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Calculus with Applications


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Table of Contents

R. Algebra ReferenceR.1 PolynomialsR.2 FactoringR.3 Rational ExpressionsR.4 EquationsR.5 InequalitiesR.6 ExponentsR.7 Radicals 1. Linear Functions1.1 Slopes and Equations of Lines1.2 Linear Functions and Applications1.3 The Least Squares LineChapter 1 ReviewExtended Application: Using Extrapolation to Predict Life Expectancy 2. Nonlinear Functions2.1 Properties of Functions2.2 Quadratic Functions; Translation and Reflection2.3 Polynomial and Rational Functions2.4 Exponential Functions2.5 Logarithmic Functions2.6 Applications: Growth and Decay; Mathematics of FinanceChapter 2 ReviewExtended Application: Characteristics of the Monkeyface Prickleback 3. The Derivative3.1 Limits3.2 Continuity3.3 Rates of Change3.4 Definition of the Derivative3.5 Graphical DifferentiationChapter 3 ReviewExtended Application: A Model for Drugs Administered Intravenously 4. Calculating the Derivative4.1 Techniques for Finding Derivatives4.2 Derivatives of Products and Quotients4.3 The Chain Rule4.4 Derivatives of Exponential Functions4.5 Derivatives of Logarithmic FunctionsChapter 4 ReviewExtended Application: Electrical Potential and Electric Field 5. Graphs and the Derivative5.1 Increasing and Decreasing Functions5.2 Relative Extrema5.3 Higher Derivatives, Concavity, and the Second Derivative Test5.4 Curve SketchingChapter 5 ReviewExtended Application: A Drug Concentration Model for Orally Administered Medications 6. Applications of the Derivative6.1 Absolute Extrema6.2 Applications of Extrema6.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand6.4 Implicit Differentiation6.5 Related Rates6.6 Differentials: Linear ApproximationChapter 6 ReviewExtended Application: A Total Cost Model for a Training Program 7. Integration7.1 Antiderivatives7.2 Substitution7.3 Area and the Definite Integral7.4 The Fundamental Theorem of Calculus7.5 The Area Between Two Curves7.6 Numerical IntegrationChapter 7 ReviewExtended Application: Estimating Depletion Dates for Minerals 8. Further Techniques and Applications of Integration8.1 Integration by Parts8.2 Volume and Average Value8.3 Continuous Money Flow8.4 Improper IntegralsChapter 8 ReviewExtended Application: Estimating Learning Curves in Manufacturing with Integrals 9. Multivariable Calculus9.1 Functions of Several Variables9.2 Partial Derivatives9.3 Maxima and Minima9.4 Lagrange Multipliers9.5 Total Differentials and Approximations9.6 Double IntegralsChapter 9 ReviewExtended Application: Using Multivariable Fitting to Create a Response Surface Design 10. Differential Equations10.1 Solutions of Elementary and Separable Differential Equations10.2 Linear First-Order Differential Equations10.3 Euler's Method10.4 Applications of Differential EquationsChapter 10 ReviewExtended Application: Pollution of the Great Lakes 11. Probability and Calculus11.1 Continuous Probability Models11.2 Expected Value and Variance of Continuous Random Variables11.3 Special Probability Density FunctionsChapter 11 ReviewExtended Application: Exponential Waiting Times 12. Sequences and Series12.1 Geometric Sequences12.2 Annuities: An Application of Sequences12.3 Taylor Polynomials at 012.4 Infinite Series12.5 Taylor Series12.6 Newton's Method12.7 L'Hopital's RuleChapter 12 ReviewExtended Application: Living Assistance and Subsidized Housing 13. The Trigonometric Functions13.1 Definitions of the Trigonometric Functions13.2 Derivatives of Trigonometric Functions13.3 Integrals of Trigonometric FunctionsChapter 13 ReviewExtended Application: The Shortest Time and The Cheapest Path

About the Author

Marge Lial was always 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. Raymond N. Greenwell earned a B.A. in Mathematics and Physics from the University of San Diego, and an M.S. in Statistics, an M.S. in Applied Mathematics, and a Ph.D. in Applied Mathematics from Michigan State University, where he earned the graduate student teaching award in 1979. After teaching at Albion College in Michigan for four years, he moved to Hofstra University in1983, where he currently is Professor of Mathematics. Raymond has published articles on fluid mechanics, mathematical biology, genetic algorithms, combinatorics, statistics, and undergraduate mathematics education. He is a member of MAA, AMS, SIAM, NCTM, and AMATYC. He is currently (2002-2005) governor of the Metropolitan New York Section of the MAA, as well as webmaster and liaison coordinator, and he received a distinguished service award from the Section in 2003. He is an outdoor enthusiast and leads trips in the Sierra Club's Inner City Outings program. Nathan P. Ritchey earned a B.A. in Mathematics with a minor in Music from Mansfield University of Pennsylvania. He earned a M.S. in Applied Mathematics and a Ph.D. in Mathematics from Carnegie Mellon University. He is currently a Professor of Mathematics and Chair of the Department of Mathematics and Statistics at Youngstown State University. He has published articles in economics, honors education, medicine, mathematics, operations research, and student recruitment. Nate is a Consultant/Evaluator for the North Central Association's Higher Learning Commission and regularly participates in program evaluations. In recognition of his numerous activities, Nate has received the Distinguished Professor Award for University Service, the Youngstown Vindicator's "People Who Make a Difference Award," the Watson Merit Award for Department Chairs, the Spirit in Education Award from the SunTex corporation, and the Provost's Merit Award for significant contributions to the Honors Program. A father of four children, Nate enthusiastically coaches soccer and softball. He also loves music, playing several instruments, and is a tenor in the Shenango Valley Chorale. More information about Nate Ritchey can be found at:

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