Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 2
Voltage Gated Ionic Currents
Christopher P. Fall and Joel E. Keizer
In Chapter 1 we introduced models of simple channel behavior but ignored the idea
that something might ow through such a c
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 6
Intercellular Communication
John Rinzel
Orchestrating the activity of cell populations for physiological functioning of the brain,
organs, and musculature depends on transmission of signals,
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 3
Transporters and Pumps
Eric S. Marland and Joel E. Keizer
Ionic channels are not the only mechanism that cells use to transport impermeant
species across membranes. Cells have developed a gr
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 7
Spatial Modeling
James P. Keener
All of the models considered in previous chapters have relied on the implicit assumption that chemical concentrations are uniform in space. This assumption i
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 8
Modeling Intracellular Calcium
Waves and Sparks
Gregory D. Smith, John E. Pearson, and Joel E. Keizer
In this chapter we shall discuss a variety of intracellular Ca2+ wave phenomena, but
alw
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 9
Biochemical Oscillations
John J. Tyson
Biochemical and biophysical rhythms are ubiquitous characteristics of living organisms, from rapid oscillations of membrane potential in nerve cells to
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 10
Cell Cycle Controls
John J. Tyson and Bela Novak
In recent years, molecular biologists have uncovered a wealth of information about
the proteins controlling cell growth and division in euka
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 12
Molecular Motors: Theory
Alex Mogilner, Timothy C. Elston, Hongyun Wang, and George Oster
Evolution has created a class of proteins that have the ability to convert chemical energy
into mec
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 13
Molecular Motors: Examples
Alex Mogilner, Timothy C. Elston, Hongyun Wang, and George Oster
13.1
Switching in the Bacterial Flagellar Motor
As an example of the use of the numerical algorit
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
APPENDIX A
Qualitative Analysis of
Differential Equations
G. Bard Ermentrout and Joel E. Keizer
Nonlinear ordinary differential equations are notoriously difcult or impossible to solve
analytically. O
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 11
Modeling the Stochastic Gating
of Ion Channels
Gregory D. Smith
In previous chapters we have seen several kinetic diagrams representing various molecular states and transitions between thes
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 4
Fast and Slow Time Scales
James P. Keener and Joel E. Keizer
One of the hallmarks of cellular processes is their complexity. For example, in Chapter
3 we described a detailed model for the S
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
Interdisciplinary Applied Mathematics
Volume 20
Editors
S.S. Antman J.E. Marsden
L. Sirovich S. Wiggins
Mathematical Biology
L. Glass, J.D. Murray
Mechanics and Materials
R.V. Kohn
Systems and Control
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
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MATH 200

Spring 2014
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MATH 200

Spring 2014
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Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
Chapter 8
Bounded Linear Operators on a Hilbert Space
In this chapter we describe some important classes of bounded linear operators on Hilbert spaces, including projections, unitary operators, and se
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
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Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
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Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
Errata Applied Analysis (Corrected in online les but not in Second Printing) p. 115: Replace statement of Theorem 5.53 with: A consistent approximation scheme is convergent if and only if it is stable
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
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Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
Measure Theory
V. Liskevich 1998
1
Introduction
We always denote by X our universe, i.e. all the sets we shall consider are subsets of X. Recall some standard notation. 2X everywhere denotes the set o
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
CHAPTER 1
Dynamic Phenomena in Cells
Christopher P. Fall and Joel E. Keizer
Over the past several decades, progress in the measurement of rates and interactions of
molecular and cellular processes has
Ordinary Differential Equations and Dynamical Systems
MATH 200

Spring 2014
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