Calculus I Linear Algebra

In this second course of Calculus the students should acquire the mathematical background needed to understand and apply the concepts and techniques appearing in Statistics which involve several real variables. In particular they should become acquainted with functions of several variables, their properties of continuity, partial differentiability, differentiability and the calculus of double and triple integrals. Moreover, they will apply also these skills to solve optimization problems.

K5: Mathematically model and Know the mathematical foundations that allow solving problems using stochastic models and Operations Research techniques K11: Know the methodology that allows to statistically describe a set of data from numerical measures and graphs, both univariate and multivariate, highlighting possible relationships between variables of interest. K12: now how to identify or be able to create the statistical or probabilistic model appropriate to the specific problem arising in each business activity (finance, marketing, production planning and control, etc.). C1: Develop and master interpersonal skills on initiative, responsibility, conflict resolution and negotiation, which are essential in the professional environment. S1: To plan and organize team work making the right decisions based on available information and gathering data in digital environments. S5: Manipulate computationally and analytically the established models, taking advantage of the power of statistical methods, optimization, etc., and perform the analysis of the results obtained. S6: Communicate the results, the conclusions of the models and the proposed solutions in a way that is intelligible to the rest of the company, so that they are accepted and implemented by the decision-makers S7: Describe, synthesize and graphically represent the information contained in a data set

1.- Vectors and scalar product. Basic topological concepts. 2.- Functions of several variables. Graphs and level sets. Limits and continuity. 3.- Partial derivatives. Directional derivatives. Differentiability: Tangent plane. 4.- Chain rule. Higher order derivatives. 5.- Double and triple integrals: properties. Iterated integrals. Changes of variables. 6.- Applications of double and triple integrals. 7.- Quadratic approximation: Taylor's theorem. 8.- Maxima and minima. Lagrange multipliers.

The course will be taught mostly through lectures, with supporting material available on the web. These classes should be complemented with the students' autonomous reading on some aspects of the syllabus, especially concerning motivation and applications. Some of the lectures will be devoted to solving exercises singled out from the collection of exercises the students will be given at the beginning of the semester. Two partial exam.