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Note: Each chapter concludes with a Chapter Summary, Review Exercises, a Chapter Test, Proofs in Mathematics, and P.S. Problem Solving | |
Functions and Their Graphs | |
Rectangular Coordinates | |
Graphs of Equations | |
Linear Equations in Two Variables | |
Functions | |
Analyzing Graphs of Functions | |
A Library of Parent Functions | |
Transformations of Functions | |
Combinations of Functions: Composite Functions | |
Inverse Functions | |
Mathematical Modeling and Variation | |
Polynomial and Rational Functions | |
Quadratic Functions and Models | |
Polynomial Functions of Higher Degree | |
Polynomial and Synthetic Division | |
Complex Numbers | |
Zeros of Polynomial Functions | |
Rational Functions | |
Nonlinear Inequalities | |
Exponential and Logarithmic Functions | |
Exponential Functions and Their Graphs | |
Logarithmic Functions and Their Graphs | |
Properties of Logarithms | |
Exponential and Logarithmic Equations | |
Exponential and Logarithmic Models Cumulative Test: Chapters 1–3 | |
Trigonometry | |
Radian and Degree Measure | |
Trigonometric Functions: The Unit Circle | |
Right Triangle Trigonometry | |
Trigonometric Functions of Any Angle | |
Graphs of Sine and Cosine Functions | |
Graphs of Other Trigonometric Functions | |
Inverse Trigonometric Functions | |
Applications and Models | |
Analytic Trigonometry | |
Using Fundamental Identities | |
Verifying Trigonometric Identities | |
Solving Trigonometric Equations | |
Sum and Difference Formulas | |
Multiple-Angle and Product-to-Sum Formulas | |
Additional Topics in Trigonometery | |
Law of Sines | |
Law of Cosines | |
Vectors in the Plane | |
Vectors and Dot Products | |
Trigonometric Form of a Complex Number Cumulative Test: Chapters 4–6 | |
Systems of Equations and Inequalities | |
Linear and Nonlinear Systems of Equations | |
Two-Variable Linear Systems | |
Multivariable Linear Systems | |
Partial Fractions | |
Systems of Inequalities | |
Linear Programming | |
Matrices and Determinants | |
Matrices and Systems of Equations | |
Operations with Matrices | |
The Inverse of a Square Matrix | |
The Determinant of a Square Matrix | |
Applications of Matrices and Determinants | |
Sequences, Series, and Probability | |
Sequences and Series | |
Arithmetic Sequences and Partial Sums | |
Geometric Sequences and Series | |
Mathematical Induction | |
The Binomial Theorem | |
Counting Principles | |
Probability Cumulative Test: Chapters 7–9 | |
Topics in Analytic Geometry | |
Lines | |
Introduction to Conics: Parabolas | |
Ellipses | |
Hyperbolas | |
Rotation of Conics | |
Parametric Equations | |
Polar Coordinates | |
Graphs of Polar Equations | |
Polar Equations of Conics | |
Analytic Geometry in Three Dimensions | |
The Three-Dimensional Coordinate System | |
Vectors in Space | |
The Cross Product of Two Vectors | |
Lines and Planes in Space | |
Limits and an Introduction to Calculus | |
Introduction to Limits | |
Techniques for Evaluating Limits | |
The Tangent Line Problem | |
Limits at Infinity and Limits of Sequences | |
The Area Problem Cumulative Test: Chapters 10–12 | |
Appendix | |
Review of Fundamental Concepts of Algebra | |
Real Numbers and Their Properties | |
Exponents and Radicals | |
Polynomials and Factoring | |
Rational Expressions | |
Solving Equations | |
Linear Inequalities in One Variable | |
Errors and the Algebra of Calculus | |
Appendix | |
Concepts in Statistics (web) | |
Representing Data | |
Measures of Central Tendency and Dispersion | |
Least Squares Regression | |
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