MISCELLANEOUS NOTES

• Lecture notes on Weak KAM theory (incomplete notes)
  (May 04, 2021)

• Some notes on Finite Difference Schemes for Hamilton-Jacobi equation
  (December 24, 2017)

• A note on Fourier-Stieltjes transforms and almost-periodic functions
  (January 17, 2017)

• Applied Math Qualifying exam
  (August 28, 2017)

These are some notes I have taken through my undergraduate study.

• Lecture note: Homogenization for viscosity solutions of Hamilton - Jacobi equations
  (July 14, 2015)
  

  In summer 2015, while attending a summer course taught by Hung V. Tran at the University of Science, Vietnam National University, HCMC, Son P.T. Van and I wrote the lecture notes for this course.

• Undergraduate thesis: Linear control systems and the regularity of the minimum time functions
  (May 31, 2015)
  

  Advisor: Khai T. Nguyen
  Abstract: Consider the linear control system $x(t)=Ax(t)+Bu(t)$ with the target $0$. The function $T(x)$ is the minimum time needed to steer a point $x$ to $0$. It is well-known that under the Rank-Kalman condition, $T$ is just continuous in the reachable set. Our main goal is to study the regularity of $T(x)$. We prove that $T$ is a.e. twice differentiable. Moreover, we also obtain an explicit formula for the set of singularities where the optimal control changes its sign.

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