|Graduate||1st four-month period
|The space R^n||The vector space R^n.
Scalar product: norms and distances.
Classification of points and sets.
Topology of R^n: bounded set, extrema.
Coordinates systems: polar, cylindrical and spherical coordinates.
|Functions of several variables||Scalar and vector functions.
Continuity in compact sets.
|Differenciation of funcions of several variables and applications||Directional derivative.
Partial derivatives: properties and practical computing.
Differential map of a function.
Gradient, relation with partial derivatives.
Relation between the differential map and partial derivatives: jacobian matrix.
Higher order partial derivatives.
Introduction to vector calculus.
Taylor theorem for scalar functions.
Critical points. Classification.
Conditioned extremes: dimension reduction, Lagrange multipliers method.
Implicit function theorem and inverse function theorem.
|Integration of funcions of one and several variables||Riemann sums.
Integral Calculus Theorems: Mean Value Theorem, Fundamental Theorem and Barrow's rule.
Numerical integration. Compound Simpson's Rule.
Application of integral calculus to computing arc lengths, volumes of revolution and surface areas of revolution.
Variable change in double and triple integrals.
Application of integrals: calculation of areas and volumes.
|Complex numbers||The field of complex numbers.
Operations: sum, produt.
Module and argument.
Operating in polar form.