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Polynomials | |
Factoring | |
Rational Expressions | |
Equations | |
Inequalities | |
Exponents | |
Radicals | |
Linear Functions | |
Slopes and Equations of Lines | |
Linear Functions and Applications | |
The Least Squares Line | |
Systems of Linear Equations and Matrices | |
Solution of Linear Systems by the Echelon Method | |
Solution of Linear Systems by the Gauss-Jordan Method | |
Addition and Subtraction of Matrices | |
Multiplication of Matrices | |
Matrix Inverses | |
Input-Output Models | |
Linear Programming: The Graphical Method | |
Graphing Linear Inequalities | |
Solving Linear Programming Problems Graphically | |
Applications of Linear Programming | |
Linear Programming: The Simplex Method | |
Slack Variables and the Pivot | |
Maximization Problems | |
Minimization Problems | |
Duality | |
Nonstandard Problems | |
Mathematics of Finance | |
Simple and Compound Interest | |
Future Value of an Annuity | |
Present Value of an Annuity | |
Amortization | |
Logic | |
Statements and Quantifiers | |
Truth Tables and Equivalent Statements | |
The Conditional and Circuits | |
More on the Conditional | |
Analyzing Arguments with Euler Diagrams | |
Analyzing Arguments with Truth Tables | |
Sets and Probability | |
Sets | |
Applications of Venn Diagrams | |
Introduction to Probability | |
Basic Concepts of Probability | |
Conditional Probability | |
Independent Events | |
Bayes' Theorem | |
Counting Principles | |
Further Probability Topics | |
The Multiplication Principle | |
Permutations | |
Combinations | |
Probability Applications of Counting Principles | |
Binomial Probability | |
Probability Distributions | |
Expected Value | |
Statistics | |
Frequency Distributions | |
Measures of Central Tendency | |
Measures of Variation | |
The Normal Distribution | |
Normal Approximation to the Binomial Distribution | |
Nonlinear Functions | |
Properties of Functions | |
Quadratic Functions | |
Translation and Reflection | |
Polynomial and Rational Functions | |
Exponential Functions | |
Logarithmic Functions | |
Applications: Growth and Decay | |
Mathematics of Finance | |
The Derivative | |
Limits | |
Continuity | |
Rates of Change | |
Definition of the Derivative | |
Graphical Differentiation | |
Calculating the Derivative | |
Techniques for Finding Derivatives | |
Derivatives of Products and Quotients | |
The Chain Rule | |
Derivatives of Exponential Functions | |
Derivatives of Logarithmic Functions | |
Graphs and the Derivative | |
Increasing and Decreasing Functions | |
Relative Extrema | |
Higher Derivatives, Concavity, and the Second Derivative Test | |
Curve Sketching | |
Applications of the Derivative | |
Absolute Extrema | |
Applications of Extrema | |
Further Business Applications: Economic Lot Size, Economic Order Quantity | |
Elasticity of Demand | |
Implicit Differentiation | |
Related Rates | |
Differentials: Linear Approximation | |
Integration | |
Antiderivatives | |
Substitution | |
Area and the Definite Integral | |
The Fundamental Theorem of Calculus | |
The Area Between Two Curves | |
Numerical Integration | |
Further Techniques and Applications of Integration | |
Integration by Parts | |
Volume and Average Value | |
Continuous Money Flow | |
Improper Integrals | |
Solutions of Elementary and Separable Differential Equations | |
Multivariable Calculus | |
Functions of Several Variables | |
Partial Derivatives | |
Maxima and Minima | |
Lagrange Multipliers | |
Total Differentials and Approximations | |
Double Integrals | |
Probability and Calculus | |
Continuous Probability Models | |
Expected Value and Variance of Continuous Random Variables | |
Special Probability Density Functions | |
Tables | |
Formulas from Geometry | |
Area Under a Normal Curve | |
Integrals | |
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