Basic Technical Mathematics

Basic Technical Mathematics focuses on the essentials you need, with no added theory or side trips. It supports understanding of mathematical techniques and how they apply on the job in fields like computer design, electronics, solar energy, lasers, and the environment. A vast number of applications create a solid foundation in algebra and trigonometry and demonstrate their applicability in various technical fields. Plenty of solved examples, problem sets, and practice exercises help reinforce skills. End-of-chapter review and test prep help you succeed on quizzes and exams. Additionally, the authors point out common errors, frequently misunderstood topics, and essential material.

1. Basic Algebraic Operations
   • 1.1 Numbers
   • 1.2 Fundamental Operations of Algebra1.3 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

• A. Solving Word Problems
• B. Units of Measurement
• E. Binary and Hexadecimal Numbers (online at bit.ly/3h1t3lt)

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.