What is included with this book?
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 | |
Table of Contents provided by Publisher. All Rights Reserved. |