Modeling the Dynamics of Life Calculus and Probability for Life Scientists (with iLrn™ Testing)

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ISBN: 9780534404864 | 0534404863
Cover: Hardcover
Copyright: 10/22/2004

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Understand the role of mathematics in biology with MODELING THE DYNAMICS OF LIFE: CALCULUS AND PROBABILITY FOR LIFE SCIENTISTS with accompanying technology! Designed to demonstrate the importance of mathematics in breakthroughs in epidemiology, genetics, statistics, physiology, and other biological areas, this mathematics text provides you with the tools you need to succeed. The accompanying iLrn testing makes studying easy by allowing you to work with real math notation in real time and providing instant analysis and feedback. Modeling problems, review problems, and over 100 graphing calculator or computer exercises help you visualize and conceptualize key concepts.

introduction To Discrete Dynamical Systems
Biology And Dynamics Growth
Models of Malaria
Maintenance: Models of Neurons
Replication: Models of Genetics
Types of Dynamical Systems
updating Functions: Describing Growth
A Model Population: Bacterial Growth
A Model Organism: A Growing Tree
Functions: Terminology and Graphs
Exercises
units And Dimensions
Converting Between Units
Translating Between Dimensions
Checking: Dimensions and Estimation
Exercises
Linear Functions And Their Graphs
Proportional Relations
The Equation of a Line
Finding Equations and Graphing Lines
Inverse Functions: Looking Backward
Exercises
Finding Solutions: Describing The Dynamics
Bacterial Population Growth
Solving for Tree Height
Composition of Functions
Exercises
Solutions And Exponential Functions
Bacterial Population Growth in General
Laws of Exponents and Logs
Expressing Results with Exponentials
Exercises
Power Functions And Allometry
Power Relations and Exponential Growth
Power Relations and Lines
Power Relations in Biology: Shape and Flight
Exercises
Oscillations And Trigonometry
Sine and Cosine: A Review
Describing Oscillations with the Cosine
More Complicated Shapes
Exercises
Modeling And Cobwebbing
A Model of the Lungs
The Lung Updating Function
Cobwebbing: A Graphical Solution Technique
Exercises
Equilibria
Equilibria: Graphical Approach
Equilibria: Algebraic Approach
Equilibria: Algebra Involving Parameters
Exercises
Nonlinear Dynamics
A Model of Selection
The General Case and Equilibria
Stable and Unstable Equilibria
Exercises
A Simple Heart
Second-Degree Block
The Wenckebach Phenomenon
Exercises
Limits And Derivatives
Differential Equations
Bacterial Growth Re-Measured
Rates of Change
The Limit
Exercises
Limits Limits of Functions
Applying the Mathematical Definition of a Limit
Properties of Limits
Exercises
More Limits
Left and Right-Hand Limits
Infinite Limits
Functions with More Complicated Limits
Exercises
Continuity
Continuous Functions
Properties of Continuous Functions
Input and Output Tolerances
Exercises
Computing Derivatives
The Derivative in General
Linear and Quadratic Derivatives
Derivatives and Graphs
Exercises
Derivatives Of Sums And Products
Derivatives of Sums
Derivatives of Products
Special Causes and Examples
Exercises
Derivatives Of Powers And Quotients
Derivatives of Power Functions
The Quotient Rule
The Power Rule: Negative Powers
Exercises
Derivatives Of Special Functions
The Derivative of the Exponential Function
The Derivative of the Natural Logarithm
The Derivatives of Trigonometric Functions
Exercises
The Chain Rule
The Derivative of a Composite Function
Derivatives of Inverse Functions
Application of the Chain Rule
Exercises
Applications Of Derivatives And Dynamical Systems
Approximating Functions
Approximating Functions; Examples
The Tangent Line in Deviation Form
Comparison with Other Linear Approximations
Exercises
Stability And The Derivative
Motivation
An Unusual Equilibrium
Computing Slopes at Equilibria
Exercises
Derivatives And Dynamics
Qualitative Dynamical Systems
The Multiplier
The Logistic Dynamical System
Exercises
Maximization
Types of Maxima
The Second Derivative
Maximizing Harvest
Exercises
Reasoning About Functions
Reasoning About Continuous Functions
Reasoning About Maximization
Rolle''s Theorem and the Mean Value Theorem
Exercises
Limits At Infinity
The Behavior of Functions at Infinity
Application to Absorption Functions
Limits of Sequences
Exercises
Leading Behavior and L''Hopital''s Rule Leading Behavior of Functions at Infinity
Leading Behavior of Functions at 0
L''Hopital''s Rule
Exercises
newton''s Method
Finding the Equilibrium of the Lung Model with Absorption
Newton''s Method
Why Newton''s Method Works and When it fails
Exercises
Panting And Deep Breathing
Breathing at Different Rates
Deep Breathing
Panting
Exercises
The Method Of Least Squares
Differential Equations, Integrals, And Their Applications
Differential Equations
Differential Equations: Examples and Terminology
Euler''s Method: Pure-Time
Euler''s Method: Autonomous
Exercises
Basic Differential Equations
Newton''s Law of Cooling
Diffusion Across a Membrane
A Continuous Time Model of Selection
Exercises
The Antiderivative
Pure-Time Differential Equations
Rules for Antiderivatives
Solving Polynomial Differential Equations
Exercises
Special Functions And Substitution
Integrals of Special Functions
The Chain Rule and Integration
Getting Rid of Excess Constants
Exercises
Integrals And Sums
Approximating Integrals with Sums
Approximating Integrals in General
The definite Integral
Exercises
Definite And Indefinite Integrals
The Fundamental Theorem of Calculus
The Summation Property of Definite Integrals
General Solution
Exercises
applications Of Integrals
Integrals and Areas
Integrals and Averages
Integrals and Mass
Exercises
Improper Integrals
Infinite Limits of Integration
Improper Integrals: Examples
Infinite Integrands
Exercises
Analysis Of Differential Equations
Autonomous Differential Equations
Review of Autonomous Differential Equations
Equilibria
Display of Differential Equations
Exercises
Stable And Unstable Equilibria
Recognizing Stable and Unstable Equilibria
Applications of the Stability Theorem
A Model of a Disease
Exercises
Solving Autonomous Equations
Separation of Variables
Pure-Time Equations Revisited
Applications of Separation of Variables
Exercises
Two Dimensional Equations
Predator-Prey Dynamics
Newton''s Law of Cooling
Euler''s Method
Exercises
The Phase-Plane
Equilibria and Nullclines: Predator-Prey Equations
Equilibria and Nullclines: Selection Equations
Equilibria and Nullclines: Newton''s Law of Cooling
Exercises
Solutions In The Phase-Plane
Euler''s Method in the Phase-Plane
Direction Arrows: Predator-Prey Equations
More Direction Arrows
Exercises
The Dynamics Of A Neuron
A Mathematician''s View of a Neuron
The Mathematics of Sodium Channels
The FitzHugh-Nagumo Equations
Exercises
Probability Theory And Descriptive Statistics
Probabilistic Models
Probability and Statistics
Stochastic Population Growth
Markov Chains
Exercises
Stochastic Models Of Diffusion
Stochastic Diffusion
Exercises
Stochastic Models Of Genetics
The Genetics of Inbreeding
The Dynamics of Height
Blending Inheritance
Exercises
Probability Theory
Sample Spaces and Events
Set Theory
Assigning Probabilities to Events
Exercises
Conditional Probability
The Law of Total Probability
Bayes'' Theorem and the Rare Disease Example
Exercises
Independence And Markov Chains
Independence
The Multiplication Rule for Independent Events
Markov Chains and Conditional Probability
Exercises
Displaying Probabilities
Probability and Cumulative Distributions
The Probability Density Function
The cumulative distribution function
Exercises
Random Variables
Types of Random Variable
Expectation: Discrete Case
Expectation: Continuous Case
Exercises
Descriptive Statistics
The Median
The Mode
The Geometric Mean
Exercises
Descriptive Statistics For Spread
Range And Percentiles
Mean Absolution Deviation
Variance
Exercises
Probability Models
Joint Distributions
Marginal Probability Distributions
Joint Distributions and Conditional Distributions
Exercises
Covariance And Correlation
Covariance
Correlation
Perfect Correlation
Exercises
Sums And Products Of Random Variables
Expectation of a Sum
Expectation of a Product
Variance of a Sum
Exercises
The Binomial Distribution The
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Modeling the Dynamics of Life Calculus and Probability for Life Scientists (with iLrn™ Testing)

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Table of Contents

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