Mathematics Department, NCSU
Biomathematics Graduate Program
B.A. 1968 Mathematics, Boston College
M.A. 1969 Mathematics, Univ. of Wisconsin
Ph.D. 1973 Mathematics, Univ of Wisconsin
E-mail: selgrade@math.ncsu.edu
My current research is focused on two problems: (1) the use of stocking, harvesting, and migration to control dynamical behavior and to restabilize a dynamical system, with applications to differential and difference equation models in population biology and genetics, and (2) modelling the estrogen (menstrual) cycle in humans and the estrous cycle in rats with the intention of understanding how environmental chemicals may be disrupting the endocrine systems of humans and animals.
James F. Selgrade and Paul M. Schlosser. 1999. A model for the production of ovarian hormones during the menstrual cycle. Fields Institute Communications 21, 429-446. Postscript Preprint
James H. Roberds and James F. Selgrade. 2000. Dynamical analysis of density-dependent selection in a discrete one-island migration model. Mathematical Biosciences 164, 1-15. Postscript Preprint
Paul M. Schlosser and James F. Selgrade. 2000. A model of gonadotropin regulation during the menstrual cycle in women: Qualitative features. Environmental Health Perspectives 108(suppl 5), 873-881.
James F. Selgrade and James H. Roberds. 2001. On the structure of attractors for discrete, periodically forced systems with applications to population models. Physica D 158, 69-82. Reprint
L. Harris Clark, Paul M. Schlosser and James F. Selgrade. 2003. Multiple stable periodic solutions in a model for hormonal control of the menstrual cycle. Bulletin of Math. Biology 65, 157-173.
John E. Franke and James F. Selgrade. 2003. Attractors for discrete periodic dynamical systems. Journal Math. Analysis and Applications 286, 64-79.
James F. Selgrade and James H. Roberds. 2005. Results on asymptotic behavior for discrete, two-patch metapopulations with density-dependent selection. Jour. of Difference Equations and Applications 11, 459-476.
James F. Selgrade and James H. Roberds. 2007. Global attractors for a discrete selection model with periodic immigration. Jour. of Difference Equations and Applications 13, 275-287.
Title: Some Deterministic Models in Mathematical Biology and Their Simulations
Instructors: James F. Selgrade (North Carolina State University),
Cammey Cole (Meredith College)
and Huseyin Kocak (University of Miami)
This course presented and
analyzed the Hodgkin-Huxley and FitzHugh-Nagumo models, chemostat
models, pharmacokinetics models and discrete population models. The class was conducted in
a computer lab where participants used the software Phaser to simulate model behavior.
For details see www.phaser.com .
A similar MAA minicourse was held at Meredith College, March 2005.
FINAL EXAM - Tuesday, April 29, 8-11 am. -- You may use notes written on a 3x5 index card.
MA 501 Course Syllabus
For on-line math courses see: on-line math
Homework:
Due Jan. 24: p. 20, # 1, 2, 4, 5; p. 26, # 1, 11*, 13; p. 69, # 5*; p. 72, # 1, 5*; p. 77, # 1, 7, 9, 13*, 17*; p. 93, # 1*, 3, 7, 11, 13, 15*, 27;
Due Feb. 7: p. 81, # 1, 2, 3*; p. 765, # 1*, 2, 3, 7*, Prob.A*;
Due Feb. 12: p. 592, # 1, 2, 5, 9* graph -3*Pi < x < 3*Pi, 13; p. 609, # 2, 5* graph -3*Pi < x < 3*Pi;
Due Feb. 28: p. 863, # 1, 4, 5, 9*, 11*, 13, 15, 16, 17, 18*; p. 785, # 1, 6;
Due Mar. 20: p. 806, # 1, 2, 4, 5, 9*, 11, 13; d'Alembert string*; p. 880, # 1, 2a; p. 883, # 1, 2, 4*, 6, 7, 9*;
Due April 1: p. 895, # 9*, 10; p. 840, # 1, 3*; p. 878, # 1*; p. 886, # 1, 3*, 9; p. 160, # 15, 19; p. 165, # 1, 4;
Due April 17: p. 173, # 7*, 9; p. 180, # 1*, 5;
Due April 22: Turn in the solution u(r, z) to Laplace's eq in a cylinder of radius r_0 and height h_0 , i.e.,
0 = u_rr + (1/r) u_r + u_zz
with (B.C.) u(r_0, z) = 0 , u(r, 0) = f(r) and u(r, h_0) = g(r).
MA 501 Homework and Test Solutions
MA 242 Course Syllabus