Calculus With Applications for the Life Sciences

by Greenwell, Raymond N.; Ritchey, Nathan P.; Lial, Margaret L.

• ISBN13: 9780201745825
• ISBN10: 0201745828
• Edition: 1st
• Format: Hardcover
• Copyright: 2002-10-14
• Publisher: Pearson

Summary

Calculus With Applications for the Life Sciences was written for the one- or two-semester applied calculus course for life science students with a focus on incorporating interesting, relevant, and realistic applications. This text includes many citations from current data sources. It also offers many opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts.

Table of Contents

Preface	xi
CHAPTER R ALGEBRA REFERENCE
R.1 Polynomials	xvi
R.2 Factoring	xix
R.3 Rational Expressions	xxii
R.4 Equations	xxv
R.5 Inequalities	xxxi
R.6 Exponents	xxxvi
R.7 Radicals	xli
CHAPTER 1 FUNCTIONS
1.1 Lines and Linear Functions	2	(17)
1.2 The Least Squares Line	19	(12)
1.3 Properties of Functions	31	(13)
1.4 Quadratic Functions; Translation and Reflection	44	(10)
1.5 Polynomial and Rational Functions	54	(14)
1.6 Review Exercises	68	(7)
1.7 Extended Application: Using Extrapolation to Predict Life Expectancy	75	(2)
CHAPTER 2 EXPONENTIAL LOGARITHMIC AND TRIGONOMETRIC FUNCTIONS
2.1 Exponential Functions	77	(12)
2.2 Logarithmic Functions	89	(14)
2.3 Applications: Growth and Decay	103	(6)
Trigonometric Functions	109	(17)
Summary of Important Functions	126	(2)
Review Exercises	128	(5)
Extended Application: Characteristics of the Monkeyface Prickleback	133	(2)
CHAPTER 3 THE DERIVATIVE
3.1 Limits	135	(19)
3.2 Continuity	154	(8)
3.3 Rates of Change	162
3.4 Definition of the Derivative	113	(77)
3.5 Graphical Differentiation	190	(1)
Review Exercises	191	(12)
CHAPTER 4 CALCULATING THE DERIVATIVE
4.1 Techniques for Finding Derivatives	203	(8)
4.2 Derivatives of Products and Quotients	211	(12)
4.3 The Chain Rule	223	(11)
4.4 Derivatives of Exponential Functions	234	(8)
4.5 Derivatives of Logarithmic Functions	242	(8)
4.6 Derivatives of Trigonometric Functions	250	(9)
Rules for Derivatives Summary	259	(1)
Review Exercises	260	(6)
CHAPTER 5 GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions	266
5.2 Relative Extrema	218	(72)
5.3 Higher Derivatives, Concavity, and the Second Derivative Test	290	(16)
5.4 Curve Sketching	306	(10)
Review Exercises	316	(6)
CHAPTER 6 APPLICATIONS OF THE DERIVATIVE
6.1 Absolute Extrema	322	(9)
6.2 Applications of Extrema	331	(11)
6.3 Implicit Differentiation	342	(7)
6.4 Related Rates	349	(7)
6.5 Differentials: Linear Approximation	356	(7)
Review Exercises	363	(4)
Extended Application: A Total Cost Model for a Training Program	367	(2)
CHAPTER 7 INTEGRATION
7.1 Antiderivatives	369	(11)
7.2 Substitution	380	(9)
7.3 Area and the Definite Integral	389	(14)
7.4 The Fundamental Theorem of Calculus	403	(11)
7.5 Integrals of Trigonometric Functions	414	(5)
7.6 The Area Between Two Curves	419	(7)
7.7 Integration Summary	426	(2)
Review Exercises	428	(5)
Extended Application: Estimating Depletion Dates for Minerals	433
CHAPTER 8 FURTHER TECHNIQUES AND APPLICATIONS OF INTEGRATION
8.1 Numerical Integration	431	(15)
8.2 Integration by Parts	446	(10)
8.3 Volume and Average Value	456	(7)
8.4 Improper Integrals	463	(6)
Review Exercises	469	(3)
Extended Application: Flow Systems	472	(4)
CHAPTER 9 MULTIVARIABLE CALCULUS
9.1 Functions of Several Variables	476	(13)
9.2 Partial Derivatives	489	(11)
9.3 Maxima and Minima	500	(9)
9.4 Total Differentials and Approximations	509	(5)
9.5 Double Integrals	514	(7)
Review Exercises	521	(10)
Extended Application: Optimization for a Predator	531	(3)
CHAPTER 10 MATRICES
10.1 Linear Systems	534	(18)
10.2 Addition and Subtraction of Matrices	552	(9)
10.3 Multiplication of Matrices	561	(12)
10.4 Matrix Inverses	573	(11)
10.5 Eigenvalues and Eigenvectors	584	(11)
Review Exercises	595	(6)
Extended Application: Contagion	601	(2)
CHAPTER 11 DIFFERENTIAL EQUATIONS
11.1 Solutions of Elementary and Separable Differential Equations	603	(13)
11.2 Linear First-Order Differential Equations	616	(7)
11.3 Euler's Method	623	(7)
11.4 Linear Systems of Differential Equations	630	(9)
11.5 Nonlinear Systems of Differential Equations	639	(7)
11.6 Applications of Differential Equations	646	(6)
Review Exercises	652	(4)
Extended Application: Pollution of the Great lakes	656	(3)
CHAPTER 12 PROBABILITY
12.1 Sets	659	(15)
12.2 Introduction to Probability	674	(17)
12.3 Conditional Probability; Independent Events; Bayes' Theorem	691	(18)
12.4 Discrete Random Variables; Applications to Decision Making	709	(12)
Probability Summary	721	(1)
Review Exercises	722	(5)
Extended Application: Medical Diagnosis	727	(2)
CHAPTER 13 PROBABILITY AND CALCULUS
13.1 Continuous Probability Models	729	(9)
13.2 Expected Value and Variance of Continuous Random Variables	738
13.3 Special Probability Density Functions	146	(614)
Review Exercises	760	(5)
Extended Application: Exponential Waiting Times	765
TABLES
Table 1 Formulas from Geometry	A-1
Table 2 Area Under a Normal Curve	A-2
Table 3 Integrals	A-4
Table 4 Integrals Involving Trigonometric Functions	A-5
Answers to Selected Exercises	A-7
Photo Acknowledgments	A-49
Index of Applications	I-1
Index	I-7