Mathematical Analysis II (Advanced Calculus II) [2ΚΠ01 - Second Semester]

Euclidean space . Neighborhoods. Classification of points of open and closed sets. Sequences. Basic theorems.  Functions of several variables. Limit of a function. Operations with limits. Continuous function. Properties of continuous functions.  Partial derivatives. Partial derivatives of higher order. Differentiable function. Total differentials. Differentials of higher orders. Differentiation of composite functions. Implicit functions.

Jacobians transformations. Inverse transformations. Directional derivatives. The mean-valued theorem and Taylor’s theorem for several functions. Extreme values. Extreme values under constraints.Double and triple integrals. Scalar and vector fields. Gradient, divergence and curl.  Line integral of first kind and second kind. Green’s formula.  Surface integral of the first and second kind.  Stokes’ theorem. Gauss’ theorem. Conservative field. Solenoidal field.