Modeling the dynamics of life: calculus and probability for life scientists

Designed to help life sciences students understand the role mathematics has played in breakthroughs in epidemiology, genetics, statistics, physiology, and other biological areas, MODELING THE DYNAMCICS OF LIFE: CALCULUS AND PROBABILTY FOR LIFE SCIENTISTS, 3E, International Edition, 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 theskills 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, with particular emphasis on those areas connected with modeling such as discrete-time dynamical systems, differential equations, and probability and statistics. INDICE: 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-TimeDynamical 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 Integralsand 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 SupplementaryProblems 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 TheNormal 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 ofFit.8.8 Hypothesis Testing with the Method of Support.8.9 Regression.8.10 Projects for Chapter 8.

• ISBN: 978-1-111-57463-5
• Editorial: South Western
• Encuadernacion: Rústica
• Páginas: 912
• Fecha Publicación: 09/01/2012
• Nº Volúmenes: 1
• Idioma: Inglés