Partial differential equations in biology

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Table of Contents......Page 4
1. Electrophysiology......Page 6
2. The cochlea......Page 11
3. The retina......Page 13
4. Pulse wave propagation in arteries......Page 15
5. Cross-bridge dynamics in muscle......Page 17
II. Fundamental Solutions of Some Partial Differential Equations......Page 19
1. The wave equation in one space dimension.......Page 20
2. The method of descent......Page 22
3. Application of the method of descent to the Klein-Gordon equation......Page 26
4. Laplace's equation......Page 29
5. The heat equation......Page 32
1. Equations of a leaky cable.......Page 36
2. Fundamental solution of the cable equations......Page 38
3. Equations for an infinite symmetrical tree.......Page 41
4. Current injection......Page 45
5. Unsymmetrical component of the response......Page 48
6. Random walk interpretation.......Page 50
IV. Equations of the Nerve Impulse.......Page 51
1. The traveling pulse......Page 55
2. The traveling pulse in the limit e -> 0.......Page 60
3. Propagation of fronts......Page 64
4. An initial value problem.......Page 68
1. Introduction......Page 74
2. Equations of motion......Page 84
3. The two dimensional cochlea of finite depth. Analytic results for the case of potential flow......Page 95
4. The two dimensional cochlea with fluid viscosity......Page 118
VI. The Retina......Page 144
1. The steady state......Page 149
2. Space-independent dynamics.......Page 151
3. Sinusoidal steady state......Page 153
VII. Pulse-wave Propagation in Arteries......Page 158
1. Derivation of the one-dimensional, inviscid theory......Page 165
2. The limit of infinite wave speed.......Page 170
3. The fundamental solution.......Page 173
4. The sinusoidal steady state......Page 182
5. The method of characteristics......Page 189
6. The Lax-Wendroff method......Page 201
VIII. An Inverse Problem in Muscle Mechanics.......Page 214
1. The steady state......Page 218
2. Transients......Page 225