Modeling the Dynamics of Life : Calculus and Probability for Life Scientists

by ADLER

• ISBN13: 9780534348168
• ISBN10: 0534348165
• Edition: 1st
• Format: Paperback
• Copyright: 1998-01-22
• Publisher: Brooks Cole

Summary

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.

Table of Contents

Introduction to Discrete-Time Dynamical Systems	1	(117)
Biology and dynamics	2	(4)
Updating Functions: Describing Growth	6	(8)
Units and Dimensions of Measurements and Functions	14	(8)
Linear Functions and Their Graphs	22	(10)
Finding Solutions: Describing the Dynamics	32	(7)
Combining and Manipulating Functions	39	(10)
Expressing Solutions with Exponential Functions	49	(10)
Power Functions and Allometry	59	(10)
Oscillations and Trigonometry	69	(9)
Modeling and Graphical Analysis of Updating Functions	78	(8)
Equilibria	86	(9)
An Example of Nonlinear Dynamics	95	(11)
Excitable Systems: The Heart	106	(12)
Limits and Derivatives	118	(94)
Introduction to Derivatives	119	(10)
Limits	129	(9)
Continuity	138	(10)
Computing Derivatives: Linear and Quadratic Functions	148	(8)
Derivatives of Sums, Powers, and Polynomials	156	(12)
Derivatives of Products and Quotients	168	(8)
The Second Derivative, Curvature, and Acceleration	176	(8)
Derivatives of Exponential and Logarithmic Functions	184	(6)
Derivatives of Trigonometric Functions	190	(9)
The Chain Rule	199	(13)
Applications of Derivatives and Dynamical Systems	212	(98)
Stability and the Derivative	213	(11)
More Complex Dynamics	224	(13)
Maximization	237	(11)
Reasoning About Functions	248	(9)
Limits at Infinity	257	(11)
Leading Behavior and L'Hopital's Rule	268	(12)
Approximating Functions with lines and Polynomials	280	(9)
Newton's Method	289	(10)
Panting and Deep Breathing	299	(11)
Differential Equations, Integrals, and Their Applications	310	(76)
Differential Equations	311	(11)
Basic Differential Equations	322	(8)
Solving Pure-Time Differential Equations	330	(10)
Integration of Special Functions and Integration by Substitution	340	(8)
Integrals and Sums	348	(8)
Definite and Indefinite Integrals	356	(10)
Applications of Integrals	366	(8)
Improper Integrals	374	(12)
Analysis of Differential Equations	386	(61)
Equilibria and Display of Autonomous Differential Equations	387	(8)
Stable and Unstable Equilibria	395	(7)
Solving Autonomous Differential Equations	402	(7)
Two-Dimensional Differential Equations	409	(8)
The Phase Plan	417	(8)
Solutions in the Phase Plane	425	(10)
The Dynamics of a Neuron	435	(12)
Probability Theory and Descriptive Statistics	447	(82)
Introduction to Probabilistic Models	448	(6)
Stochastic Models of Diffusion	454	(8)
Stochastic Models of Genetics	462	(6)
Probability Theory	468	(6)
Conditional Probability	474	(6)
Independence and Markov Chains	480	(6)
Displaying Probabilities	486	(11)
Random Variables	497	(9)
Descriptive Statistics	506	(9)
Descriptive Statistics for Spread	515	(14)
Probability Models	529	(89)
Joint Distributions	530	(8)
Covariance and Correlation	538	(9)
Sums and Products of Random Variables	547	(10)
The Binomial Distribution	557	(10)
Applications of the Binomial Distribution	567	(7)
Waiting Times: Geometric and Exponential Distributions	574	(10)
The Poisson Distribution	584	(8)
The Normal Distribution	592	(10)
Applying the Normal Approximation	602	(16)
Introduction to Statistical Reasoning	618	(67)
Statistics: Estimating Parameters	619	(8)
Confidence Limits	627	(9)
Estimating the Mean	636	(11)
Hypothesis Testing	647	(7)
Hypothesis Testing: Normal Theory	654	(9)
Comparing Experiments: Unpaired data	663	(8)
Regression	671	(14)
Answers	685	(92)
Index	777