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
Mailbox:  SAS 3151


My current research is focused on two areas: (1) modelling the estrogen (menstrual) cycle in humans to study cycle abnormalities, and (2) the use of stocking, harvesting and migration to control the dynamical behavior of deterministic models in population biology and genetics.




Selected Recent Publications

Angelean O. Hendrix, Claude L. Hughes and James F. Selgrade (preprint). (2014) Modeling endocrine control of the pituitary-ovarian axis: Androgenic influence and chaotic dynamics. Bull. Math. Biology 76, 136-156.

Alison Margolskee and James F. Selgrade (2013). A lifelong model for the female reproductive cycle with an antimullerian hormone treatment to delay menopause. J. Theoretical Biology 326, 21-35.

Alison Margolskee and James F. Selgrade (2011). Dynamics and bifurcation of a model for hormonal control of the menstrual cycle with inhibin delay, Math. Biosciences 234, 95-107.

James F. Selgrade (2010). Bifurcation analysis of a model for hormonal regulation of the menstrual cycle, Math. Biosciences 225, 97-103.

James F. Selgrade, L.A. Harris and R.D. Pasteur (2009). A model for hormonal control of the menstrual cycle: Structural consistency but sensitivity with regard to data, J. Theoretical Biology 260, 572-580.

James F. Selgrade, Jordan W. Bostic and James H. Roberds (2009). Dynamical behavior of a discrete selection-migration model with arbitrary dominance, Jour. of Difference Equations and Appl. 15, 371-385.

James F. Selgrade and James H. Roberds (2007). Global attractors for a discrete selection model with periodic immigration, Jour. of Difference Equations and Appl. 13, 275-287.

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 Appl. 11, 459-476.

John E. Franke and James F. Selgrade (2003). Attractors for discrete periodic dynamical systems, J. Math. Analysis and Applications 286, 64-79.

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.

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

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.






RESEARCH   MATERIALS






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.






Spring 2014 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 wave equation with gravity
Maple worksheet to plot solution to wave equation for plucked string
Series solutions to ODE's via Maple
Maple worksheet to plot the fundamental vibrations of a drum head independent of theta



 




MA 537-001    

Final Exam -- Monday, May 5, 8-11 am: Ch. 1-14 -- Notes on one side of paper


MA 537-001 textbook for Spring 2014:
    "A First Course in Chaotic Dynamical Systems" by R.L. Devaney


MA 537 Course Policy and Problems # 1 - 5


Homework:
Due Jan. 10:   Problems # 1*, 2*, 3* on handout;
Due Jan. 13:   Problems # 4*, 5* on handout;
Due Jan. 24:   Newton's Method*,   p 26,   # 6, 8, 12*, 13*, 14*;   p 34,   # 2;   p 50,   # 1 a*, b*, c*;
Due Feb. 7:   State the f''' test,   p 50,   # 4 a, f*, g* (use f''' test), 5, 6, 7, 8, 9;   p 67,   # 1 a*(SN or P), d*(SN or P), e, i;   Transcritical Bif*;
Due Feb. 14:   ODE Problem*: Draw Bif curve, Verify Bif, Draw phase portrait for 1. x^2+lambda; 2. lambda*x-x^3; 3. lambda*x+x^2; 4. 3*x-x^3-lambda;
Due Mar. 3:   p 67,   # 1 a,b,c,d,e,i, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11; Problem sheet*;   p 80,   # 2, 9-15;   p 111,   # 1, 3, 5;
Due Mar. 28:   p 131,   # 6, 10, 15*, 16*, 17*, 21*;
Due April 7:   p 151,   # 1*, 2, 3, 4* Show one has a 3-cycle and other does not., 6;
Due April 21:   p 173,   # 1b,d, 2, 8*a,b,c,d-Discuss basins of attraction;   p 199,   # 1a,b, 1c*, 2, 4-10;


MA 537 Homework and Test Solutions  
 
 



 
 
 

Some General Information on Policy for Mathematics Courses