Algebra and Trigonometry – John Coburn – 2nd Edition

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
4-6 Business, Finance, and Science Applications

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
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