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Equations and Inequalities | |
Linear Equations, Formulas, and Problem Solving | |
Linear Inequalities in One Variable | |
Absolute Value Equations and Inequalities | |
Complex Numbers | |
Solving Quadratic Equations | |
Solving Other Types of Equations | |
Relations, Functions and Graphs | |
Rectangular Coordinates; Graphing Circles and Relations | |
Graphs of Linear Equations | |
Linear Equations and Rates of Change | |
Functions, Notation, and Graphs of Functions | |
Analyzing the Graph of a Function | |
Toolbox Functions and Transformations | |
Piecewise-Defined Functions | |
The Algebra and Composition of Functions | |
Polynomial and Rational Functions | |
Quadratic Functions and Applications | |
Synthetic Division; The Remainder and Factor Theorems | |
The Zeroes of Polynomial Functions | |
Graphing Polynomial Functions | |
Graphing Rational Functions | |
Additional Insights into Rational Functions | |
Polynomial and Rational Inequalities | |
Variation: Function Models in Action | |
Exponential and Logarithmic Functions | |
One-to-One and Inverse Functions | |
Exponential Functions | |
Logarithms and Logarithmic Functions | |
Properties of Logarithms; Solving Exponential and Logarithmic Equations | |
Applications from Business, Finance, and Science | |
Business, Finance, and Science Applications | |
Introduction to Trigonometric Functions | |
Angle Measure, Special Triangles, and Special Angles | |
Unit Circles and the Trigonometry of Real Numbers | |
Graphs of Sine and Cosine Functions; Cosecant and Secant Functions | |
Graphs of Tangent and Cotangent Functions | |
Transformations and Applications of Trigonometric Graphs | |
The Trigonometry of Right Triangles | |
Trigonometry and the Coordinate Plane | |
Trigonometric Identities, Inverses, and Equations | |
Fundamental Identities and Families of Identities | |
Constructing and Verifying Identities | |
The Sum and Difference Identities | |
Double Angle, Half Angle & Product-to-Sum Identities | |
The Inverse Trigonometric Functions and Their Applications | |
Solving Basic Trigonometric Equations | |
General Trigonometric Equations and Applications | |
Applications of Trigonometry | |
Oblique Triangles and the Law of Sines | |
The Law of Cosines; Area of a Triangle | |
Vectors and Vector Diagrams | |
Vector Applications and the Dot Product | |
Complex Numbers in Trigonometric Form | |
DemoivreG++s Theorem and the Theorem on nth Roots | |
Systems of Equations and Inequalities | |
Linear Systems in Two Variables with Applications | |
Linear Systems in Three Variables with Applications | |
Partial Fraction Decomposition | |
Systems of Inequalities and Linear Programming | |
Solving Systems Using Matrices and Row Operations | |
The Algebra of Matrices | |
Solving Linear Systems Using Matrix Equations | |
Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More | |
Analytical Geometry | |
Introduction to Analytic Geometry | |
The Circle and the Ellipse | |
The Hyperbola | |
The Analytic Parabola | |
Nonlinear Systems of Equations and Inequalities | |
Polar Coordinates, Equations, and Graphs | |
More on Conic Sections: Rotation of Axes and Polar Form | |
Parametric Equations and Graphs | |
Additional Topics in Algebra | |
Sequences and Series | |
Arithmetic Sequences | |
Geometric Sequences | |
Mathematical Induction | |
Counting Techniques | |
Introduction to Probability | |
The Binomial Theorem | |
Bridges to Calculus | |
An Introduction to Limits | |
Finding Limits Numerically and Graphically | |
Algebraic Methods for Finding Limits; One-Sided Limits and Continuity | |
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