Courses : (Spring 2012) M2221 - Elementary Differential Equations, M3221 – Methods in Differential Equations
Office Hours: Monday: 12:15 - 3pm (Math Tutor Center 12:30-1:00), Tuesday: 4:15 – 4:30pm, Wednesday: 12:15 - 3pm (Math Tutor Center 12:30-1:00), Thursday: 4:15 – 4:30pm.
Incompressible fluids (Euler's equations) and solids (elastodynamics)
Liquid crystals (Calogero type equations)
Quasilinear hyperbolic-parabolic systems and elliptic equations
On the Influence of Damping in Hyperbolic Equations with Parabolic Degeneracy (QAM, in press)
Heat propagation with phase transitions in low temperature solids, with K. Saxton, " Trends in Applications of Mathematics to Mechanics", STAMM 2004, Shaker-Verlag, 463-472 (2005).
Phase transitions and aspects of heat propagation in low temperature solids, with K. Saxton, EQUADIFF 2003, World Scientific, 1128-1130 (2005).
Some Effects of Phase Transitions on Heat Propagation, with K. Saxton, Arch. Mech., 54, 5-6 (2002).
Nonlinear PDEs, Dynamics and Continuum Physics, with J. Bona and K. Saxton (editors), American Mathematical Society (2000). MR2000m:35003
Nonlinearity and memory effects in low temperature heat propagation, with K. Saxton, Arch. Mech., 52, 1 (2000).
On second sound at the critical temperature, with K. Saxton and W. Kosinski, Quart. Appl. Math., LVII, 4, 723-740 (1999). MR2000h:35158
Second Sound Speed in a Crystal of NaF at Low Temperature, with W. Kosinski and K. Saxton, Arch. Mech., 49, 1, 189-196 (1997).
Singularity Formation in Systems of Nonstrictly Hyperbolic Equations, with V. Vinod, Elec. J. Diff. Eq., 9, 1-15 (1995). MR96g:35118
Nonstrictly Hyperbolic Systems of Partial Differential Equations, with V. Vinod, "Recent Developments in Evolution Equations", Pitman Research Notes in Mathematics, 324, 239-243, Longman (1995). MR1 417 07
On second sound at the critical temperature, with W. Kosinski and K. Saxton, Society of Engineering Science, 32nd Annual Meeting, 505-506 (1995).
Blow Up at the Boundary of Solutions to Nonlinear Evolution Equations, "Evolution Equations", Lecture Notes in Pure and Applied Mathematics, 168, 383-392 (1994). MR95i:35025
Radial Solutions to a Nonlinear p-Harmonic Dirichlet Problem, with D. Wei, Applic. Anal., 51, 1-4, 59-80 (1993). MR95e:35079
Formation of Singularities for a Class of Nonlinear, Hyperbolically Degenerate Initial-Boundary Value Problems, Appl. Math. Lett., 5, 3, 73-75 (1992). MR93d:35104
Finite Time Boundary Blowup for a Degenerate, Quasilinear Cauchy Problem, "Partial Differential Equations", Pitman Research Notes in Mathematics Series, 273, 212-215, Longman (1992).
Dynamics of Director Fields, with J. Hunter, SIAM J. Appl. Math., 51, 6, 1498-1521 (1991). MR93a:76005
Instability of the Liquid Crystal Director, Contemporary Mathematics, 100, 325-330 (1989). MR90k:35246
The Equations of Incompressible Elasticity, with D. Ebin, Contemporary Mathematics, 60, 25-34 (1987). MR88a:73034
Solitary Wave Interaction in Elastic Rods, with P. Clarkson and R. LeVeque, Stud. Appl. Math. LXXV, 2, 95-123 (1986). MR87j:73034
The Initial-Value Problem for Elastodynamics of Incompressible Bodies, with D. Ebin, Arch. Rat. Mech. Anal. 94, 1, 15-38 (1986). MR87h:58028
Existence of Solutions for a Finite Nonlinear Hyperelastic Rod, J. Math. Anal. Appl. 105, 1, 15-38 (1985). MR86m:3511
The Cauchy and Backward Cauchy Problem for a Nonlinear Hyperelastic/Viscoelastic Infinite Rod, Lecture Notes in Mathematics, 1032, Springer Verlag (1982). MR85k:35215
Solitary and Travelling Waves in a Rod, Lecture Notes in Mathematics, 964, Springer Verlag (1982). MR84j:35150
The Nonlinear Pochhammer-Chree Equation, PhD thesis, Heriot-Watt University (1981).
Why Study Mathematics (from the Mathematical Association of America)?
PhDs.org Science, Math, and Engineering Career Resources
Some mathematical resources
American Mathematical Society journals
SIAM journals
Oxford University Press
JSTOR archives
Joint Summer Research Conferences in the Mathematical Sciences
In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
Carl Sagan, 1987 CSICOP keynote address
I don't see how anybody understands what is happening in physics today. Even I don't understand much which I would like to learn from physics books. But with me, if I don't understand something, then I go to the telephone and call up Debye or Born, and they come and explain it to me. And then I understand it -- but what do other people do?David Hilbert, quoted in Constance Reid's biography of HilbertI was always delighted by the way in which Thom discussed mathematics, using sentences obviously having no strict logical meaning at all. While I was never able to completely free myself from the straitjacket of logic, I was forever poisoned by the dream of the irresponsible mathematical speculation with no exact meaning. "One can always find imbeciles to prove theorems" was, according to Thom's students, his principle.
from "An Interview with Vladimir Arnol'd"