Biology in Time and Space: A Partial Differential Equation Modeling Approach

ISBN-13: 9781470454289

James P. Keener

Opis

How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.

Spis treści

• Background material
• Conservation-Learning how to count
• The diffusion equation-Derivations
• Realizations of a diffusion process
• Solutions of the diffusion equation
• Diffusion and reaction
• The bistable equation-Part I: Derivations
• The bistable equation-Part II: Analysis
• Advection and reaction
• Advection with diffusion
• Chemotaxis
• Spatial patterns
• Dispersal-renewal theory
• Collective behavior
• Introduction to Matlab
• Constants, units, and functions
• Selected answers to exercises
• Bibliography
• Index