### 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 Inequalities
1-1Linear Equations, Formulas, and Problem Solving
1-2Linear Inequalities in One Variable
1-3Absolute Value Equations and Inequalities
1-4Complex Numbers
1-5Solving Quadratic Equations
1-6Solving Other Types of Equations
Chapter 2: Relations, Functions and Graphs
2-1Rectangular Coordinates; Graphing Circles and Relations
2-2Graphs of Linear Equations
2-3Linear Equations and Rates of Change
2-4Functions, Notation, and Graphs of Functions
2-5Analyzing the Graph of a Function
2-6Toolbox Functions and Transformations
2-7Piecewise-Defined Functions
2-8The Algebra and Composition of Functions
Chapter 3: Polynomial and Rational Functions
3-1Quadratic Functions and Applications
3-2Synthetic Division; The Remainder and Factor Theorems
3-3The Zeroes of Polynomial Functions
3-4Graphing Polynomial Functions
3-5Graphing Rational Functions
3-6Additional Insights into Rational Functions
3-7Polynomial and Rational Inequalities
3-8Variation: Function Models in Action
Chapter 4: Exponential and Logarithmic Functions
4-1One-to-One and Inverse Functions
4-2Exponential Functions
4-3Logarithms and Logarithmic Functions
4-4Properties of Logarithms; Solving Exponential and Logarithmic Equations
4-5Applications from Business, Finance, and Science
Chapter 5: Introduction to Trigonometric Functions
5-1Angle Measure, Special Triangles, and Special Angles
5-2Unit Circles and the Trigonometry of Real Numbers
5-3Graphs of Sine and Cosine Functions; Cosecant and Secant Functions
5-4Graphs of Tangent and Cotangent Functions
5-5Transformations and Applications of Trigonometric Graphs
5-6The Trigonometry of Right Triangles
5-7Trigonometry and the Coordinate Plane
Chapter 6: Trigonometric Identities, Inverses, and Equations
6-1Fundamental Identities and Families of Identities
6-2Constructing and Verifying Identities
6-3The Sum and Difference Identities
6-4Double Angle, Half Angle & Product-to-Sum Identities
6-5The Inverse Trigonometric Functions and Their Applications
6-6Solving Basic Trigonometric Equations
6-7General Trigonometric Equations and Applications
Chapter 7: Applications of Trigonometry
7-1Oblique Triangles and the Law of Sines
7-2The Law of Cosines; Area of a Triangle
7-3Vectors and Vector Diagrams
7-4Vector Applications and the Dot Product
7-5Complex Numbers in Trigonometric Form
7-6Demoivre’s Theorem and the Theorem on nth Roots
Chapter 8: Systems of Equations and Inequalities
8-1Linear Systems in Two Variables with Applications
8-2Linear Systems in Three Variables with Applications
8-3Partial Fraction Decomposition
8-4Systems of Inequalities and Linear Programming
8-5Solving Systems Using Matrices and Row Operations
8-6The Algebra of Matrices
8-7Solving Linear Systems Using Matrix Equations
8-8Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More
Chapter 9: Analytical Geometry
9-1Introduction to Analytic Geometry
9-2The Circle and the Ellipse
9-3The Hyperbola
9-4The Analytic Parabola
9-5Nonlinear Systems of Equations and Inequalities
9-6Polar Coordinates, Equations, and Graphs
9-7More on Conic Sections: Rotation of Axes and Polar Form
9-8Parametric Equations and Graphs
Chapter 10: Additional Topics in Algebra
10-1 Sequences and Series
10-2 Arithmetic Sequences
10-3 Geometric Sequences
10-4 Mathematical Induction
10-5 Counting Techniques
10-6 Introduction to Probability
10-7 The Binomial Theorem
Chapter 11: Bridges to Calculus - An Introduction to Limits
11-1 Finding Limits Numerically and Graphically
11-2 Algebraic Methods for Finding Limits; One-Sided Limits and Continuity
11-3 Infinite Limits and Limits at Infinity
11-4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve

APPENDICES
A-1A Review of Basic Concepts and Skills
A-2US Standard Units and the Metric System
A-3Rational Expressions and the Least Common Denominator
A-4Deriving the Equation of a Conic
A-5More on Matrices
A-6Deriving the Equation of a Conic