In the left navigation column you see the names of the academic subjects that I teach at the Institute of Mathematics and Statistics. By clicking on the corresponding link you will see a short description of an academic subject and the corresponding supporting materials.
Analytic Geometry (analüütiline geomeetria) is a course of lectures for students of first semester (given at autumn term), but other students can also take this course of lectures. The central part of this course is vector algebra and the concept of a coordinate system. In addition to the rectangular coordinate system, we also consider polar coordinates, spherical and cylindrical coordinates. We investigate straight lines and planes using equations. In the second part of the course, we study conics (ellipse, hyperbola, parabola).
Differential Geometry (diferentsiaalgeomeetria) studies curves and surfaces by means of the methods of algebra, differential and integral calculus. In this course, I use the moving frame method to study curves and derive the basic formulas of this method, that is, the Frenet-Serret formulas. Curvature of a surface is explored using principal curvatures, mean curvature, and Gaussian curvature. I explain the concept of connection and making use of differential forms derive the equations of connection in curvilinear coordinates.
Within the framework of Global Analysis (globaalanalüüs) , I explain the concept of a manifold, tangent bundle on a manifold, vector fields, Lie brackets, and Lie derivative. In addition, I consider the algebra of differential forms on a manifold. I describe applications of differential forms in Maxwell's theory.