|Calculus for the Life Sciences: Global Edition||
Calculus for the Life Sciences: Global Edition
|74.20||approx. 7-9 days|
Calculus for the Life Sciences features interesting, relevant applications that motivate students and highlight the utility of mathematics for the life sciences. This edition also features new ways to engage students with the material, such as Your Turn exercises. The MyMathLab® course for the text provides online homework supported by learning resources such as video tutorials, algebra help, and step-by-step examples.
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Motivation: Students constantly see the math applied to the life sciences.
Built for student success: Proven pedagogy, robust exercise sets, and comprehensive end-of-chapter material help students succeed in the course.
New and Revised Content
Changes in the presentation were made throughout to increase clarity, including adding some examples and rewriting others. In Section 1.1, a new example has been added which models the prevalence of cigarette smoking in the U.S., and then uses the model to make predictions. Section 1.2 has been revised, giving the formulas for the least squares line explicitly and making them more consistent with the formula for the correlation coefficient. In Section 1.4, an example on vaccination coverage, which illustrates how to derive a quadratic model, both by hand and with technology, has been added. In Section 1.5, material on identifying the degree of a polynomial has been rewritten as an example to better highlight the concept. An example on tuberculosis in the U.S., which illustrates how to derive a cubic model, has also been added. Throughout the chapter, real life exercises have been updated and new exercises on topics such as cancer, diabetes, gender ratio, energy consumption, meat consumption, the demand for nurses, organic farming, and ideal partner height have been added.
In Section 2.1, a new example has been added, which covers the surplus of food, illustrating how to derive an exponential model, both by hand and with technology. In Section 2.4, an example using a trigonometric function to model the pressure on the eardrum has been included. A new Extended Application on Power Functions has been added. Throughout the chapter, real life exercises have been updated and new exercises on topics such as the bald eagle population, minority population growth, carbon monoxide emissions, wind energy, metabolic rate, physician demand, and music have been added.
In Section 3.1, the introduction of limits was completely revised. The opening discussion and example were transformed into a series of examples that progress through different limit scenarios: a function defined at the limit, a function undefined at that limit (a “hole” in the graph), a function defined at the limit but with a different value than the limit (a piecewise function), and then finally, attempting to find a limit when one does not exist. New figures were added to illustrate the different scenarios. In Section 3.2, the definition and examples of continuity have been revised using a simple process to test for continuity. A medical devise cost analysis has been added as an example. In Section 3.3, an example calculating the rate of change of the number of households with landlines has been added. The opening discussion of Section 3.5, showing how to sketch the graph of the derivative given the graph of the original function, was rewritten as an example. An Extended Application on the modeling of drugs administered intravenously has been added. Throughout the chapter, real life exercises have been updated and new exercises on topics such as Alzheimer’s disease, body mass index, and immigration have been added.
The introduction to the chain rule was rewritten as an example in Section 4.3. In Section 4.4, a new example illustrates the use of a logistic function to develop a model for the weight of cactus wrens. In the Chapter Review, a list of important formulas and definitions has been included. An Extended Application on managing renewable resources has been added. Throughout the chapter, real life exercises have been updated and new exercises on topics such as tree growth, genetics, insect competition, whooping cranes, cholesterol, involutional psychosis, radioactive iron, radioactive albumin, heat index, Jukes-Cantor distance, eardrum pressure, online learning, and minority populations have been added.
Twenty-six new exercises were added throughout Chapter 5, 9 of them applications based on scientific sources, such as three on foraging and two on cohesivene
R. Algebra Reference
R.3 Rational Expressions
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
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
Extended Application: Power Functions
3. The Derivative
3.3 Rates of Change
3.4 Definition of the Derivative
3.5 Graphical Differentiation
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
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
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
Extended Application: A Total Cost Model for a Training Program
7.3 Area and the Definite Integral
7.4 The Fundamental Theorem of Calculus
7.5 The Area Between Two Curves
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
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
Extended Application: Optimization for a Predator
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
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
Extended Application: Pollution of the Great Lakes
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.