Special Topics in Mathematics

1st Vector calculus, scalar, cross and triple product, vector functions.
2nd Differential calculus of functions of two or more real variables: domain, graph, limit and continuity.
3rd Partial derivatives, total differential, tangent plane and normal to a surface.
4th Implicit function and its derivatives.
5th Extremes of functions, calculation via derivatives.
6th Constrained extremes, Lagrange's method.
7th Global extremes. Taylor's theorem.
8th Two-dimensional integrals on a rectangle and on a general domain.
9th Calculations of two-dimensional integrals, applications in geometry and physics.
10th Three-dimensional integrals, calculation and application.
11th Line integral of the first and second kind, calculation methods.
12th Applications of curved integrals, Green's theorem, independence of the integration path.
13th Surface integrals and their calculation.
14th Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.