This course is an introduction to the functions of several variables. Topics include continuous transformations of metric spaces, Euclidean spaces, continuous functions of several real variables, partial derivatives, linear transformations, and determinants. The inverse function theorem, the implicit function theorem, and functional dependence also are studied.
- Teacher: Tr Math 002
This course introduces general topology. Separation axioms, compactness, the concept of product topology, and examples are discussed in detail.
- Teacher: Tr Math 002
This course is intended for ring theory. Definitions and examples of rings, some simple results on rings, ideals, homomorphisms, quotient rings and maximal ideals are discussed.
- Teacher: Tr Math 002
This course introduces fluid dynamics. The main topics are vortex motion and waves.
For vortex motion, vorticity, vortex line, vortex tube, vortex filament, rectilinear vortices, two vortex filaments, vortex pair, vortex doublet, the motion of any vortex, image of a vortex filament in a plane, vortex inside an infinite circular cylinder, vortex outside a circular cylinder, image of a vortex outside/inside a circular cylinder, vortex rows, Karman vortex street, Rankine's combined vortex are studied.
For waves, mathematical representation of a wave motion, standing or stationary waves, types of liquid waves, surface waves, the energy of progressive waves, the energy of stationary waves, waves at the interface of two liquids, waves at the interface of two liquids with an upper surface free, group velocity are studied.
- Teacher: Tr Math 002
This course studies graph theory with applications. Topics include graphs, subgraphs, and tree.
- Teacher: Tr Math 002
This course considers the qualitative theory of ordinary differential Equations. Existence theory, stability of linear and almost linear systems are emphasized.
- Teacher: Tr Math 008