I have recently completed a year-long sequence of graduate-level courses on both finite difference and finite element methods. In the finite difference course, I gained expertise in solving elliptic partial differential equations and applying explicit and implicit methods to parabolic and hyperbolic equations. The course focused on the theory of stability, accuracy, and convergence, including von Neumann analysis, modified equations, and the Courant-Friedrichs-Lewy condition.
The finite element course provided a rigorous understanding of how FEM can be utilized to solve various PDE problems in both high and low dimensions. I have gained experience in using MATLAB, a numerical computing environment, to solve PDEs.
I completed a graduate-level course in Numerical Linear Algebra and Numerical Analysis, where I gained a comprehensive understanding of several important topics both algorithmically and theoretically. Through the Numerical Linear Algebra course, I acquired a thorough knowledge of LU factorization, QR factorization, linear least squares, singular value decomposition, eigenvalue problems, and iterative methods for solving large linear systems. In the Numerical Analysis course, I developed a deep understanding and proficiency in various numerical techniques for solving algebraic, transcendental, differential, and integral equations with a focus on ensuring stability, accuracy, efficiency, and reliability of numerical algorithms. I utilized the MATLAB and Python numerical computing environments for both courses.
For the past seven years, I have extensively used two popular numerical computing environments, MATLAB and Wolfram Mathematica, for research, laboratory work, and coursework in both graduate and undergraduate programs. My experience in working with these tools has provided me with a profound understanding of their capabilities and how to utilize them efficiently. I am confident that my expertise in these tools will enable me to work more productively on my current research project.
Furthermore, I am proficient in programming languages such as C++ and Python. In particular, I have worked with various scientific and numerical computation libraries, including NumPy and SciPy, using Python. Recently, I took an option course in Python Programming to update my knowledge of the basics and remain current with the latest developments.
In conclusion, my expertise in these technical tools and programming languages has equipped me with a solid foundation to tackle complex research problems and deliver high-quality results.