Calculus for the Life Sciences

Calculus for the Life Sciences, 2nd edition

  • Raymond N. Greenwell, 
  • Nathan P. Ritchey, 
  • Margaret L. Lial

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Overview

Calculus for the Life Sciences features interesting, relevant applications that highlight the utility of mathematics for the life sciences. Step-by-step examples guide you to the correct answer while reviews and exercises provide easy ways to stop and check your understanding along the way.

Published by Pearson (July 14th 2021) - Copyright © 2015

ISBN-13: 9780137553457

Table of contents

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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