Mathematics for biology : an introduction
General information: The
course will follow the book by B. Perthame : Transport Equations in
Biology, Birkhäuser, Frontiers in Mathematics 2007.
The scilab software can be
downloaded here
Classes start Sept. 7, 2009
Schedule :
Office hours : P-E Jabin : Thursday 15:15-17:15
Exercises :
Short Program : it will be updated along the course. The section and chapter numbers are always given
with respect to the book by Perthame.
1st class :
0. Quick presentation.
1. section 1.1 : Invasion and space structure.
2. section 1.2.1 : The 2 by 2 Lotka-Volterra system.
3. section 1.2.3 : Chemostat.
4. section 1.6 : Ecological model of competition for resources.
2nd Class : Chapter 3, Population balance equations: the renewal equation
1. section 3.1 : The renewal equation
2. section 3.2 : Eigenelements
3. section 3.3 : Existence theory
3rd class : Part of Chapter 6, General mathematical tools
1. section 6.3.1 : Generalized relative entropy, The Perron-Frobenius theorem
2. section 6.4.1 : Generalized relative entropy, parabolic and integral PDEs
3. section 6.6 : The Krein-Rutman theorem
4th class : End of Chapter 3, Population balance equations: the renewal equation
1. section 3.5 : Generalized relative entropy
2. section 3.6 : Long time asymptotic, entropy method
3. section 3.7 : Long time asymptotic, exponential decay
5th class : Chapter 4
1. section 4.1 : Equal mitosis
2. section 4.2 :
Size structured model for asymmetric cell division
6th-8th class
Chapter 5 and section 6.1