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# College Mathematics

## Overview

In this revision of his best-selling text, Soo Tan builds on the features that have made his texts best-sellers: a problem-solving approach, accurate mathematical development, a concise yet accessible writing style, and a wealth of interesting and appropriate applications. These features are combined with practical pedagogical tools to help students understand and comprehend the material. Tan also now includes innovative use of technology that is optional, yet well integrated throughout the book.

## Product Details

ISBN-13: | 9780534465315 |
---|---|

Publisher: | Cengage Learning |

Publication date: | 02/23/2004 |

Pages: | 1144 |

## Read an Excerpt

In this revision of his best-selling text, Soo Tan builds on the features that have made his texts best-sellers: a problem-solving approach, accurate mathematical development, a concise yet accessible writing style, and a wealth of interesting and appropriate applications. These features are combined with practical pedagogical tools to help students understand and comprehend the material. Tan also now includes innovative use of technology that is optional, yet well integrated throughout the book.

## First Chapter

In this revision of his best-selling text, Soo Tan builds on the features that have made his texts best-sellers: a problem-solving approach, accurate mathematical development, a concise yet accessible writing style, and a wealth of interesting and appropriate applications. These features are combined with practical pedagogical tools to help students understand and comprehend the material. Tan also now includes innovative use of technology that is optional, yet well integrated throughout the book.

## Table of Contents

## Reading Group Guide

1. STRAIGHT LINES AND LINEAR FUNCTIONS. The Cartesian Coordinate System. Straight Lines. Linear Functions and Mathematical Models. Intersection of Straight Lines. The Method of Least Squares (Optional). Summary of Principal Formulas and Terms. Review Exercises. 2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Systems of Linear Equations-Introduction. Solving Systems of Linear Equations I. Solving Systems of Linear Equations II. Matrices. Multiplication of Matrices. The Inverse of a Square Matrix. Leontief Input-Output Model (Optional). Summary of Principal Formulas and Terms. Review Exercises. 3. LINEAR PROGRAMMING: A GEOMETRIC APPROACH. Graphing Systems of Linear Inequalities in Two Variables. Linear Programming Problems. Graphical Solution of Linear Programming Problems. Summary of Principal Formulas and Terms. Review Exercises. 4. LINEAR PROGRAMMING: AN ALGEBRAIC APPROACH. The Simplex Method: Standard Maximization Problems. The Simplex Method: Standard Minimization Problems. Summary of Principal Formulas and Terms. Review Exercises. 5. MATHEMATICS OF FINANCE. Compound Interest. Annuities. Amortization and Sinking Funds. Arithmetic and Geometric Progressions (Optional). Summary of Principal Formulas and Terms. Review Exercises. 6. SETS AND COUNTING. Sets and Set Operations. The Number of Elements in a Finite Set. The Multiplication Principle. Permutations and Combinations. Summary of Principal Formulas and Terms. Review Exercises. 7. PROBABILITY. Experiments, Sample Spaces, and Events. Definition of Probability. Rules of Probability. Use of Counting Techniques in Probability. Conditional Probability and Independent Events. Bayes' Theorem. Markov Chains (Optional). Summary ofPrincipal Formulas and Terms. Review Exercises. 8. PROBABILITY DISTRIBUTIONS AND STATISTICS. Distributions of Random Variables. Expected Value. Variance and Standard Deviation. The Binomial Distribution. The Normal Distribution. Applications of the Normal Distribution. Summary of Principal Formulas and Terms. Review Exercises. 9. PRECALCULUS REVIEW. Exponents and Radicals. Algebraic Expressions. Algebraic Fractions. Inequalities and Absolute Values. Summary of Principal Formulas and Terms. Review Exercises. 10. FUNCTIONS, LIMITS, AND THE DERIVATIVE. Functions and Their Graphs. The Algebra of Functions. Functions and Mathematical Models in Calculus. Limits. One-Sided Limits and Continuity. The Derivative. Summary of Principal Formulas and Terms. Review Exercises. 11. DIFFERENTIATION. Basic Rules of Differentiation. The Product and Quotient Rules. The Chain Rule. Marginal Functions in Economics. Higher-Order Derivatives. Implicit Differentiation and Related Rates. Differentials. Summary of Principal Formulas and Terms. Review Exercises. 12. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Applications of the Second Derivative. Curve Sketching. Optimization I. Optimization II. Summary of Principal Formulas and Terms. Review Exercises. 13. EXPONENTIAL AND LOGARITHMIC. Exponential Functions. Logarithmic Functions. Differentiation of Exponential Functions. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models. Summary of Principal Formulas and Terms. Review Exercises. 14. INTEGRATION. Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Evaluating Definite Integrals. Area Between Two Curves. Applications of the Definite Integral to Business and Economics. Summary of Principal Formulas and Terms. Review Exercises. 15. ADDITIONAL TOPICS IN INTEGRATION. Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals. Applications of Probability to Calculus. Summary of Principal Formulas and Terms. Review Exercises. 16. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. Constrained Maxima and Minima and the Method of LaGrange Multipliers. Double Integrals. Summary of Principal Formulas and Terms. Review Exercises . APPENDIX A: THE SYSTEM OF REAL NUMBERS. APPENDIX B: TABLES. Table I Binomial Probabilities/ Table II The Standard Normal Distribution. INDEX.

## Interviews

1. STRAIGHT LINES AND LINEAR FUNCTIONS. The Cartesian Coordinate System. Straight Lines. Linear Functions and Mathematical Models. Intersection of Straight Lines. The Method of Least Squares (Optional). Summary of Principal Formulas and Terms. Review Exercises. 2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Systems of Linear Equations-Introduction. Solving Systems of Linear Equations I. Solving Systems of Linear Equations II. Matrices. Multiplication of Matrices. The Inverse of a Square Matrix. Leontief Input-Output Model (Optional). Summary of Principal Formulas and Terms. Review Exercises. 3. LINEAR PROGRAMMING: A GEOMETRIC APPROACH. Graphing Systems of Linear Inequalities in Two Variables. Linear Programming Problems. Graphical Solution of Linear Programming Problems. Summary of Principal Formulas and Terms. Review Exercises. 4. LINEAR PROGRAMMING: AN ALGEBRAIC APPROACH. The Simplex Method: Standard Maximization Problems. The Simplex Method: Standard Minimization Problems. Summary of Principal Formulas and Terms. Review Exercises. 5. MATHEMATICS OF FINANCE. Compound Interest. Annuities. Amortization and Sinking Funds. Arithmetic and Geometric Progressions (Optional). Summary of Principal Formulas and Terms. Review Exercises. 6. SETS AND COUNTING. Sets and Set Operations. The Number of Elements in a Finite Set. The Multiplication Principle. Permutations and Combinations. Summary of Principal Formulas and Terms. Review Exercises. 7. PROBABILITY. Experiments, Sample Spaces, and Events. Definition of Probability. Rules of Probability. Use of Counting Techniques in Probability. Conditional Probability and Independent Events. Bayes' Theorem. Markov Chains (Optional). Summary ofPrincipal Formulas and Terms. Review Exercises. 8. PROBABILITY DISTRIBUTIONS AND STATISTICS. Distributions of Random Variables. Expected Value. Variance and Standard Deviation. The Binomial Distribution. The Normal Distribution. Applications of the Normal Distribution. Summary of Principal Formulas and Terms. Review Exercises. 9. PRECALCULUS REVIEW. Exponents and Radicals. Algebraic Expressions. Algebraic Fractions. Inequalities and Absolute Values. Summary of Principal Formulas and Terms. Review Exercises. 10. FUNCTIONS, LIMITS, AND THE DERIVATIVE. Functions and Their Graphs. The Algebra of Functions. Functions and Mathematical Models in Calculus. Limits. One-Sided Limits and Continuity. The Derivative. Summary of Principal Formulas and Terms. Review Exercises. 11. DIFFERENTIATION. Basic Rules of Differentiation. The Product and Quotient Rules. The Chain Rule. Marginal Functions in Economics. Higher-Order Derivatives. Implicit Differentiation and Related Rates. Differentials. Summary of Principal Formulas and Terms. Review Exercises. 12. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Applications of the Second Derivative. Curve Sketching. Optimization I. Optimization II. Summary of Principal Formulas and Terms. Review Exercises. 13. EXPONENTIAL AND LOGARITHMIC. Exponential Functions. Logarithmic Functions. Differentiation of Exponential Functions. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models. Summary of Principal Formulas and Terms. Review Exercises. 14. INTEGRATION. Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Evaluating Definite Integrals. Area Between Two Curves. Applications of the Definite Integral to Business and Economics. Summary of Principal Formulas and Terms. Review Exercises. 15. ADDITIONAL TOPICS IN INTEGRATION. Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals. Applications of Probability to Calculus. Summary of Principal Formulas and Terms. Review Exercises. 16. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. Constrained Maxima and Minima and the Method of LaGrange Multipliers. Double Integrals. Summary of Principal Formulas and Terms. Review Exercises . APPENDIX A: THE SYSTEM OF REAL NUMBERS. APPENDIX B: TABLES. Table I Binomial Probabilities/ Table II The Standard Normal Distribution. INDEX.