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

Adler, Frederick R.

ISBN 10: 0534348165 / ISBN 13: 9780534348168

Published by Brooks Cole, 1998

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Bibliographic Details

Title: Modeling the Dynamics of Life: Calculus and ...

Publisher: Brooks Cole

Publication Date: 1998

Binding: hardcover

Condition: Good

About this title

Synopsis:

Designed to help students understand the role mathematics plays in the life sciences, this text provides a thorough grounding in mathematics, the language, and the "technology of thought" with which these developments are created and controlled. The book follows three themes throughout: growth, diffusion, and selection. Each theme is studied in turn with the three kinds of models that structure the course: discrete-time dynamical systems, differential equations, and stochastic processes. Techniques and insights build on each other throughout the book. Along the way, students learn and apply the standard material of a calculus course (differentiation, integration, and their applications).

Review:

1 Discrete-Time Dynamical Systems. 1.2 Variables And Functions. 1.3 Units And Dimensions. 1.4 Linear Functions And Their Graphs. 1.5 Discrete-Time Dynamical Systems. 1.6 Analysis Of Discrete-Time Dynamical Systems. 1.7 Solutions And 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 Excitable Systems I: The Heart. 1.12 Supplementary Problems for Chapter 1. 1.13 Projects for Chapter 1. 2 Limits and Derivatives. 2.1 Introduction to Derivatives. 2.2 Limits. 2.3 Continuity. 2.4 Computing Derivatives. 2.5 Derivatives of Sums, Powers and Polynomials. 2.6 Derivatives of Products and Quotients. 2.7 The Second Derivative. 2.8 Exponentials and Logarithms. 2.9 The Chain Rule. 2.10 Derivatives of Trigonometric Functions. 2.11 Supplementary Problems for Chapter 2. 2.12 Projects for Chapter 2. 3 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'Hosptal's Rule. 3.7 Approximating Functions. 3.8 Newton's Method. 3.9 Panting and Deep Breathing. 3.10 Supplementary Problems for Chapter 3. 3.11 Projects for Chapter 3. 4 Differential Equations and Integrals. 4.1 Differential Equations. 4.2 Antiderivatives and Indefinite Integrals. 4.3 Special Functions and Methods of Integration. 4.4 Integrals and Sums. 4.5 Definite and Indefinite Integrals. 4.6 Applications of Integrals. 4.7 Improper Integrals. 4.8 Supplementary Problems for Chapter 4. 4.9 Projects for Chapter 4. 5 Autonomous Differential Equations. 5.1 Basic Differential Equations. 5.2 The Phase-Line Diagram. 5.3 Stable and Unstable Equilibria. 5.4 Solving Autonomous Equations. 5.5 Two Dimensional Equations. 5.6 The Phase-Plane. 5.7 Solutions in the Phase-Plane. 5.8 The Dynamics of Neuron. 5.9 Supplementary Problems for Chapter 5. 5.10 Projects for Chapter 5. 6 Probability Theory and 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 Marcov Chains. 6.6 Displaying Probabilities. 6.7 Random Variables. 6.8 Descriptive Statistics. 6.9 Descriptive Statistics for Spread. 6.10 Supplementary Problems for Chapter 6. 6.11 Projects for Chapter 6. 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 Exponential Distributions. 7.7 The Poisson Distribution. 7.8 The Normal Distribution. 7.9 Applying the Normal Approximation. 7.10 Supplementary Problems for Chapter 7. 7.11 Projects for Chapter 7. 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. 8.7 Analysis of Contingency Tables and Goodness of Fit. 8.8 Hypothesis Testing with the Method of Support. 8.9 Regression. 8.10 Projects for Chapter 8.