Mathematical Analysis III 0600-MS1-2AM3#a
Ćwiczenia (CW) Rok akademicki 2018/19

Learning outcomes and verification methods:

Can integrate function of several variables. - Quizzes Homework presentation of solutions continous evaluation

Knows Stokes theorem, can apply it and understands vector versions of this theorem. - Quizzes Homework presentation of solutions continous evaluation

Knows definitions and basic properties of operators such as gradient, rotation and divergence. - Quizzes Homework presentation of solutions

Knows and can apply differential calculus of functions of several variables: knows basic theorems in this topic. - Quizzes Homework presentation of solutions continous evaluation

Possesses basic knowledge on the spaces of continuous linear and multilinear maps. - Quizzes Homework presentation of solutions continous evaluation

Contents of the course

Functions of several real variables: strong derivative, directional derivatives. Spaces of linear continuous maps. Equivalence of norms in R^n. Th. on local invertibility of mappings. Higher order derivatives. Taylor Th. Extrema of functions. Implicit functions. Lusternik-Lagrange theorem on conditional extrema. Smooth functions with compact support and decompositions of unity. Riemann integral of function of several variables. Elements of the theory of manifolds submerged in R^n. Differential forms and external differentiation. Stokes Theorem. Differential operators. Fourier transform.

Teaching methods: exercises, consultations, studying literature, home works, discussions in groups.