Modeling the Dynamics of Life: Calculus and Probability for Life Scientists / Edition 3

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Overview

Understand the role of mathematics in biology with MODELING THE DYNAMICS OF LIFE: CALCULUS AND PROBABILITY FOR LIFE SCIENTISTS, Third Edition! 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. Modeling problems, review problems, and over 100 graphing calculator or computer exercises help you visualize and conceptualize key concepts.

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Product Details

  • ISBN-13: 9780840064189
  • Publisher: Cengage Learning
  • Publication date: 1/4/2012
  • Edition number: 3
  • Pages: 960
  • Product dimensions: 7.44 (w) x 9.69 (h) x 0.79 (d)

Meet the Author

After graduating from Harvard University with a B.A. in Mathematics, Fred Adler received his Ph.D. in Applied Mathematics at Cornell University, where he began his study of mathematical biology. Currently a professor in the departments of mathematics and biology at the University of Utah, he teaches courses in mathematical modeling with a wide range of backgrounds. Prof. Adler's research focuses on mathematical ecology, with emphases in mathematical epidemiology, evolutionary ecology, and community ecology.

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Table of Contents

1. Introduction to Discrete-Time Dynamical Systems. 1.1 Biology and Dynamics. 1.2 Variables. Parameters. and Functions in Biology. 1.3 The Units and Dimensions of Measurements and Functions. 1.4 Linear Functions and Their Graphs. 1.5 Discrete-Time Dynamical Systems. 1.6 Analysis of Discrete-Time Dynamical Systems. 1.7 Expressing Solutions with Exponential Functions. 1.8 Oscillations and Trigonometry. 1.9 A Model of Gas Exchange in the Lung. 1.10 An Example of Nonlinear Dynamics. 1.11 An Excitable Systems I: The Heart. 2. Limits and Derivatives. 2.1 Introduction to Derivatives. 2.2 Limits. 2.3 Continuity. 2.4 Computing Derivatives: Linear and Quadratic Functions. 2.5 Derivatives of Sums. Powers. and Polynomials. 2.6 Derivatives of Products and Quotients. 2.7 The Second Derivative. Curvature. and Acceleration. 2.8 Derivatives of Exponential and Logarithmic Functions. 2.9 The Chain Rule. 2.10 Derivatives of Trigonometric Functions. 3. Applications of Derivatives and Dynamical Systems. 3.1 Stability and the Derivative. 3.2 More Complicated Dynamics. 3.3 Maximization. 3.4 Reasoning About Functions. 3.5 Limits at Infinity. 3.6 Leading Behavior and L'Hopital's Rule. 3.7 Approximating Functions with Lines and Polynomials. 3.8 Newton's Method. 3.9 Panting and Deep Breathing. 4. Differential Equations. Integrals. and Their Applications. 4.1 Differential Equations. 4.2 Solving Pure-Time Differential Equations. 4.3 Integration of Special Functions. Integration by Substitution. by Parts. and by Partial Fractions. 4.4 Integrals and Sums. 4.5 Definite and Indefinite Integrals. 4.6 Applications of Integrals. 4.7 Improper Integrals. 5. Analysis of Autonomous Differential Equations. 5.1 Basic Differential Equations. 5.2 Equilibria and Display of Autonomous Differential Equations. 5.3 Stable and Unstable Equilibria. 5.4 Solving Autonomous Differential Equations. 5.5 Two Dimensional Differential Equations. 5.6 The Phase Plane. 5.7 Solutions in the Phase Plane. 5.8 The Dynamics of a Neuron. 6. Probability Theory and Descriptive Statistics. 6.1 Introduction to Probabilistic Models. 6.2 Stochastic Models of Diffusion and Genetics. 6.3 Probability Theory. 6.4 Conditional Probability. 6.5 Independence and Markov Chains. 6.6 Displaying Probabilities. 6.7 Random Variables. 6.8 Descriptive Statistics. 6.9 Descriptive Statistics for Spread. 7. Probability Models. 7.1 Joint Distributions. 7.2 Covariance and Correlation. 7.3 Sums and Products of Random Variables. 7.4 The Binomial Distribution. 7.5 Applications of the Binomial Distribution. 7.6 Waiting Times: Geometric and Exponential Distributions. 7.7 The Poisson Distribution. 7.8 The Normal Distribution. 7.9 Applying the Normal Approximation. 8. Introduction to Statistical Reasoning. 8.1 Statistics: Estimating Parameters. 8.2 Confidence Limits. 8.3 Estimating the Mean. 8.4 Hypothesis Testing. 8.5 Hypothesis Testing: Normal Theory. 8.6 Comparing Experiments: Normal Theory. 8.7 Analysis of Contingency Tables and Goodness of Fit. 8.8 Hypothesis Testing with the Method of Support. 8.9 Regression.

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