Algebra & Trigonometry

Chapter R: A Review of Basic Concepts and Skills

R-1 The Language, Notation, and Numbers of Mathematics

R-2 Algebraic Expressions and the Properties of Real Numbers

R-3 Exponents, Scientific Notation, and a Review of Polynomials

R-4 Factoring Polynomials

R-5 Rational Expressions

R-6 Radicals and Rational Exponents

Chapter 1: Equations and Inequalities

1-1 Linear Equations, Formulas, and Problem Solving

1-2 Linear Inequalities in One Variable

1-3 Absolute Value Equations and Inequalities

1-4 Complex Numbers

1-5 Solving Quadratic Equations

1-6 Solving Other Types of Equations

Chapter 2: Relations, Functions and Graphs

2-1 Rectangular Coordinates; Graphing Circles and Relations

2-2 Graphs of Linear Equations

2-3 Linear Equations and Rates of Change

2-4 Functions, Notation, and Graphs of Functions

2-5 Analyzing the Graph of a Function

2-6 Toolbox Functions and Transformations

2-7 Piecewise-Defined Functions

2-8 The Algebra and Composition of Functions

Chapter 3: Polynomial and Rational Functions

3-1 Quadratic Functions and Applications

3-2 Synthetic Division; The Remainder and Factor Theorems

3-3 The Zeroes of Polynomial Functions

3-4 Graphing Polynomial Functions

3-5 Graphing Rational Functions

3-6 Additional Insights into Rational Functions

3-7 Polynomial and Rational Inequalities

3-8 Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1 One-to-One and Inverse Functions

4-2 Exponential Functions

4-3 Logarithms and Logarithmic Functions

4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations

4-5 Applications from Business, Finance, and Science

Chapter 5: Introduction to Trigonometric Functions

5-1 Angle Measure, Special Triangles, and Special Angles

5-2 The Trigonometry of Right Triangles

5-3 Trigonometry and the Coordinate Plane

5-4 Unit Circles and the Trigonometric of Real Numbers

5-5 Graphs of Sine and Cosine Functions; Cosecant and Secant Functions

5-6 Graphs of Tangent and Cotangent Functions

5-7 Transformations and Applications of Trigonometric Graphs

Chapter 6: Trigonometric Identities, Inverses, and Equations

6-1 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 Identities

6-5 The Inverse Trigonometric Functions and Their Applications

6-6 Solving Basic Trigonometric Equations

6-7 General Trigonometric Equations and Applications

Chapter 7: Applications of Trigonometry

7-1 Oblique Triangles and the Law of Sines

7-2 The Law of Cosines; Area of a Triangle

7-3 Vectors and Vector Diagrams

7-4 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 Inequalities

8-1 Linear Systems in Two Variables with Applications

8-2 Linear Systems in Three Variables with Applications

8-3 Nonlinear Systems of Equations and Inequalities

8-4 Systems of Inequalities and Linear Programming

Chapter 9: Matrices and Matrix Applications

9-1 Solving Systems Using Matrices and Row Operations

9-2 The Algebra of Matrices

9-3 Solving Linear Systems Using Matrix Equations

9-4 Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More

Chapter 10: Analytical Geometry and Conic Sections

10-1 Introduction to Analytic Geometry

10-2 The Circle and the Ellipse

10-3 The Hyperbola

10-4 The Analytic Parabola

10-5 Polar Coordinates, Equations, and Graphs

10-6 More on Conic Sections: Rotation of Axes and Polar Form

10-7 Parametric Equations and Graphs

Chapter 11: Additional Topics in Algebra

11-1 Sequences and Series

11-2 Arithmetic Sequences

11-3 Geometric Sequences

11-4 Mathematical Induction

11-5 Counting Techniques

11-6 Introduction to Probability

11-7 The Binomial Theorem Summary and Concept Review

APPENDICES

A-1 More on Synthetic Division

A-2 More on Matrices

A-3 Deriving the Equation of a Conic

A-4 Proof Positive - A Selection of Proofs from Algebra and Trigonometry

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 Algebra & Trigonometry 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, Algebra & Trigonometry 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.