Mathematical Analysis MAT1203

Course content:
Sequences and series of functions.
Differentiation and integrations of series of functions.
Taylor series.
Fourier series.
Differentiability of functions of several variables.
Taylor theorem. Global extrema.
Conditional extrema.
Functions of several variables with vector values.
Theorem on increments. Inverse function theorem.
Implicit function theorem. Rank theorem.
Double integrals. Polar coordinates.
Applications of double integrals.
Triple integrals. Cylinder and spheric coordinates.
Applications of triple integrals.
Euler's beta and gamma functions.

Learning outcomes:
knowledge of basic theorems on sequences and series of functions,
ability to check convergence of sequences and series of functions,
knowledge of theorems on functions of several variables with vector values,
knowledge of basic theorems on multiple integrals,
ability to compute multiple integrals and to apply them.