Frank Liou
PHD Student
Department of Mathematics
University of California Davis


My Blog (In Chinese)
My Blog (In English)
FrankMath World
Facebook

TA Teaching 

2007 Fall Quarter/21B

2007 Winter Quarter/21C

2007 Spring Quarter/16B

2008 Fall Quarter/280 Special TA3

2008 Winter/ MAT 167 

2009 Spring/ MAT 129

2009 Fall / MAT118A

Course that I've taken

1. 2007 Fall/Analysis A/Math Fluid dynamics/Math Quantum mechanics
2. 2008 Winter/Analysis B/Partial Differential Equations/Ordinary Differential Equations
3. 2008 Spring/Analysis C/Partial Differential Equations/Differential Topology/Lie groups
4. 2008 Fall/A short review of Modern Mathematicas/Algebra A/ Numerical of Partial Differential Equations/Method of Mathematical Physics (PHY 204)
5. 2009 Winter/Numerical Partial Differential Equations/Statistic Mechanics and Quantum Field Theory
6. 2009 Spring/None

Master Thesis

The Math Field That I am Interested with:
My Teaching As An instructor

        2008 Summer Session 2/Mat 21B Integral Calculus. (You can find all the tests in Frankmath world)

Lecture Notes

When I was a research asistant of National Center Theoretical Science in Taiwan, I gave a series of talks about the analysis on  Riemannian Manifolds.  What I focused on were spectral problems on Riemannian manifolds.  Before studying this topic, we need the gradient estimates, the Harnack inequality, of the Laplace equations on manifolds with possitive Ricci curvature.

The Harnack Inequality on manifolds with positive Ricci curvature

I have studied the inverse spectral theory for several years and also studied the infinite dimensional Hilbert manifolds related to the inverse spectral theory. The isospectral set of  the Schrodinger equation forms an infinite dimensional submanifold of the Hilbert space L^2[0,1]. We can construct the local chart to some l^2 space by using variational calculus. Here is one note about the basic idea of the construction of local chart.

The Inverse Dirichlet Problem


Some Useful Notel