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Graphs | |
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Rectangular Coordinates; Graphing Utilities; Introduction to Graphing Equations | |
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Intercepts; Symmetry; Graphing Key Equations | |
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Solving Equations Using a Graphing Utility | |
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Lines | |
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Circles | |
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Functions and Their Graphs | |
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Functions | |
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The Graph of a Function | |
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Properties of Functions | |
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Library of Functions; Piecewise-defined Functions | |
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Graphing Techniques: Transformations | |
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Mathematical Models: Building Functions | |
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Linear and Quadratic Functions | |
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Linear Functions, Their Properties, and Linear Models | |
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Building Linear Models from Data; Direct Variation | |
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Quadratic Functions and Their Properties | |
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Building Quadratic Models from Verbal Descriptions and Data | |
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Inequalities Involving Quadratic Functions | |
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Polynomial and Rational Functions | |
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Polynomial Functions and Models | |
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Properties of Rational Functions | |
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The Graph of a Rational Function | |
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Polynomial and Rational Inequalities | |
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The Real Zeros of a Polynomial Function | |
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Complex Zeros; Fundamental Theorem of Algebra | |
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Exponential and Logarithmic Functions | |
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Composite Functions | |
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One-to-One Functions; Inverse Functions | |
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Exponential Functions | |
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Logarithmic Functions | |
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Properties of Logarithms | |
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Logarithmic and Exponential Equations | |
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Financial Models | |
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Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models | |
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Building Exponential, Logarithmic, and Logistic Models from Data | |
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Trigonometric Functions | |
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Angles and Their Measure | |
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Trigonometric Functions: Unit Circle Approach | |
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Properties of the Trigonometric Functions | |
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Graphs of the Sine and Cosine Functions | |
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Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions | |
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Phase Shift; Building Sinusoidal Models | |
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Analytic Trigonometry | |
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The Inverse Sine, Cosine, and Tangent Functions | |
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The Inverse Trigonometric Functions (Continued) | |
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Trigonometric Identities | |
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Sum and Difference Formulas | |
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Double-angle and Half-angle Formulas | |
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Product-to-Sum and Sum-to-Product Formulas | |
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Trigonometric Equations (I) | |
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Trigonometric Equations (II) | |
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Applications of Trigonometric Functions | |
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Applications Involving Right Triangles | |
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The Law of Sines | |
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The Law of Cosines | |
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Area of a Triangle | |
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Simple Harmonic Motion; Damped Motion; Combining Waves | |
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Polar Coordinates; Vectors | |
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Polar Coordinates | |
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Polar Equations and Graphs | |
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The Complex Plane; DeMoivre's Theorem | |
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Vectors | |
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The Dot Product | |
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Vectors in Space | |
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The Cross Product | |
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Analytic Geometry | |
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Conics | |
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The Parabola | |
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The Ellipse | |
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The Hyperbola | |
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Rotation of Axes; General Form of a Conic | |
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Polar Equations of Conics | |
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Plane Curves and Parametric Equations | |
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Systems of Equations and Inequalities | |
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Systems of Linear Equations: Substitution and Elimination | |
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Systems of Linear Equations: Matrices | |
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Systems of Linear Equations: Determinants | |
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Matrix Algebra | |
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Partial Fraction Decomposition | |
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Systems of Nonlinear Equations | |
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Systems of Inequalities | |
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Linear Programming | |
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Sequences; Induction; the Binomial Theorem | |
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Sequences | |
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Arithmetic Sequences | |
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Geometric Sequences; Geometric Series | |
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Mathematical Ind<$$$> | |