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University of Washington
University of Washington
AMATH 353 Fourier Analysis and Partial Differential Equations
AMATH 352 Numerical Analysis and Linear Algebra
AMATH 351 Ordinary Differential Equations
AMATH 383 Continuous Mathematical Modeling
Graduate
AMATH 570 Asymptotic & Perturbation Methods (Guest lecturer; Invited by Prof. R.E.O'Malley, Jr.)
Northwestern University
Northwestern University
MATH 234-0 (now MATH 228-2) Multiple Integration and Vector Calculus
Graduate
ES APPM 420 Asymptotic & Perturbation Methods (Guest lecturer; Invited by Prof. Bernard Matkowsky)
Imperial College London
Imperial College London
CE1-07 Mathematics I (Calculus & Differential Equations)
Course Development
Course Development
I proposed, developed and taught a three-semester sequence of Methods of Mathematical Physics/Applied Mathematics/Engineering Mathematics in Australia. Enrollment rose to 300+ as it was adopted by both Arts & Sciences and the Engineering School. It culminated in an end-of-semester written project and student team-presentations in a conference-like setting.
Undergraduate Research
Undergraduate Research
Amplitude equations for the equations of Mathematical Physics such as the phase-field equation (open area)
Variational description of odd viscous liquids (open area)
Bifurcations for two-dimensional systems. Structural stability, bifurcations at nonhyperbolic fixed point, Hopf bifurcation, Reference: Perko Differential Equations and Dynamical Systems (Chapter 4), Wiggins Applied Dynamical Systems, Arrowsmith and Place Dynamical Systems. Apply to the thin liquid film equations (open area)
Monodromy matrix, Mathieu equation and Arnold tongues. References: Bender & Orzag, Arnold (ODEs, Mathematical Methods of Classical Mechanics). Apply to the dynamics of migrating droplets (open area)
Dynamics of heavy particles in a Burger’s vortex. Study the stability of the flow under the combined effects of particle inertia, Stokes drag, and gravity. Formulation of a dynamical system, calculation of eigenvalues, eigenvectors and numerical analysis. See Marcu, Meiburg, Newton (1995).
Patterns in a heated rotated cylinder. Broken symmetry. Reference: Ecke & Knobloch (1993), Knobloch (1995). How the broken reflection symmetry affects waves in thin liquid films. Thiele and Knobloch (2003).
Differential Geometry of curves and surfaces. Navier-Stokes equations for a liquid flowing on a surface. Reference: B.O’Neil, Elementary Differential Geometry, Aris Basic equations of Fluid Mechanics (Chapter 10)
Discrete-state random processes. Stationarity. Linear systems. White noise. Differential Equations. Power spectrum. Discrete-time processes. Reference: Papoulis and Pillai Ch. 9.
Efficiency of energy conversion in electrokinetic systems. Understand the Onsager symmetry principle, solve the nonlinear Poisson-Boltzmann equation and calculate the figure-of-merit. See Morrison & Osterle (1965).
End-of-Semester Projects (presented by students in a conference-like setting)
End-of-Semester Projects (presented by students in a conference-like setting)
Special functions of Mathematical Physics and their applications
Curve fitting and interpolation of experimentally obtained data in a turbulent round jet
University of Washington Undergraduate Research Symposium: "the country's largest "show and tell" for undergraduate research ". In some sense, this is where I adopted the end-of-semester student presentations from.
University of Washington Undergraduate Research Symposium: "the country's largest "show and tell" for undergraduate research ". In some sense, this is where I adopted the end-of-semester student presentations from.
V.I. Arnold on Teaching mathematics; R.P. Feynman on teaching; Some Reminiscences of My Teaching Career, by Arnold Sommerfeld
Dave Fultz (University of Chicago) explains various effects taking place in rotating liquids including Taylor columns. See our work on Taylor columns in (non-rotating) odd viscous liquids and on their rotating counterparts.
Dave Fultz (University of Chicago) explains various effects taking place in rotating liquids including Taylor columns. See our work on Taylor columns in (non-rotating) odd viscous liquids and on their rotating counterparts.
G.I.Taylor (University of Cambridge) explains various effects taking place in low Reynolds number flows. See some of our work in low Reynolds number hydrodynamics.
National Committee for Fluid Mechanics. Illustrated Experiments in Fluid Mechanics: The NCFMF Book of Film Notes . Videos. See some of our experimental and computational Videos
Quantum Magazine
Quantum Magazine
Quantum's target audience was high school and college students and their teachers. Content: Mathematics and Physics. Quantum was published by the National Science Teachers Association and Springer-Verlag New York, Inc. All issues archived in the National Science Teachers Association page.
Awards
Awards
Boeing Award for Excellence in Teaching (University of Washington - twice)
Fellow of the UK Higher Education Academy (Imperial College London)
Thanks
Thanks
My vision on teaching was shaped by a number of exceptional teachers: Gerald Miller (Physics, University of Washington, teaching the graduate QM III), Marjorie Olmstead (Physics, University of Washington, teaching undergraduate statistical physics), Dana Dabiri (Aeronautics & Astronautics, University of Washington, teaching graduate Fluid Mechanics), Peter Schmidt (Applied Mathematics, University of Washington, teaching graduate Asymptotics & Differential Equations), Summit Roy (Electrical Engineering, University of Washington, teaching the graduate Probability & Random Processes), David Cobden (Physics, University of Washington, teaching the undergraduate EM I, II & III series).
Header Image: Guggenheim Hall University of Washington 3940 Benton Ln NE, Seattle, WA 98105, United States of America. Photograph by Eleftherios Kirkinis
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