Basic Technical Mathematics with Calculus 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.

Table of Contents:
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Variation 18.1 Ratio and Proportion 18.2 Variation Key Formulas and Equations, Review Exercises, and Practice Test 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 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 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 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 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 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 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 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 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 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 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 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 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 Solving Word Problems Units of Measurement Newton's Method A Table of Integrals 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