Basic Technical Mathematics with Calculus

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.

• Basic Algebraic Operations 1.1 Numbers1.2 Fundamental Operations of Algebra1.3 Calculators and Approximate Numbers1.4 Exponents and Unit Conversions1.5 Scientific Notation1.6 Roots and Radicals1.7 Addition and Subtraction of Algebraic Expressions1.8 Multiplication of Algebraic Expressions1.9 Division of Algebraic Expressions1.10 Solving Equations1.11 Formulas and Literal Equations1.12 Applied Word ProblemsKey Formulas and Equations, Review Exercises, and Practice TestGeometry 2.1 Lines and Angles2.2 Triangles2.3 Quadrilaterals2.4 Circles2.5 Measurement of Irregular Areas2.6 Solid Geometric FiguresKey Formulas and Equations, Review Exercises, and Practice TestFunctions and Graphs 3.1 Introduction to Functions3.2 More about Functions3.3 Rectangular Coordinates3.4 The Graph of a Function3.5 Graphs on the Graphing Calculator3.6 Graphs of Functions Defined by Tables of DataReview Exercises and Practice TestThe Trigonometric Functions 4.1 Angles4.2 Defining the Trigonometric Functions4.3 Values of the Trigonometric Functions4.4 The Right Triangle4.5 Applications of Right TrianglesKey Formulas and Equations, Review Exercises, and Practice TestSystems of Linear Equations;Determinants 5.1 Linear Equations and Graphs of Linear Functions5.2 Systems of Equations and Graphical Solutions5.3 Solving Systems of Two Linear Equations in Two Unknowns Algebraically5.4 Solving Systems of Two Linear Equations in Two Unknowns by Determinants5.5 Solving Systems of Three Linear Equations in Three Unknowns Algebraically5.6 Solving Systems of Three Linear Equations in Three Unknowns by DeterminantsKey Formulas and Equations, Review Exercises, and Practice TestFactoring and Fractions 6.1 Factoring: Greatest Common Factor and Difference of Squares6.2 Factoring Trinomials6.3 The Sum and Difference of Cubes6.4 Equivalent Fractions6.5 Multiplication and Division of Fractions6.6 Addition and Subtraction of Fractions6.7 Equations Involving FractionsKey Formulas and Equations, Review Exercises, and Practice TestQuadratic Equations 7.1 Quadratic Equations; Solution by Factoring7.2 Completing the Square7.3 The Quadratic Formula7.4 The Graph of the Quadratic FunctionKey Formulas and Equations, Review Exercises, and Practice TestTrigonometric Functions of Any Angle 8.1 Signs of the Trigonometric Functions8.2 Trigonometric Functions of Any Angle8.3 Radians8.4 Applications of Radian MeasureKey Formulas and Equations, Review Exercises, and Practice TestVectors and Oblique Triangles 9.1 Introduction to Vectors9.2 Components of Vectors9.3 Vector Addition by Components9.4 Applications of Vectors9.5 Oblique Triangles, the Law of Sines9.6 The Law of CosinesKey Formulas and Equations, Review Exercises, and Practice TestGraphs of the Trigonometric Functions 10.1 Graphs of y = a sin x and y = a cos x10.2 Graphs of y = a sin bx and y = a cos bx10.3 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 x10.5 Applications of the Trigonometric Graphs10.6 Composite Trigonometric CurvesKey Formulas and Equations, Review Exercises, and Practice TestExponents and Radicals 11.1 Simplifying Expressions with Integer Exponents11.2 Fractional Exponents11.3 Simplest Radical Form11.4 Addition and Subtraction of Radicals11.5 Multiplication and Division of RadicalsKey Formulas and Equations, Review Exercises, and Practice TestComplex Numbers 12.1 Basic Definitions12.2 Basic Operations with Complex Numbers12.3 Graphical Representation of Complex Numbers12.4 Polar Form of a Complex Number12.5 Exponential Form of a Complex Number12.6 Products, Quotients, Powers, and Roots of Complex Numbers12.7 An Application to Alternating-current (ac) CircuitsKey Formulas and Equations, Review Exercises, and Practice TestExponential and Logarithmic Functions 13.1 Exponential Functions13.2 Logarithmic Functions13.3 Properties of Logarithms13.4 Logarithms to the Base 1013.5 Natural Logarithms13.6 Exponential and Logarithmic Equations13.7 Graphs on Logarithmic and Semilogarithmic PaperKey Formulas and Equations, Review Exercises, and Practice TestAdditional Types of Equations and Systems of Equations 14.1 Graphical Solution of Systems of Equations14.2 Algebraic Solution of Systems of Equations14.3 Equations in Quadratic Form14.4 Equations with RadicalsReview Exercises and Practice TestEquations of Higher Degree 15.1 The Remainder and Factor Theorems; Synthetic Division15.2 The Roots of an Equation15.3 Rational and Irrational RootsKey Formulas and Equations, Review Exercises, and Practice TestMatrices; Systems of Linear Equations 16.1 Matrices: Definitions and Basic Operations16.2 Multiplication of Matrices16.3 Finding the Inverse of a Matrix16.4 Matrices and Linear Equations16.5 Gaussian Elimination16.6 Higher-order DeterminantsKey Formulas and Equations, Review Exercises, and Practice TestInequalities 17.1 Properties of Inequalities17.2 Solving Linear Inequalities17.3 Solving Nonlinear Inequalities17.4 Inequalities Involving Absolute Values17.5 Graphical Solution of Inequalities with Two Variables17.6 Linear ProgrammingKey Formulas and Equations, Review Exercises, and Practice TestVariation 18.1 Ratio and Proportion18.2 VariationKey Formulas and Equations, Review Exercises, and Practice TestSequences and the Binomial Theorem 19.1 Arithmetic Sequences19.2 Geometric Sequences19.3 Infinite Geometric Series19.4 The Binomial TheoremKey Formulas and Equations, Review Exercises, and Practice TestAdditional Topics in Trigonometry 20.1 Fundamental Trigonometric Identities20.2 The Sum and Difference Formulas20.3 Double-Angle Formulas20.4 Half-Angle Formulas20.5 Solving Trigonometric Equations20.6 The Inverse Trigonometric FunctionsKey Formulas and Equations, Review Exercises, and Practice TestPlane Analytic Geometry 21.1 Basic Definitions21.2 The Straight Line21.3 The Circle21.4 The Parabola21.5 The Ellipse21.6 The Hyperbola21.7 Translation of Axes21.8 The Second-degree Equation21.9 Rotation of Axes21.10 Polar Coordinates21.11 Curves in Polar CoordinatesKey Formulas and Equations, Review Exercises, and Practice TestIntroduction to Statistics 22.1 Graphical Displays of Data22.2 Measures of Central Tendency22.3 Standard Deviation22.4 Normal Distributions22.5 Statistical Process Control22.6 Linear Regression22.7 Nonlinear RegressionKey Formulas and Equations, Review Exercises, and Practice TestThe Derivative 23.1 Limits  23.2 The Slope of a Tangent to a Curve23.3 The Derivative23.4 The Derivative as an Instantaneous Rate of Change23.5 Derivatives of Polynomials23.6 Derivatives of Products and Quotients of Functions23.7 The Derivative of a Power of a Function23.8 Differentiation of Implicit Functions23.9 Higher DerivativesKey Formulas and Equations, Review Exercises, and Practice TestApplications of the Derivative 24.1 Tangents and Normals24.2 Newton's Method for Solving Equations24.3 Curvilinear Motion24.4 Related Rates24.5 Using Derivatives in Curve Sketching  24.6 More on Curve Sketching24.7 Applied Maximum and Minimum Problems24.8 Differentials and Linear Approximations Key Formulas and Equations, Review Exercises, and Practice TestIntegration 25.1 Antiderivatives25.2 The Indefinite Integral25.3 The Area Under a Curve25.4  The Definite Integral25.5  Numerical Integration: The Trapezoidal Rule25.6  Simpson's RuleKey Formulas and Equations, Review Exercises, and Practice TestApplications of Integration 26.1  Applications of the Indefinite Integral26.2  Areas by Integration26.3  Volumes by Integration26.4  Centroids26.5  Moments of Inertia26.6  Other Applications Key Formulas and Equations, Review Exercises, and Practice TestDifferentiation of Transcendental Functions 27.1  Derivatives of the Sine and Cosine Functions27.2  Derivatives of the Other Trigonometric Functions27.3  Derivatives of the Inverse Trigonometric Functions27.4  Applications27.5  Derivative of the Logarithmic Function27.6  Derivative of the Exponential Function27.7  L'Hopital's Rule27.8  ApplicationsKey Formulas and Equations, Review Exercises, and Practice TestMethods of Integration 28.1  The Power Rule for Integration28.2  The Basic Logarithmic Form28.3  The Exponential Form28.4  Basic Trigonometric Forms28.5  Other Trigonometric Forms28.6  Inverse Trigonometric Forms28.7  Integration by Parts28.8  Integration by Trigonometric Substitution28.9  Integration by Partial Fractions: Non-repeated Linear Factors28.10  Integration by Partial Fractions: Other Cases28.11  Integration by Use of TablesKey Formulas and Equations, Review Exercises, and Practice TestPartial Derivatives and Double Integrals 29.1 Functions of Two Variables29.2 Curves and Surfaces in Three Dimensions29.3 Partial Derivatives29.4 Double IntegralsKey Formulas and Equations, Review Exercises, and Practice TestExpansion of Functions in Series 30.1 Infinite Series30.2 Maclaurin Series30.3 Operations with Series30.4 Computations by Use of Series Expansions30.5 Taylor Series30.6 Introduction to Fourier Series30.7 More About Fourier Series Key Formulas and Equations, Review Exercises, and Practice TestDifferential Equations 31.1 Solutions of Differential Equations31.2 Separation of Variables31.3 Integrating Combinations31.4 The Linear Differential Equation of the First Order31.5 Numerical Solutions of First-order Equations31.6 Elementary Applications31.7 Higher-order Homogeneous Equations31.8 Auxiliary Equation with Repeated or Complex Roots31.9 Solutions of Nonhomogeneous Equations31.10 Applications of Higher-order Equations31.11 Laplace Transforms31.12 Solving Differential Equations by Laplace TransformsAPPENDICES Solving Word ProblemsUnits of MeasurementNewton's MethodA Table of IntegralsBinary 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