College Algebra and Trigonometry – Margaret L. Lial – 6th Edition

R. Review of Basic Concepts
R-1 Sets
R-2 Real Numbers and Their Properties
R-3 Polynomials
R-4 Factoring Polynomials
R-5 Rational Expressions
R-6 Rational Exponents
R-7 Radical Expressions

1. Equations and Inequalities
1-1 Linear Equations
1-2 Applications and Modeling with Linear Equations
1-3 Complex Numbers
1-4 Quadratic Equations
1-5 Applications and Modeling with Quadratic Equations
1-6 Other Types of Equations and Applications
1-7 Inequalities
1-8 Absolute Value Equations and Inequalities

2. Graphs and Functions
2-1 Rectangular Coordinates and Graphs
2-2 Circles
2-3 Functions
2-4 Linear Functions
2-5 Equations of Lines and Linear Models
2-6 Graphs of Basic Functions
2-7 Graphing Techniques
2-8 Function Operations and Composition

3. Polynomial and Rational Functions
3-1 Quadratic Functions and Models
3-2 Synthetic Division
3-3 Zeros of Polynomial Functions
3-4 Polynomial Functions: Graphs, Applications, and Models
3-5 Rational Functions: Graphs, Applications, and Models
3-6 Variation

4. Inverse, Exponential, and Logarithmic Functions
4-1 Inverse Functions
4-2 Exponential Functions
4-3 Logarithmic Functions
4-4 Evaluating Logarithms and the Change-of-Base Theorem
4-5 Exponential and Logarithmic Equations
4-6 Applications of Models of Exponential Growth and Decay

5. Trigonometric Functions
5-1 Angles
5-2 Trigonometric Functions
5-3 Trigonometric Function Values and Angle Measures
5-4 Solutions and Applications of Right Triangles

6. The Circular Functions and Their Graphs
6-1 Radian Measure
6-2 The Unit Circle and Circular Functions
6-3 Graphs of the Sine and Cosine Functions
6-4 Translations of the Graphs of the Sine and Cosine Functions
6-5 Graphs of the Tangent and Cotangent Functions
6-6 Graphs of the Secant and Cosecant Functions
6-7 Harmonic Motion

7. Trigonometric Identities and Equations
7-1 Fundamental Identities
7-2 Verifying Trigonometric Identities
7-3 Sum and Difference Identities
7-4 Double-Angle and Half-Angle Identities
7-5 Inverse Circular Functions
7-6 Trigonometric Equations
7-7 Equations Involving Inverse Trigonometric Functions

8. Applications of Trigonometry
8-1 The Law of Sines
8-2 The Law of Cosines
8-3 Geometrically Defined Vectors and Applications
8-4 Algebraically Defined Vectors and the Dot Product
8-5 Trigonometric (Polar) Form of Complex Numbers, Products and Quotients
8-6 De Moivre’s Theorem, Powers and Roots of Complex Numbers
8-7 Polar Equations and Graphs
8-8 Parametric Equations, Graphs, and Applications

9. Systems and Matrices
9-1 Systems of Linear Equations
9-2 Matrix Solution of Linear Systems
9-3 Determinant Solution of Linear Systems
9-4 Partial Fractions
9-5 Nonlinear Systems of Equations
9-6 Systems of Inequalities and Linear Programming
9-7 Properties of Matrices
9-8 Matrix Inverses

10. Analytic Geometry
10-1 Parabolas
10-2 Ellipses
10-3 Hyperbolas
10-4 Summary of the Conic Sections

11. Further Topics in Algebra
11-1 Sequences and Series
11-2 Arithmetic Sequences and Series
11-3 Geometric Sequences and Series
11-4 The Binomial Theorem
11-5 Mathematical Induction
11-6 Counting Theory
11-7 Basics of Probability

Appendices