Written Notes

Here are the notes that I take in class or after class, written on iPad with iPad Pencil.

• Tensor Calulus , an evolving short notes on basics of tensors based on Lecture Notes on Diff. Geo. by Prof Peter Petersen, Lecture notes on Diff. Mnflds. & Rie. Geo. by Prof Fong Tsz Ho, YouTube on tensor calculus.
• Surfaces theory in $R^3$ A and Surfaces theory in $R^3$ B. These notes are about classical differential geometry, based on my review notes of MATH 120A UCLA. References are Lecture Notes on Diff. Geo. by Prof Peter Petersen, Lecture notes on Diff. Mnflds. & Rie. Geo. by Prof Fong Tsz Ho, ICTP’s video on Diff. Geo. and Elementary Diff. Geo. by Andrew Pressley.
• Real analysis. These are notes I took down in MATH 5011 Advanced Analysis at HKUST in Fall 2019. It covers Lebesgue Integration theory, $L^p$ spaces, Lebesgue Diff. Thm. and Fubini Thm. Egorov, Luzin Thm and basics of Hausdorff measure at the level of Year 1 Graduate course.
• An incomplete elementary notes on differential manifolds. It covers tangent & cotangent bundle, differential forms and Lie derivatives.
• An ongoing notes on Partial Differential Equations. In Spring 2021, I am taking a course on PDEs taught by Prof Gunther Uhlmann. These notes are what I dropped down in class. He started with theory of distributions and Fourier transforms. Notes on fundamental PDEs (Heat, Waave etc) will be uploaded once ready.
• Functional Analysis. These notes are based on a course on YouTube channel of IMPA, taught by Prof Claudio Landim. I am currently studying it hence new notes are uploaded periodically. It covers Vector Space, Normed Space, Examples of Normed Space, Finite Dimensional Space, Infinite Dimensional Space…
• PDEs. These notes are from MATH6050H, Fall 2020 taught by Prof Li Dong, HKUST. It covers Chapter 5 & 6 of Evans’ PDE. Sobolev Space I, Sobolev Space II, Sobolev Space III, Sobolev Space IV, Elliptic Equation I, Elliptic Equation II.