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외국도서
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대학교재/전문서적
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자연과학/순수과학계열
Modeling the Dynamics of Life : Calculus and Probability for Life Scientists
2013년 9월 9일 이후 누적수치입니다.
- 저 : Adler, Frederick R.
- 출판사 : Brooks/Cole
- 발행 : 2004년 10월 22일
- 쪽수 : 0
- ISBN : 9780534404864
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42,000원 |
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42,000원
1,260P (3%적립)
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이벤트/기획전
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연관도서
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상품권
이상품의 분류
목차
| 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. |
책소개
Designed to help life sciences students understand the role mathematics has played in breakthroughs in epidemiology, genetics, statistics, physiology, and other biological areas, this text provides students with a thorough grounding in mathematics, the language, and 'the technology of thought' with which these developments are created and controlled. The text teaches the skills of describing a system, translating appropriate aspects into equations, and interpreting the results in terms of the original problem. The text helps unify biology by identifying dynamical principles that underlie a great diversity of biological processes. Standard topics from calculus courses are covered, but with particular emphasis on those areas connected with modeling: discrete-time dynamical systems, differential equations, and probability and statistics.
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