Student Solutions Manual for Calculus for the Life Sciences

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 in 1983, 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 has served as 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 the Dean of the College of Science and Health Professions at Edinboro 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: http://www.as.ysu.edu/~nate/.  Marge Lial (late) 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, was affiliated with American River College. An avid reader and traveler, her travel experiences often find their way into her books as applications, exercise sets, and feature sets. Her interest in archeology lead to trips to various digs and ruin sites, producing 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.

• Table of Contents Algebra Reference R.1 PolynomialsR.2 FactoringR.3 Rational ExpressionsR.4 EquationsR.5 InequalitiesR.6 ExponentsR.7 Radicals Functions 1.1 Lines and Linear Functions1.2 The Least Squares Line1.3 Properties of Functions1.4 Quadratic Functions; Translation and Reflection1.5 Polynomial and Rational Functions Chapter ReviewExtended Application: Using Extrapolation to Predict Life ExpectancyExponential, Logarithmic, and Trigonometric Functions 2.1 Exponential Functions2.2 Logarithmic Functions2.3 Applications: Growth and Decay2.4 Trigonometric Functions Chapter ReviewExtended Application: Power FunctionsThe Derivative 3.1 Limits3.2 Continuity3.3 Rates of Change3.4 Definition of the Derivative3.5 Graphical Differentiation Chapter ReviewExtended Application: A Model For Drugs Administered IntravenouslyCalculating the Derivative 4.1 Techniques for Finding Derivatives4.2 Derivatives of Products and Quotients4.3 The Chain Rule4.4 Derivatives of Exponential Functions4.5 Derivatives of Logarithmic Functions4.6 Derivatives of Trigonometric Functions Chapter ReviewExtended Application: Managing Renewable ResourcesGraphs and the Derivative 5.1 Increasing and Decreasing Functions5.2 Relative Extrema5.3 Higher Derivatives, Concavity, and the Second Derivative Test5.4 Curve Sketching Chapter ReviewExtended Application: A Drug Concentration Model for Orally Administered MedicationsApplications of the Derivative 6.1 Absolute Extrema6.2 Applications of Extrema6.3 Implicit Differentiation6.4 Related Rates6.5 Differentials: Linear Approximation Chapter ReviewExtended Application: A Total Cost Model for a Training ProgramIntegration 7.1 Antiderivatives7.2 Substitution7.3 Area and the Definite Integral7.4 The Fundamental Theorem of Calculus7.5 The Area Between Two Curves Chapter ReviewExtended Application: Estimating Depletion Dates for MineralsFurther Techniques and Applications of Integration 8.1 Numerical Integration8.2 Integration by Parts8.3 Volume and Average Value8.4 Improper Integrals Chapter ReviewExtended Application: Flow SystemsMultivariable Calculus 9.1 Functions of Several Variables9.2 Partial Derivatives9.3 Maxima and Minima9.4 Total Differentials and Approximations9.5 Double Integrals Chapter ReviewExtended Application: Optimization for a PredatorMatrices 10.1 Solution of Linear Systems10.2 Addition and Subtraction of Matrices10.3 Multiplication of Matrices10.4 Matrix Inverses10.5 Eigenvalues and Eigenvectorsx Chapter ReviewExtended Application: ContagionDifferential Equations 11.1 Solutions of Elementary and Separable Differential Equations11.2 Linear First-Order Differential Equations11.3 Euler’s Method11.4 Linear Systems of Differential Equations11.5 Non-Linear Systems of Differential Equations11.6 Applications of Differential Equations Chapter ReviewExtended Application: Pollution of the Great LakesProbability 12.1 Sets12.2 Introduction to Probability12.3 Conditional Probability; Independent Events; Bayes’ Theorem12.4 Discrete Random Variables; Applications to Decision Making Chapter ReviewExtended Application: Medical DiagnosisProbability and Calculus 13.1 Continuous Probability Models13.2 Expected Value and Variance of Continuous Random Variables.13.3 Special Probability Density Functions Chapter ReviewExtended Application: Exponential Waiting TimesDiscrete Dynamical Systems 14.1 Sequences14.2 Equilibrium Points14.3 Determining Stability Chapter ReviewExtended Application: Mathematical Modeling in a Dynamic WorldSpecial Topics (available online) Sequences and Series Geometric SequencesAnnuities: An Application of SequencesTaylor PolynomialsInfinite SeriesTaylor SeriesNewton’s MethodL’Hôpital’s RuleMarkov Chains