Course Content (Syllabus)
Basic topological concepts in n-dimensional space - Differential calculus of real functions of several variables with real arguments (geometrical picture of a function of several variables, limits, continuity, partial derivatives, differentiability, total differentials) - Composite function of several variables (Chain rule, Eulers theorem, the mean value theorem, Taylor's theorem) - Implicit function of several variables (Jacobians, transformations) - Calculus of real function with vector variables and vector functions of vector variables (divergence and curl of a vector function) - Geometrical application of differential calculus of several variables - Extreme values of a function of several variables and extreme values under constrains