### Overview

### Main description

Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text encourages students to see beyond procedures in an effort to gain a greater understanding of the big ideas behind mathematical concepts.

Written in a readable, yet mathematically mature manner appropriate for college algebra level students, Coburn’s Precalculus uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn’s hallmark applications are born out of the author’s extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area.

Benefiting from the feedback of hundreds of instructors and students across the country, Precalculus second edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in college algebra.

### Table of contents

Chapter 1: Equations and Inequalities1-1 Linear Equations, Formulas, and Problem Solving1-2 Linear Inequalities in One Variable1-3 Absolute Value Equations and Inequalities1-4 Complex Numbers1-5 Solving Quadratic Equations1-6 Solving Other Types of EquationsChapter 2: Relations, Functions and Graphs2-1 Rectangular Coordinates; Graphing Circles and Relations2-2 Graphs of Linear Equations2-3 Linear Equations and Rates of Change2-4 Functions, Notation, and Graphs of Functions2-5 Analyzing the Graph of a Function2-6 Toolbox Functions and Transformations2-7 Piecewise-Defined Functions2-8 The Algebra and Composition of FunctionsChapter 3: Polynomial and Rational Functions3-1 Quadratic Functions and Applications3-2 Synthetic Division; The Remainder and Factor Theorems3-3 The Zeroes of Polynomial Functions3-4 Graphing Polynomial Functions3-5 Graphing Rational Functions3-6 Additional Insights into Rational Functions3-7 Polynomial and Rational Inequalities3-8 Variation: Function Models in ActionChapter 4: Exponential and Logarithmic Functions4-1 One-to-One and Inverse Functions4-2 Exponential Functions4-3 Logarithms and Logarithmic Functions4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations4-5 Applications from Business, Finance, and ScienceChapter 5: Introduction to Trigonometric Functions5-1 Angle Measure, Special Triangles, and Special Angles5-2 Unit Circles and the Trigonometry of Real Numbers5-3 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions 5-4 Graphs of Tangent and Cotangent Functions 5-5 Transformations and Applications of Trigonometric Graphs5-6 The Trigonometry of Right Triangles 5-7 Trigonometry and the Coordinate Plane Chapter 6: Trigonometric Identities, Inverses, and Equations6-1 Fundamental Identities and Families of Identities 6-2 Constructing and Verifying Identities 6-3 The Sum and Difference Identities 6-4 Double Angle, Half Angle & Product-to-Sum Identities6-5 The Inverse Trigonometric Functions and Their Applications6-6 Solving Basic Trigonometric Equations6-7 General Trigonometric Equations and ApplicationsChapter 7: Applications of Trigonometry7-1 Oblique Triangles and the Law of Sines 7-2 The Law of Cosines; Area of a Triangle7-3 Vectors and Vector Diagrams7-4 Vector Applications and the Dot Product 7-5 Complex Numbers in Trigonometric Form 7-6 Demoivre’s Theorem and the Theorem on nth Roots Chapter 8: Systems of Equations and Inequalities8-1 Linear Systems in Two Variables with Applications8-2 Linear Systems in Three Variables with Applications8-3 Partial Fraction Decomposition8-4 Systems of Inequalities and Linear Programming8-5 Solving Systems Using Matrices and Row Operations8-6 The Algebra of Matrices8-7 Solving Linear Systems Using Matrix Equations8-8 Applications of Matrices and Determinants: Cramer's Rule, Geometry, and MoreChapter 9: Analytical Geometry9-1 Introduction to Analytic Geometry9-2 The Circle and the Ellipse9-3 The Hyperbola9-4 The Analytic Parabola9-5 Nonlinear Systems of Equations and Inequalities9-6 Polar Coordinates, Equations, and Graphs9-7 More on Conic Sections: Rotation of Axes and Polar Form9-8 Parametric Equations and GraphsChapter 10: Additional Topics in Algebra10-1 Sequences and Series10-2 Arithmetic Sequences10-3 Geometric Sequences10-4 Mathematical Induction10-5 Counting Techniques10-6 Introduction to Probability10-7 The Binomial TheoremChapter 11: Bridges to Calculus - An Introduction to Limits11-1 Finding Limits Numerically and Graphically11-2 Algebraic Methods for Finding Limits; One-Sided Limits and Continuity11-3 Infinite Limits and Limits at Infinity11-4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve

APPENDICESA-1 A Review of Basic Concepts and SkillsA-2 US Standard Units and the Metric SystemA-3 Rational Expressions and the Least Common DenominatorA-4 Deriving the Equation of a ConicA-5 More on MatricesA-6 Deriving the Equation of a Conic