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Calculus for the Life Sciences

By Marvin L. Bittinger, Neal Brand, John Quintanilla

Published by Pearson

Published Date: Oct 18, 2005

Table of Contents

Chapter 1    Functions and Graphs

                    1.1    Slope and Linear Functions

                    1.2    Polynomial Functions

                    1.3    Rational and Radical Functions

                    1.4    Trigonometric Functions

                    1.5    Trigonometric Functions and the Unit Circle

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Carbon Dioxide Concentrations

 

Chapter 2    Differentiation

                    2.1    Limits and Continuity:  Numerically and Graphically

                    2.2    Limits: Algebraically

                    2.3    Average Rates of Change

                    2.4    Differentiation Using Limits of Difference Quotients

                    2.5    Differentiation Techniques: Introduction

                    2.6    Instantaneous Rates of Change

                    2.7    Differentiation Techniques:  The Product and Quotient Rules

                    2.8    The Chain Rule

                    2.9    Higher-Order Derivatives

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Rate of Epidemic Spread: SARS

 

Chapter 3    Applications of Differentiation

                    3.1    Using the First Derivatives to Find Maximum and Minimum Values and Sketch Graphs

                    3.2    Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs

                    3.3    Graph Sketching:  Asymptotes and Rational Functions

                    3.4    Using Derivatives to Find Absolute Maximum and Minimum Values

                    3.5    Maximum-Minimum Problems

                    3.6    Approximation Techniques

                    3.7    Implicit Differentiation of Related Rates

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Polymorphism

 

Chapter 4    Exponential and Logarithmic Functions

                    4.1    Exponential Functions

                    4.2    Logarithmic Functions

                    4.3    Applications:  The Uninhibited Growth Model, dP/dt = kP

                    4.4    Applications:  Decay

                    4.5    The Derivatives of ax and logax

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Maximum Sustainable Harvest

 

Chapter 5    Integration

                    5.1    Integration

                    5.2    Riemann Sums and Definite Integrals

                    5.3    Fundamental Theorem of Calculus

                    5.4    Properties of Definite Integrals

                    5.5    Integration Techniques: Substitution

                    5.6    Integration Techniques:  Integration by Parts

                    5.7    Integration Techniques:  Tables and Technology

                    5.8    Volume

                    5.9    Improper Integrals

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Estimating Dinosaur Mass

 

Chapter 6    Matrices

                    6.1    Matrix Operations

                    6.2    Solving Linear Systems of Equations

                    6.3    Finding a Matrix Inverse and Determinant

                    6.4    Computing Eigenvalues and Eigenvectors

                    6.5    Solving Difference Equations

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Population Growth

 

Chapter 7    Functions of Several Variables

                    7.1    Functions of Several Variables

                    7.2    Partial Derivatives

                    7.3    Maximum-Minimum Problems

                    7.4    An Application:  The Method of Least Squares

                    7.5    Multiple Integration

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Stocking Fish

 

Chapter 8    First-Order Differential Equations

                    8.1    Differential Equations and Initial-Value Problems

                    8.2    Linear First-Order Differential Equations

                    8.3    Stability of Autonomous Differential Equations

                    8.4    Separable Differential Equations

                    8.5    Numerical Solutions of Differential Equations

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Larvae and Forest Defoliation

 

Chapter 9    Higher-Order and Systems of Differential Equations

                    9.1    Higher-Order Homogeneous Differential Equations

                    9.2    Higher-Order Nonhomogeneous Differential Equations

                    9.3    Systems of Linear Differential Equations

                    9.4    Matrices and Trajectories

                    9.5    Models of Population Biology

                    9.6    Numerical Methods

                    Summary and Review

                    Test

                    EXTENDED LIFE SCIENCE CONNECTION:  Epidemics

 

Chapter 10    Probability

                      10.1    Probability

                      10.2    Multiplication Trees and Bayes’ Rule

                      10.3    The Binomial Distribution

                      10.4    Expected Value and Standard Deviation for Discrete Random Variables

                      10.5    Continuous Random Variables

                      10.6    Poisson Process

                      10.7    The Normal Distribution

                      Summary and Review

                      Test

                      EXTENDED LIFE SCIENCE CONNECTION:  Axenic Cultures

 

Appendix A:    Review of Basic Algebra

Appendix B:    Functions

 

Tables

                Integration Formulas

                Areas for a Standard Normal Distribution

 

Answers

 

Index

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Package ISBN-13: 9780321481238

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    Marvin L. Bittinger, Neal Brand, John Quintanilla

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