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Topics from Algebra | |
Real Numbers | |
Exponents and Radicals | |
Algebraic Expressions | |
Equations | |
Complex Numbers | |
Inequalities | |
Review Exercises | |
Discussion Exercises | |
Graphs and Functions | |
Rectangular Coordinate Systems | |
Graphs of Equations | |
Lines | |
Definition of Function | |
Graphs of Functions | |
Quadratic Functions | |
Operations on Functions | |
Review Exercises | |
Discussion Exercises | |
Polynomial and Rational Functions | |
Polynomial Functions of Degree Greater Than | |
Properties of Division | |
Zeros of Polynomials | |
Complex and Rational Zeros of Polynomials | |
Rational Functions | |
Variation | |
Review Exercises | |
Discussion Exercises | |
Inverse, Exponential, and Logarithmic Functions | |
Inverse Functions | |
Exponential Functions | |
The Natural Exponential Function | |
Logarithmic Functions | |
Properties of Logarithms | |
Exponential and Logarithmic Equations | |
Review Exercises | |
Discussion Exercises | |
Trigonometric Functions | |
Angles | |
Trigonometric Functions of Angles | |
Trigonometric Functions of Real Numbers | |
Values of the Trigonometric Functions | |
Trigonometric Graphs | |
Additional Trigonometric Graphs | |
Applied Problems | |
Review Exercises | |
Discussion Exercises | |
Analytic Trigonometry | |
Verifying Trigonometric Identities | |
Trigonometric Equations | |
The Additions and Subtraction of Formulas | |
Multiple-Angle Formulas | |
Product-To-Sum and Sum-To-Product Formulas | |
The Inverse Trigonometric Functions | |
Review Exercises | |
Discussion Exercises | |
Applications of Trigonometry | |
The Law of Sines | |
The Law of Cosines | |
Vectors | |
The Dot Product | |
Trigonometric Form for Complex Numbers | |
De Moivre's Theorem and nth Roots of Complex Numbers | |
Review Exercises | |
Discussion Exercises | |
Systems of Equations and Inequalities | |
Systems of Equations | |
Systems of Linear Equations in Two Variables | |
Systems of Inequalities | |
Linear Programming | |
Systems of Linear Equations in More Than Two Variables | |
The Algebra of Matrices | |
The Inverse of a Matrix | |
Determinants | |
Properties of Determinants | |
Partial Fractions | |
Review Exercises | |
Discussion Exercises | |
Sequences, Series, and Probability | |
Infinite Sequences and Summation Notation | |
Arithmetic Sequences | |
Geometric Sequences | |
Mathematical Induction | |
The Binomial Theorem | |
Permutations | |
Distinguishable Permutations and Combinations | |
Probability | |
Review Exercises | |
Discussion Exercises | |
Topics from Analytical Geometry | |
Parabolas | |
Ellipses | |
Hyperbolas | |
Plane Curves and Parametric Equations | |
Polar Coordinates | |
Polar Equations of Conics | |
Review Exercises | |
Discussion Exercises | |
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