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Mathematics with Applications


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Table of Contents

Chapter 1: Algebra and Equations1.1 The Real Numbers1.2 Polynomials1.3 Factoring1.4 Rational Expressions1.5 Exponents and Radicals1.6 First-Degree Equations1.7 Quadratic EquationsChapter 1 SummaryChapter 1 Review ExercisesCase Study 1: Consumers Often Defy Common Sense Chapter 2: Graphs, Lines, and Inequalities2.1 Graphs2.2 Equations of Lines2.3 Linear Models2.4 Linear Inequalities2.5 Polynomial and Rational InequalitiesChapter 2 SummaryChapter 2 Review ExercisesCase Study 2: Using Extrapolation to Predict Life Expectancy Chapter 3: Functions and Graphs3.1 Functions3.2 Graphs of Functions3.3 Applications of Linear Functions3.4 Quadratic Functions3.5 Applications of Quadratic Functions3.6 Polynomial Functions3.7 Rational FunctionsChapter 3 SummaryChapter 3 Review ExercisesCase Study 3: Architectural Arches Chapter 4: Exponential and Logarithmic Functions4.1 Exponential Functions4.2 Applications of Exponential Functions4.3 Logarithmic Functions4.4 Logarithmic and Exponential EquationsChapter 4 SummaryChapter 4 Review ExercisesCase Study 4: Characteristics of the Monkeyface Prickleback Chapter 5: Mathematics of Finance5.1 Simple Interest and Discount5.2 Compound Interest5.3 Annuities, Future Value, and Sinking Funds5.4 Annuities, Present Value, and AmortizationChapter 5 SummaryChapter 5 Review ExercisesCase Study 5: Continuous Compounding Chapter 6: Systems of Linear Equations and Matrices6.1 Systems of Two Linear Equations in Two Variables6.2 Larger Systems of Linear Equations6.3 Applications of Systems of Linear Equations6.4 Basic Matrix Operations6.5 Matrix Products and Inverses6.6 Applications of MatricesChapter 6 SummaryChapter 6 Review ExercisesCase Study 6: Matrix Operations and Airline Route Maps Chapter 7: Linear Programming7.1 Graphing Linear Inequalities in two Variables7.2 Linear Programming: The Graphical Method7.3 Applications of Linear Programming7.4 The Simplex Method: Maximization7.5 Maximization Applications7.6 The Simplex Method: Duality and Minimization7.7 The Simplex Method: Nonstandard ProblemsChapter 7 SummaryChapter 7 Review ExercisesCase Study 7: Cooking with Linear Programming Chapter 8: Sets and Probability8.1 Sets8.2 Applications of Venn Diagrams8.3 Introduction to Probability8.4 Basic Concepts of Probability8.5 Conditional Probability and Independent Events8.6 Bayes' FormulaChapter 8 SummaryChapter 8 Review ExercisesCase Study 8: Medical Diagnosis Chapter 9: Counting, Probability Distributions, and Further Topics in Probability9.1 Probability Distributions and Expected Value9.2 The Multiplication Principle, Permutations, and Combinations9.3 Applications of Counting9.4 Binomial Probability9.5 Markov Chains9.6 Decision MakingChapter 9 SummaryChapter 9 Review ExercisesCase Study 9: QuickDraw (R) from the New York State Lottery Chapter 10: Introduction to Statistics10.1 Frequency Distributions10.2 Measures of Central Tendency10.3 Measures of Variation10.4 Normal Distributions10.5 Normal Approximation to the Binomial DistributionChapter 10 SummaryChapter 10 Review ExercisesCase Study 10: Statistics in the Law-The Castaneda Decision Chapter 11: Differential Calculus11.1 Limits11.2 One-sided Limits and Limits Involving Infinity11.3 Rates of Change11.4 Tangent Lines and Derivatives11.5 Techniques for Finding Derivatives11.6 Derivatives of Products and Quotients11.7 The Chain Rule11.8 Derivatives of Exponential and Logarithmic Functions11.9 Continuity and DifferentiabilityChapter 11 SummaryChapter 11 Review ExercisesCase Study 11: Price Elasticity of Demand Chapter 12: Applications of the Derivative12.1 Derivatives and Graphs12.2 The Second Derivative12.3 Optimization Applications12.4 Curve SketchingChapter 12 SummaryChapter 12 Review ExercisesCase Study 12: A Total Cost Model for a Training Program Chapter 13: Integral Calculus13.1 Antiderivatives13.2 Integration by Substitution13.3 Area and the Definite Integral13.4 The Fundamental Theorem of Calculus13.5 Applications of Integrals13.6 Tables of Integrals13.7 Differential EquationsChapter 13 SummaryChapter 13 Review ExercisesCase Study 13: Bounded Population Growth Chapter 14: Multivariate Calculus14.1 Functions of Several Variables14.2 Partial Derivatives14.3 Extrema of Functions of Several Variables14.4 Lagrange MultipliersChapter 14 SummaryChapter 14 Review ExercisesCase Study 14: Global Warming and the Method of Least Squares AppendixesAppendix A: Graphing CalculatorsAppendix B: Tables Table 1: Formulas from Geometry Table 2: Areas under the Normal Curve Table 3: Integrals Answers to Selected ExercisesIndex of ApplicationsIndex

About the Author

Marge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. Thomas W. Hungerford received his bachelor's degree from Holy Cross and his Ph.D. from the University of Chicago. He taught for many years at the University of Washington (Seattle) before moving to Cleveland State University in 1980. He has been at St. Louis University since 2003. He has written a number of research articles in algebra and several in mathematics education. Dr. Hungerford is the author or coauthor of more than a dozen mathematics textbooks, ranging from high school to graduate level, several of which are published by Addison-Wesley. He is active in promoting the effective use of technology in mathematics instruction. Dr. Hungerford has also been a referee and reviewer for various mathematical journals and has served on National Science Foundation panels for selecting grant recipients. John P. Holcomb, Jr. received his bachelor's degree from St. Bonaventure University and his Ph.D. from the University at Albany, State University of New York. He taught for five years at Youngstown State University prior to arriving at Cleveland State University in Fall 2000. He is an associate professor and frequently collaborates with researchers in a variety of disciplines where he provides statistical analysis. Dr. Holcomb has also authored several papers in statistical education and is very active in the American Statistical Association and the Mathematical Association of America. He was named a Carnegie Scholar in 2000 by the Carnegie Foundation for the Advancement of Teaching and Learning and in 2003 received the Waller Award from the American Statistical Association for outstanding teaching of introductory statistics.

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