Mathematical Analysis 3 MAT2302

Course content:
Curves in the Euclidean space.
Nonoriented curve integral. Methods of computing. Applications.
Vector fields in Euclidean spaces. Oriented curve integral.
Surfaces in the three-dimensional space. Parameterization, area of surface.
Nonoriented surface integral. Methods of computing. Applications.
Orientation of a surface. Orientable and nonorientable surfaces.
Oriented surface integral. Applications.
Divergence and rotation of a vetor field. Gauss-Ostrogradski theorem.
Stokes and Green theorems.
Independence of path integral from the path.
Potential vector fields. Potential.
Curvature and torsion of a curve.
Fourier transformation.
Discrete Fourier transformation.
Banach and Hilbert spaces.

Learning outcomes:
Knowledge of concepts and ability to compute curve and surface integrals.
Knowledge of theorems concerning curve and surface integrals and ability to apply them.