Department of Mathematics

      University of Dayton
 
Muhammad Usman, Ph.D.
 Assistant Professor,
Department of Mathematics
University of Dayton

Education:

Ph.D. (Mathematics) University of Cincinnati, 2007

M.S. (Nuclear Engg.) University of Cincinnati, 2007

M.S. (Mathematics) Ohio University, 2001

M.A. (Physics) Ohio University, 2001
Address 300 College Park,

Dayton, OH 45469-2316, USA
Office Science Center 103 C
Phone 937-229-2101
Fax 937-229-2566
E-Mail Muhammad.Usman@udayton.edu


Schedule | Research Interests  | Publications | Professional Activities | Teaching| Links | Student Mentoring

Research Interests

Numerical Analysis, Mathematical Biology, Nonlinear PDEs and Applications, Scientific Computing,  Analytical Mechanics

Recent Publications

  1. With Bingyu Zhang, Forced Oscillations of a Class of Nonlinear Dispersive Wave Equations and their Stability, Springer, Journal of Systems Science and Complexity, Vol. 20, No.2, p 284--292, June 2007.
  2. With Miriam Poteet*, Stability of Steady State Solutions of the Forced Kuramoto-Sivashinsky (KS) Equation, Advances in Differential Equations and Control Processes, Vol. 4, Issue 2, p 119--131, 2009.
  3. With Bingyu Zhang, Forced Oscillations of the Korteweg-de Vries Equation on a Bounded Domain and their Stability, Discrete and Continuous Dynamical Systems-Series A, Vol. 26, No.4, p 1509--1523, 2010.
  4. With Syed Tauseef Mohyud-Din, Ahmet Yildirim, Sefa Anil Sezer, Modified Variational Iteration Method for Free-Convective Boundary-Layer Equation Using Pade´ Approximation, Mathematical Problems in Engineering, Volume 2010 (2010), Article ID 318298, doi:10.1155/2010/318298
  5. With Syed Tauseef Mohyud-Din, M. M. Hosseini, H. Ghaneai, Auxiliary Parameter in the Variational Iteration Method and its Optimal Determination, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 11, No. 7, July 2010, Pages 495--501.
  6. With Sirajul Haq, Nagina Bibi, S.I.A. Tirmizi, Meshless method of lines for the numerical solution of generalized Kuramoto-Shivashinsky equation, Applied Mathematics and Computation, Volume 217, Issue 6, 15 November 2010, Pages 2404-2413.
  7. With Elham Negahdary*, Syed Tauseef Mohyud-Din, A meshless numerical solution of the family of generalized fifth-order Korteweg-de Vries equations, International Journal of Numerical Methods for Heat and Fluid Flow , Vol. 22, Issue 5, 2012.
  8. With Syed Tauseef Mohyud-Din, Ahmet Yildirim, An Iterative Algorithm for Nonlinear BVPs Using Pade´ Approximants,World Applied Sciences Journal, 10(6): 637--644, 2010.
  9. With Bingyu Zhang and Ivonne Rivas, Global well-posedness and asymptotic behavior of a class of initial-boundary-value problems of the KdV equation on a finite domain, Mathematical Control and Related Fields, Volume 1, Issue 1: 61--81, 2011.
  10. With Rahmat Ali Khan, Long Time Dynamics of Forced Oscillations of the Korteweg-de Vries Equation Using Homotopy Perturbation Method, Studies in Nonliear Sciences, 1(3): 57--62, 2010.
  11. With Paul Eloe, Bifurcations in Steady State Solutions of a Class of Nonlinear Dispersive Wave Equation,  Nonlinear Studies, The International Journal, Vol.19(2), 2012, pp 161--170.
  12. With Jian Gao* and Syed Tauseef Mohyud-Din, Numerical Solution of Heat Propagation in Living Tissue Using Method of Lines, Nonlinear Science Letters C: Nano, Biology and Environment, Vol. 1, No. 1, 2011, 15--20.
  13. With Paul Eloe, Fully Nonlinear Boundary Value Problems with Impulse, E. J. Qualitative Theory of Diff. Equ., No. 21 (2011), pp. 1-11.
  14. With Syed Tauseef Mohyud-Din, Ahmet Yildirim, Homotopy analysis method for fractional partial differential equations, International Journal of the Physical Sciences Vol. 6(1), 4 January, 2011, pp. 136-145.
  15. With Rahmat Ali Khan, Eventual Periodicity of Forced Oscillations of Korteweg-de Vries Type Equation, Applied Mathematical Modelling, Volume 36, Issue 2(2012), 736--742.

  16. With Amit Singh, A New Undergraduate Curriculum on Mathematical Biology at University of Dayton , Journal of STEM Education: Innovation and Research, Volume 12. Issue 5 & 6 (2011), 58--66.

  17. With Giacomo Flora* and Syed Tauseef Mohyud-Din, FALSKAN: A GUI Interface for the Numerical Solution of the Falkner-Skan Problem (under review)

* Graduate Students

Professional Activities

Referee Work For Journals 

  1.  Mathematics With Computer Applications
  2. Applications and Applied Mathematics
  3. International Journal of Computer Mathematics
  4. World Applied Sciences Journal
  5. Zeitschrift für Naturforschung A (A Journal of Physical Sciences)
  6. Mathematical and Computer Modelling
  7. Applied Mathematics and Computation
  8. Engineering Computations
  9. Progresses in Computational Fluid Dynamics
  10. International Journal of Physical Sciences
  11. Applied Mathematics Letters A
  12. The Open Mathematics Journal
  13. Nonlinear Analysis: Modelling and Control
  14. International Journal for Numerical Methods for Heat and Fluid Flow
  15. Journal Of King Saud University-Science
  16. Electronic Journal of Qualitative Theory of Differential Equations
  17. Communications in Mathematical Analysis
  18. Asia-Pacific Journal of Chemical Engineering
  19. Reviewer for Mathematical Reviews

Teaching

Calculus with Analytic Geometry I (MTH 168-Z2)

Linear Algebra (MTH 310-81)

Computational Finance (MTH 563-81)

For previous teaching click here

Useful Links

LaTeX Resources for Students

UD Links: