Calculus for the Life Sciences

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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.

R. Algebra Reference

R.1 Polynomials

R.2 Factoring

R.3 Rational Expressions

R.4 Equations

R.5 Inequalities

R.6 Exponents

R.7 Radicals

1. Functions

1.1 Lines and Linear Functions

1.2 The Least Squares Line

1.3 Properties of Functions

1.4 Quadratic Functions; Translation and Reflection

1.5 Polynomial and Rational Functions

            Chapter Review

            Extended Application: Using Extrapolation to Predict Life Expectancy

2. Exponential, Logarithmic, and Trigonometric Functions

2.1 Exponential Functions

2.2 Logarithmic Functions

2.3 Applications: Growth and Decay

2.4 Trigonometric Functions

            Chapter Review

            Extended Application: Power Functions

3. The Derivative

3.1 Limits

3.2 Continuity

3.3 Rates of Change

3.4 Definition of the Derivative

3.5 Graphical Differentiation

            Chapter Review

            Extended Application: A Model For Drugs Administered Intravenously

4. Calculating the Derivative

4.1 Techniques for Finding Derivatives

4.2 Derivatives of Products and Quotients

4.3 The Chain Rule

4.4 Derivatives of Exponential Functions

4.5 Derivatives of Logarithmic Functions

4.6 Derivatives of Trigonometric Functions

            Chapter Review

            Extended Application: Managing Renewable Resources

5. Graphs and the Derivative

5.1 Increasing and Decreasing Functions

5.2 Relative Extrema

5.3 Higher Derivatives, Concavity, and the Second Derivative Test

5.4 Curve Sketching

            Chapter Review

            Extended Application: A Drug Concentration Model for Orally Administered Medications

6. Applications of the Derivative

6.1 Absolute Extrema

6.2 Applications of Extrema

6.3 Implicit Differentiation

6.4 Related Rates

6.5 Differentials: Linear Approximation

            Chapter Review

            Extended Application: A Total Cost Model for a Training Program

7. Integration

7.1 Antiderivatives

7.2 Substitution

7.3 Area and the Definite Integral

7.4 The Fundamental Theorem of Calculus

7.5 The Area Between Two Curves

            Chapter Review

            Extended Application: Estimating Depletion Dates for Minerals

8. Further Techniques and Applications of Integration

8.1 Numerical Integration

8.2 Integration by Parts

8.3 Volume and Average Value

8.4 Improper Integrals

            Chapter Review

            Extended Application: Flow Systems

9. Multivariable Calculus

9.1 Functions of Several Variables

9.2 Partial Derivatives

9.3 Maxima and Minima

9.4 Total Differentials and Approximations

9.5 Double Integrals

            Chapter Review

            Extended Application: Optimization for a Predator

10. Matrices

10.1 Solution of Linear Systems

10.2 Addition and Subtraction of Matrices

10.3 Multiplication of Matrices

10.4 Matrix Inverses

10.5 Eigenvalues and Eigenvectors

            Chapter Review

            Extended Application: Contagion

11. Differential Equations

11.1 Solutions of Elementary and Separable Differential Equations

11.2 Linear First-Order Differential Equations

11.3 Euler's Method

11.4 Linear Systems of Differential Equations

11.5 Non-Linear Systems of Differential Equations

11.6 Applications of Differential Equations

            Chapter Review

            Extended Application: Pollution of the Great Lakes

12. Probability

12.1 Sets

12.2 Introduction to Probability

12.3 Conditional Probability; Independent Events; Bayes' Theorem

12.4 Discrete Random Variables; Applications to Decision Making

            Chapter Review

            Extended Application: Medical Diagnosis

13. Probability and Calculus

13.1 Continuous Probability Models

13.2 Expected Value and Variance of Continuous Random Variables.

13.3 Special Probability Density Functions

            Chapter Review

            Extended Application: Exponential Waiting Times

14. Discrete Dynamical Systems

14.1 Sequences

14.2 Equilibrium Points

14.3 Determining Stability

            Chapter Review

            Extended Application: Mathematical Modeling in a Dynamic World

Special Topics (available online)

Sequences and Series

            Geometric Sequences

            Annuities: An Application of Sequences

            Taylor Polynomials

            Infinite Series

            Taylor Series

            Newton’s Method

            L’Hôpital’s Rule

Markov Chains

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