Syllabus
(1) Introduction Matlab basics, global and local functions, function handles, scripts, live scripts, basic mathematical operations, the numerical representation of matrices, linear indexing, matrix inversion, numerical integration, interpolation, extrapolation, data smoothing by polynomial function or by median (2) Graphical tools in Matlab Plotting function of one and two variables, drawing 2D and 3D graphs, plot labels, shading, lighting, curves in 3D, creating dynamical animations (3) Non-linear algebraic equations Fermi level in a doped semiconductor with impurities. Chemical potential temperature dependence. (4) Non-linear curve fitting Curve fitting, including the estimation of the fitted parameters' errors. (5) Ordinary differential equations Explicitly and implicitly defined ordinary differential equations, sets of ODEs (6) Partial differential equations in 1D Solving PDE in one spatial coordinate and time (7) Partial differential equations in 2D Definition of problems, eigenvalue problem, geometry specification, triangulation, mesh refining, drawing edges and domains, boundary conditions of the Dirichlet, Neumann and Robin type. Evaluating the solution, drawing the solution, gradient calculation, vector field (8) Partial differential equations in 3D Major differences with 2D, defining geometry (AutoCAD, Blender), drawing the solution, solution cross-sections, flows, surface solution (9) Tight-binding method Band structure of the graphene nanoribbons. (10) Selected methods of machine learning Non-negative matrix factorization, spectral clustering, K-means, K-medoids, Singular value decomposition, etc. are used for advanced experimental data analysis.
Annotation
The main objective of the course is to provide fundamental concepts of a high-level programming in Matlab. The course is intended for students who want to gain hands-on experience with advanced numerical simulations.
The numerical methods are demonstrated on several practical examples during the lecture. The hands-on experience will ease understanding several concepts taught in Solid State Physics courses.
The modern methods employing machine learning algorithms will be beneficial for all students who want to perform in-depth analysis of their experimental data.