Course information

The Euclidean space Rn. Functions between Euclidean spaces, limit and continuity of functions. Differentiation of vector-valued functions of one variable, applications in mechanics and differential geometry, polar, cylindrical and spherical coordinates. Differentiable functions, partial and directional derivative, the concept of differential. Vector fields, gradient-divergence-curl. Fundamental theorems of differentiable functions: differentiability of composite functions, mean value theorem, Taylor’s formula, implicit function theorems, functional dependence. Local and conditional extremes, Lagrange multipliers. Double and triple integrals: definitions, integrability criteria, properties, change of variables, applications. Contour integrals: Contour integral of the first and second kind, contour integrals independent of path, Green’s Theorem. Elements of surface theory. Surface integrals of the first and second kind. Fundamental theorems of vector analysis (Stokes and Gauss Theorems), applications.