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 and Models of Exponential Growth and Decay
5. Trigonometric Functions
5.1 Angles
5.2 Trigonometric Functions
5.3 Evaluating Trigonometric Functions
5.4 Solving 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, Cotangent, Secant, and Cosecant
6.6 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 Vectors, Operation, and the Dot Product
8.4 Applications of Vectors
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 Parametic 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
Appendix A. Polar Form of Conic Sections
Appendix B. Rotation of Axes
Appendix C. Geometry Formulas
Glossary
Solutions to Selected Exercises
Answers to Selected Exercises
Index of Applications
Index
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