
    • Hundreds of new assignable algorithmic exercises help address students’ homework needs. All these new exercises are accessible via mobile devices.
    • 223 new instructional videos augment the existing 203 videos, and help students do their homework with a modern presentation format.
    • A new Graphing Calculator Manual, created specifically for this text, features instructions for the TI-84 and TI-89 family of calculators.
    • New PowerPoint® slides feature animations designed to help better teach key concepts.
    • Study skills modules help students with the life skills (e.g., time management) that can make the difference between passing and failing.   

Table of Contents

  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
  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 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
  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
  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 Trigonometric Curves
  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
  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
    • 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 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
  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
  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 Applications
  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 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
  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
  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
  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

Appendix A Solving Word Problems

Appendix B Units of Measurement

Appendix C Newton’s Method

Appendix D A Table of Integrals

Allyn J. Washington received his Masters Degree from Brown University, Providence, Rhode Island. Allyn taught mathematics at Trinity College, Hartford, Connecticut, after graduating Phi Beta Kappa from Trinity. 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 is a founding member of the New York State Mathematics Association of Two Year Colleges and also 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 presently 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, Poughkeepsie, New York. Allyn has authored several textbooks in Technical Mathematics for over 50 years, including this edition of Basic Technical Mathematics with Calculus.

Richard Evans received a Master’s Degree in mathematics from Binghamton University in 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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