Modeling the Dynamics of Life Calculus and Probability for Life Scientists

ISBN-10: 0534404863
ISBN-13: 9780534404864
Edition: 2nd 2005 (Revised)
List price: $295.95
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Description: 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,  More...

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Book details

List price: $295.95
Edition: 2nd
Copyright year: 2005
Publisher: Brooks/Cole
Publication date: 10/22/2004
Binding: Hardcover
Pages: 912
Size: 8.75" wide x 10.75" long x 1.50" tall
Weight: 4.642
Language: English

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.

Discrete-Time Dynamical Systems
Biology and Dynamics
Growth: Models of Malaria
Maintenance: Models of Neurons
Replication: Models of Genetics
Types of Dynamical Systems
Variables and Functions
Describing Measurements with Variables, Parameters and Graphs
Describing Relations Between Measurements with Functions
Combining Functions
Units and Dimensions
Converting Between Units
Translating Between Dimensions
Checking: Dimensions and Estimation
Linear Functions and their Graphs
Proportional Relations
Linear Functions and the Equation of a Line
Finding Equations and Graphing Lines
Solving Equations Involving Lines
Finding Inverse Functions
Discrete-Time Dynamical Systems
Discrete-time Dynamical Systems and Updating Functions
Manipulating Updating Functions
Discrete-Time Dynamical Systems: Units and Dimensions
Solutions
Analysis of Discrete-Tie Dynamical Systems
Cobwebbing: A Graphical Solution Technique
Equilibria: Graphical Approach
Equilibria: Algebraic Approach
Solutions and Exponential Functions
Bacterial Population Growth in General
Laws of Exponents and Logs
Expressing Results with Exponentials
Oscillations and Trigonometry
Sine and Cosine: A Review
Describing Oscillations with the Cosine
More Complicated Shapes
A Model of Gas Exchange in the Lung
A Model of the Lungs
The Lung System in General
Lung Dynamics with Absorption
An Example of Nonlinear Dynamics
A Model of Selection
The Discrete-Time Dynamical System and Equilibria
Stable and Unstable Equilibria
Excitable Systems I: The Heart
A Simple Heart
Second Degree Block
The Wenckeback Phenomenon
Limits and Derivatives
Introduction to Derivatives
The Average Rate of Change
Instantaneous Rates of Change
Limits and Derivatives
Differential Equations: A Preview
Limits
Limits of Functions
Left and Right-Hand Limits
Properties of Limits
Infinite Limits
Continuity
Continuous Functions
Input and Output Tolerances
Hysteresis
Computing Derivatives
Differentiable Functions
The Derivative of a Linear Function
A Quadratic Function
Derivatives of Sums, Powers, and Polynomials
The Sum Rule
Derivatives of Power Functions
Derivatives of Polynomials
Derivatives of Products and Quotients
The Product Rule
Special Cases and Examples
The Quotient Rule
The Second Derivative
The Second Derivative
Using the Second Derivative for Graphing
Acceleration
Exponentials snd Logarithms
The Exponential Function
The Natural Logarithm
Applications
The Chain Rule
The Derivative of a Composite Function
Derivatives of Inverse Functions
Applications
Derivatives of Trigonometric Functions
Deriving the Derivatives of Sine and Cosine
Other Trigonometric Functions
Applications
Derivatives and Dynamical Systems
Stability and the Derivative
Motivation
Stability and the Slope
Evaluating Stability with the Derivative
More Complex Dynamics
The Logistic Dynamical System
Qualitative Dynamical Systems
Analysis of the Logistic Dynamical System
Maximization
Minima and Maxima
Maximizing Food Intake Rate
Maximizing Fish Harvest
Reasoning About Functions
The Intermediate Value Theorem
Maximization: The Extreme Value Theorem
Rolle's Theorem and the Mean Value Theorem
Limits at Infinity
The Behavior of Functions at Infinity
Application to Absorption Functions
Limits of Sequences
Leading Behavior and L'hopital's Rule
Leading Behavior of Functions at Infinity
Leading Behavior of Functions at 0
The Method of Matched Leading Behaviors
L'Hopital's Rule
Approximating Functions
The Tangent and Secant Lines
Quadratic Approximation
Taylor Polynomials
Newton's Method
Finding the Equilibrium
Newton's Method
Why Newton's Method Works and When it Fails
Panting and Deep Breathing
Breathing at Different Rates
Deep Breathing
Panting
Intermediate Optimum
Differential Equations, Integrals, and their Applications
Differential Equations
Differential Equations: Examples and Terminology
Graphical Solution of Pure-Time Differential Equations
Euler's Method: Pure-Time
Antiderivatives and Indefinite Integrals
Pure-Time Differential Equations
Rules for Antiderivatives
Solving Polynomial Differential Equations
Special Functions, Substitution, and Parts
Integrals of Special Functions
The Chain Rule and Integration
Using Substitution to Eliminate Constants
Integrals and Sums
Approximating Integrals with Sums
Approximating Integrals in General
The Definite Integral
Definite and Indefinite Integrals
The Fundamental Theorem of Calculus
The Summation Property of Definite Integral
Proof of the Fundamental Theorem of Calculus
Applications of Integrals
Integrals and Areas
Integrals and Averages
Integrals and Mass
Improper Integrals
Infinite Limits of Integration
Improper Integrals: Examples
Infinite Integrands
Autonomous Differential Equations
Autonomous Differential Equations
Review of Autonomous Differential Equations
Newton's Law of Cooling
Diffusion Across a Membrane
A Continuous Time Model of Competition
The Phase-Line Diagram
Equilibria
Display of Differential Equations
Stable and Unstable Equilibria
Recognizing Stable and Unstable Equilibria
Applications of the Stability Theorem
A Model of a Disease
Solving Autonomous Equations
Separation of Variables
Pure-Time Equations Revisited
Applications of Separation of Variables
Two Dimensional Equations
Predator-Prey Dynamics
Newton's Law of Cooling
Euler's Method
The Phase-Plane
Equilibria and Nullclines: Predator-Prey Equations
Equilibria and Nullclines: Competition Equations
Equilibria and Nullclines: Newton's Law of Cooling
Solutions in the Phase-Plane
Euler's Method in the Phase-Plane
Direction Arrows: Predator-Prey Equations
Direction Arrows for the Competition Equations
Directions Arrows for newton's Law of Cooling
The Dynamics of a Neuron
A Mathematician's View of a Neuron
The Mathematics of Sodium Channels
The Mathematics of Sodium Channel Blocking
The FitzHugh-Nagumo Equations
Weak Channel Blocking Mechanism
The Effects of Constant Applied Current
Probability Theory and Statistics
Introduction to Probabilistic Models
Probability and Statistics
Stochastic Population Growth: Stochastic Reproduction
Stochastic Population Growth: Stochastic Immigration
Markov Chains
Stochastic Models of Diffusion and Genetics
Stochastic Diffusion
The Genetics of Inbreeding
The Dynamics of Height
Blending Inheritance
Probability Theory
Sample Spaces and Events
Set Theory
Assigning Probabilities to Events
Exercises
Conditional Probability
Conditional Probability
The Law of Total Probability
Bayes' Theorem and the Rare Disease Example
Independence and Markov Chains
Independence
The Multiplication Rule for Independent Events
Markov Chains and Conditional Probability
Displaying Probabilities
Probability and Cumulative Distributions
The Probability Density Function: Derivation
Using the Probability Density Function
The Cumulative Distribution Function
Random Variables
Types of Random Variable
Expectation: Discrete Case
Expectation: Continuous Case
Descriptive Statistics
The Median
The Mode
The Geometric Mean
Descriptive Statistics for Spread
Range And Percentiles
Mean Absolute Deviation
Variance
The Coefficient of Variation
Supplementary Problems For Chapter 6
Probability Models
Joint Distributions
Joint Distributions
Marginal Probability Distributions
Joint Distributions and Conditional Distributions
Covariance and Correlation
Covariance
Correlation
Perfect Correlation
Sums and Products of Random Variables
Expectation of a Sum
Expectation of a Product

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