Donald A. French

Donald A. French

Full Professor and Graduate Program Director

Department of Mathematical Sciences
University of Cincinnati
P.O. Box 210025
Cincinnati OH 45221-0025 USA

Email: french@ucmail.uc.edu
Phone: 513-556-4039
Fax : 513-556-3417
Office : 5510 French Hall
URL : http://homepages.uc.edu/~french/index.html

On the left, hanging out in Yellow Springs (Also, on top of Mt. Pilatus in Switzerland in 2007, in China in 2001, the Berkshires in 2003 and a Seattle coffee shop in 2005.). Above is photograph of a sculpture by Lee Bontecou scanned from the Smithsonian.

Biography:

Current research is on mathematics problems involving partial differential equations with applications in olfactory cilia, neuronal networks, biofilms and the spread of alcohol abuse.

See the Mathematical Modeling and Scientific Computation in the Biosciences web page.

See also Applied Mathematics Seminar web page.

Past and some continuing research is on error analysis for finite element methods for partial differential equations including finite element and meshfree schemes. Also a part-time contractor at the Wright-Patterson Air Force Base in Dayton, OH.

Permanent position is at the University of Cincinnati. Visiting Assistant Professor at Purdue University (1985-7), Assistant Professor at Carnegie Mellon (1987-90), Visiting Professor at University of Maryland Baltimore County (1995-6), and a visitor at University of Minnesota (1997-8). Graduate student in applied mathematics at Cornell University, obtained Ph.D. in 1985. Thesis advisor was Lars B. Wahlbin. See Curriculum Vita for more information.

PhD Students:

  • Jiyeon Oh (2000-2005)
  • Dorjsuren Badamdorj
    (Assistant Professor at Tennessee State (2009-Present).
  • Zeynep Teymuroglu (2006-2008).
    (Rollins College, Orlando, FLa.)
  • Mauricio L. Osorio (2007-2010).
    (Universidad Nacional
    de Colombia, Medellín, Colombia in 2010.)
  • Jhules Clack (2005-2014)
  • Suayip Toprakseven (2009-2014)
    (Artvin Coruh University, Turkey).
  • Kristen Fox-Neff

Specialty Courses:

Courses for 2017-2018 :

Autumn Semester:

  • Numerical Analysis 6006.
  • Mathematical Modeling 3006.

    Spring Semester:

  • Advanced Numerical Analysis 8010.
  • Partial Differential Equations and Fourier Analysis 6007.

    • Selected Recent Publications:

    Mathematical Neuroscience:
  • Clustering of CNG channels in the cilia of frog olfactory receptor neurons (with R. Flannery and S.J. Kleene), Biophys. J., 91 (2006), 179-188.
  • An Integrate-and-Fire Model for Synchronized Bursting in a Network of Cultured Cortical Neurons (with E. Gruenstein), J. Comp. Neurosci., 21 (2006), 227-241.
  • Identification of a free energy functional in an integro-differential equation model for neuronal activity, Appl. Math. Lett., 17 (2004), 1047-1051.

    Applied Mathematics:

  • Continuum models of the spread of alcoholism (with R. Braun, Z. Teymuorglu and T. Lewis), Journal of Integral Equations and Applications, 22 (2010), 441-462.
  • Analysis of the convergence behavior of the localized nonlinear approximation for electromagnetic scattering, J. Comp. Appl. Math., 161 (2003), 27-39.

    Error Analysis of Numerical Methods for PDE's

  • Finite element approximation of solutions to a class of nonlinear hyperbolic-parabolic equations, (with S. Jensen and T. Seidman), Appl. Numer. Math., 31 (1999), 429-450.
  • Error Analysis of a Modified Discontinuous Galerkin Recovery Scheme for Diffusion Problems (with M. C. Galbraith and M. Osorio), Applied Mathematics and Computation, (2012), doi 10.1016/j.amc.2011.12.082.
  • Error estimates for an element free Galerkin method with diffuse derivatives and penalty stabilization (with Mauricio Osorio), Computational Mechanics, doi 10.1007/s00466-012-0697-7.