| |
| |
| |
| A Library of Elementary Functions | |
| |
| |
| |
| Linear Equations and Graphs | |
| |
| |
| |
| Linear Equations and Inequalities | |
| |
| |
| |
| Graphs and Lines | |
| |
| |
| |
| Linear Regression | |
| |
| |
| |
| Quadratic Functions | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Functions and Graphs | |
| |
| |
| |
| Functions | |
| |
| |
| |
| Elementary Functions: Graphs and Transformations | |
| |
| |
| |
| Quadratic Functions | |
| |
| |
| |
| Polynomial and Rational Functions | |
| |
| |
| |
| Exponential Functions | |
| |
| |
| |
| Logarithmic Functions | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Finite Mathematics | |
| |
| |
| |
| Mathematics of Finance | |
| |
| |
| |
| Simple Interest | |
| |
| |
| |
| Compound and Continuous Compound Interest | |
| |
| |
| |
| Future Value of an Annuity; Sinking Funds | |
| |
| |
| |
| Present Value of an Annuity; Amortization | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Systems of Linear Equations; Matrices | |
| |
| |
| |
| Review: Systems of Linear Equations in Two Variables | |
| |
| |
| |
| Systems of Linear Equations and Augmented Matrices | |
| |
| |
| |
| Gauss-Jordan Elimination | |
| |
| |
| |
| Matrices: Basic Operations | |
| |
| |
| |
| Inverse of a Square Matrix | |
| |
| |
| |
| Matrix Equations and Systems of Linear Equations | |
| |
| |
| |
| Leontief Input-Output Analysis | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Linear Inequalities and Linear Programming | |
| |
| |
| |
| Inequalities in Two Variables | |
| |
| |
| |
| Systems of Linear Inequalities in Two Variables | |
| |
| |
| |
| Linear Programming in Two Dimensions: A Geometric Approach | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Linear Programming: Simplex Method | |
| |
| |
| |
| A Geometric Introduction to the Simplex Method | |
| |
| |
| |
| The Simplex Method: Maximization with Problem Constraints of the Form = | |
| |
| |
| |
| The Dual; Minimization with Problem Constraints of the form = | |
| |
| |
| |
| Maximization and Minimization with Mixed Problem Constraints | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Logic, Sets, and Counting | |
| |
| |
| |
| Logic | |
| |
| |
| |
| Sets | |
| |
| |
| |
| Basic Counting Principles | |
| |
| |
| |
| Permutations and Combinations | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Probability | |
| |
| |
| |
| Sample Spaces, Events, and Probability | |
| |
| |
| |
| Union, Intersection, and Complement of Events; Odds | |
| |
| |
| |
| Conditional Probability, Intersection, and Independence | |
| |
| |
| |
| Bayes' Formula | |
| |
| |
| |
| Random Variables, Probability Distribution, and Expected Value | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Markov Chains | |
| |
| |
| |
| Properties of Markov Chains | |
| |
| |
| |
| Regular Markov Chains | |
| |
| |
| |
| Absorbing Markov Chains | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Calculus | |
| |
| |
| |
| Limits and the Derivative | |
| |
| |
| |
| Introduction to Limits | |
| |
| |
| |
| Infinite Limits and Limits at Infinity | |
| |
| |
| |
| Continuity | |
| |
| |
| |
| The Derivative | |
| |
| |
| |
| Basic Differentiation Properties | |
| |
| |
| |
| Differentials | |
| |
| |
| |
| Marginal Analysis in Business and Economics | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Additional Derivative Topics | |
| |
| |
| |
| The Constant e and Continuous Compound Interest | |
| |
| |
| |
| Derivatives of Logarithmic and Exponential Functions | |
| |
| |
| |
| Derivatives of Products and Quotients | |
| |
| |
| |
| The Chain Rule | |
| |
| |
| |
| Implicit Differentiation | |
| |
| |
| |
| Related Rates | |
| |
| |
| |
| Elasticity of Demand | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Graphing and Optimization | |
| |
| |
| |
| First Derivative and Graphs | |
| |
| |
| |
| Second Derivative and Graphs | |
| |
| |
| |
| L'Hopitals's Rule | |
| |
| |
| |
| Curve Sketching Techniques | |
| |
| |
| |
| Absolute Maxima and Minima | |
| |
| |
| |
| Optimization | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Integration | |
| |
| |
| |
| Antiderivatives and Indefinite Integrals | |
| |
| |
| |
| Integration by Substitution | |
| |
| |
| |
| Differential Equations; Growth and Decay | |
| |
| |
| |
| The Definite Integral | |
| |
| |
| |
| The Fundamental Theorem of Calculus | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Additional Integration Topics | |
| |
| |
| |
| Area Between Curves | |
| |
| |
| |
| Applications in Business and Economics | |
| |
| |
| |
| Integration by Parts | |
| |
| |
| |
| Integration Using Tables | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| |
| Multivariable Calculus | |
| |
| |
| |
| Functions of Several Variables | |
| |
| |
| |
| Partial Derivatives | |
| |
| |
| |
| Maxima and Minima | |
| |
| |
| |
| Maxima and Minima Using Lagrange Multipliers | |
| |
| |
| |
| Method of Least Squares | |
| |
| |
| |
| Double Integrals Over Rectangular Regions | |
| |
| |
| |
| Double Integrals Over More General Regions | |
| |
| |
| |
| Review | |
| |
| |
| Review Exercise | |
| |
| |
| Appendixes | |
| |
| |
| |
| Basic Algebra Review | |
| |
| |
| Self-Test on Basic Algebra | |
| |
| |
| |
| Algebra and Real Numbers | |
| |
| |
| |
| Operations on Polynomials | |
| |
| |
| |
| Factoring Polynomials | |
| |
| |
| |
| Operations on Rational Expressions | |
| |
| |
| |
| Integer Exponents and Scientific Notation | |
| |
| |
| |
| Rational Exponents and Radicals | |
| |
| |
| |
| Quadratic Equations | |
| |
| |
| |
| Special Topics | |
| |
| |
| |
| Sequences, Series, and Summation Notation | |
| |
| |
| |
| Arithmetic and Geometric Sequences | |
| |
| |
| |
| Binomial Theorem | |
| |
| |
| |
| Tables | |
| |
| |
| |
| Area Under the Standard Normal Curve | |
| |
| |
| |
| Basic Geometric Formulas | |
| |
| |
| Answers | |
| |
| |
| Index | |
| |
| |
| Applications Index | |
| |
| |
| A Library of Elementary Functions | |