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Preliminary Contents | |
Algebraic Concepts | |
Sets | |
The Real Numbers | |
Integral Exponents | |
Radicals and Rational Exponents | |
Operations with Algebraic Expressions | |
Factoring | |
Algebraic Fractions | |
Linear Equations and Functions | |
Solution of Linear Equations and Inequalities in one Variable | |
Functions | |
Linear Functions | |
Graphs and Graphing Utilities | |
Solutions of Systems of Linear Equations | |
Applications of Functions in Business and Economics | |
Special Functions | |
Quadratic Equations | |
Quadratic Functions: Parabolas | |
Business Applications of Quadratic Functions | |
Special Functions and Their Graphs | |
Modeling; Fitting Curves to Data with Graphing Utilities | |
Matrices | |
Matrices | |
Multiplication of Matrices | |
Gauss-Jordan Elimination: Solving Systems of Equations | |
Inverse of a Square Matrix; Matrix Equations | |
Applications of Matrices: Leontief Input-Output Models | |
Inequalities and Linear Programming | |
Linear Inequalities in Two Variables | |
Linear Programming: Graphical Methods | |
The Simplex Method: Maximization | |
The Simplex Method: Duality and Minimization | |
The Simplex Method with Mixed Constraints | |
Exponential and Logarithmic Functions | |
Exponential Functions | |
Logarithmic Functions and Their Properties | |
Solution of Exponential Equations: Applications of Exponential and Logarithmic Functions | |
Mathematics of Finance | |
Simple Interest; Sequences | |
Compound Interest; Geometric Sequences | |
Future Value of Annuities | |
Present Value of Annuities | |
Loans and Amortization | |
Introduction to Probability | |
Probability: Odds | |
Unions and Intersections of Events: One-Trial Experiments | |
Conditional Probability: The Product Rule | |
Probability Trees and Bayes' Formula | |
Counting: Permutations and Combinations | |
Permutations, Combinations, and Probability | |
Markov Chains | |
Further Topics in Probability: Data Description | |
Binomial Probability Experiments | |
Data Description | |
Discrete Probability Distributions | |
Normal Probability Distribution | |
Derivatives | |
Limits | |
Continuous Functions; Limits at Infinity | |
Average and Instantaneous Rates of Change: The Derivative | |
Derivative Formulas | |
The Product Rule and the Quotient Rule | |
The Chain Rule and the Power Rule | |
Using Derivative Formulas | |
Higher-Order Derivatives | |
Applications of Derivatives in Business and Economics | |
Applications of Derivatives | |
Relative Maxima and Minima: Curve Sketching | |
Concavity: Points of Inflection | |
Optimization in Business and Economics | |
Applications of Maxima and Minima | |
Asymptotes: More Curve Sketching | |
Derivatives Continued | |
Derivatives of Logarithmic Functions | |
Derivatives of Exponential Functions | |
Implicit Differentiation | |
Related Rates | |
Applications in Business and Economics | |
Indefinite Integrals | |
The Indefinite Integral | |
The Power Rule | |
Integrals Involving Exponential and Logarithmic Functions | |
Applications of the Indefinite Integral in Business and Economics | |
Differential Equations | |
Definite Integrals: Techniques of Integration | |
Area Under a Curve | |
The Definite Integral: The Fundamental Theorem of Calculus | |
Area Between Two Curves | |
Applications of Definite Integrals in Business and Economics | |
Using Tables of Integrals | |
Integration by Parts | |
Improper Integrals and Their Applications | |
Numerical Integration Methods: Trapezoidal Rule and Simpson's Rule | |
Functions of Two or More Variables | |
Functions of Two or more Variables | |
Partial Differentiation | |
Applications of Functions of Two Variables in Business and Economics | |
Maxima and Minima | |
Maxima and Minima of Functions Subject to Constraints: Lagrange Multipliers | |
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