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Modeling the Dynamics of Life : Calculus and Probability for Life Scientists
ISBN: 9780534404864 | 0534404863
Edition: 2ndFormat: Hardcover
Publisher: Cengage Learning
Pub. Date: 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 problem... MORE
| 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: Ter... MORE | |
| 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. |
