MATHEMATICS FACULTY: James F. Selgrade

James F. Selgrade, Professor

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.

Selected Recent Publications

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.

MAA Minicourse at the New Orleans Joint Meeting, January 2007

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.

AIM Workshop, August 2008

Reference Papers:

J.F. Selgrade and P. Schlosser (1999). A model for the production of ovarian hormones during the menstrual cycle, Fields Institute Communications, vol. 21, 429-446.

P. Schlosser and J.F. Selgrade (2000). A model of gonadotropin regulation during the menstrual cycle in women: Qualitative features. Environmental Health Perspectives, vol. 108(suppl 5), 873-881.

J.F. Selgrade (2001). Modeling hormonal control of the menstrual cycle, Comments on Theoretical Biology, vol. 6, 79-101.

L. Harris Clark, P. Schlosser and J.F. Selgrade (2003). Multiple stable periodic solutions in a model for hormonal control of the menstrual cycle, Bulletin of Math. Biology, vol. 65, 157-173.

Fall 2009 Courses

For on-line math courses see: on-line math
For help with integrals see: http://integrals.wolfram.com
Text for Maple worksheet to compute Fourier Trig. Series
Maple worksheet to compute Fourier Trig. Series
Maple worksheet to plot solution to heat equation
Maple worksheet to plot solution to wave equation for plucked string
Series solutions to ODE's via Maple

MA 501

FINAL EXAM, Dec. 16, 8-11 am.

MA 501 Course Policy
MA 501 Course Schedule

Homework:
Due Aug. 28: p. 14, # 3, 5a; p. A8, # 1, 2*, 3, 8, 11*, 15, 21a*,b*, 23, 25*, 27; p. A26, # 1, 3, 7, 11*; p. A19, # 1, 5, 9, 13, 17*, 21;
Due Sept. 11: p. A19, # 25, 27, 29*, 35, 61, 63*, 65; p. A26, # 21, 27, 31, 33, 35*, 37, 43; p. 331, # 1, 3, 9*, 11; p. 343, # 1, 3, 5, 8*, 11, 12, 13*, 15, 16, 17(optional);
Due Sept. 25: p 23, # 1 a,b, 3, 4*, 6, 7, 11, 12*; p 35, # 1, 3, 5, 13*(N=1,2,3,10), 18; p 45, # 1*, 2; p 52, # 1*, 2; p 144, # 1, 2*, 3, 7a; p 151, # 1, 2*, 5, 15*; p 145, # 11, 13, 15;
Due Oct. 26: p 123, # 1, 3a*, 5a, 13*; p 145, # 16*; D'Alembert Problem*; p 162, # 1a, 2a*, 5a, 11*, 13, 17; p 168, # 1, 3, 5*, 11a,b; p A38, # 1, 13, 29*, 31; p A49, # 1, 5, 7*, 24a,b,c;
Due Nov. ?: p A62, # 1, 3, 7*, 13, 15; p 244, # 1, 3, 5, 15a,b, 29; p 205, # 1, 10, 11a; p 230, # 5*; p 215, # 7; Legendre formula*; p 280, # 10;

MA 501 Homework and Test Solutions

MA 303

FINAL EXAM, Dec. 15, 1-4 pm. -- no calculators

MA 303 Course Policy
MA 303 Course Schedule

Homework:
Due Sept. 1: p. 2, # 1a,c, 2a, 3a,c, 4*, 5*, 6, 7*; p. 6, # 1a,c*, 2a,b, 3a,c*,e, 4a; p. 10, # 1*, 2, 3, 4*, 7;
Due Sept. 10: p. 12, # 1, 2, 3*, 4a, 5a, 6*, 7*; p. 15, # 1, 2, 4*; p. 19, # 1, 2, 4, 5*, 6*, 8, 10, 11;
Due Sept. ?: p. 26, # 1, 2, 3a,b, 6, 8, 10; p. 33, # 2, 3;
Due Oct. 6: p. 35, # 1, 2, 3*, 4*, 5, 7*, 9, 10*, 12; p. 38, # 1, 2, 3*, 4*, 5, 6, 7; p. 41, # 1, 2*;
Due Oct. ?: p. 44, # 1, 2, 4*, 5*; p. 47, # 1*, 3, 4, 5*, 7, 9, 10*; p. 49, # 1, 2*, 5, 7*, 8*, 9*, 12, 13*, 14, 15;
Due Oct. 22: EXTRA CREDIT p. 49, # 2*, 7*, 8*, 9*, 13*;
Due Nov. 10: p. 79, # 1, 2b*, 3b; p. 83, # 1, 2a,b*, 3a, 4; p. 86, # 1, 2*, 3, 4, 6; p. 89, # 1, 2*, 3; p. 97, # 1, 2, 3, 4*, 6, 7, 9a,b*;
Due Nov. ?: p. 106, # 1b*, 2a,c,d*, 3, 4a,d,e*, 6, 7*, 8;
Due Dec. 1: p. 110, #1, 6, 7, 11, 12; p. 115, # 1, 2, 3, 4*, 7, 9*, 12, 13*, 14, 16; p. 129 , #1*;

MA 303 Homework and Test Solutions

Some General Information on Policy for Mathematics Courses