To understand objects in two and three dimensions that are described by sufficiently "smooth" functions of several variables, and in particular, to differentiate and integrate such functions.

K1: To know the main techniques of mathematical proof, as well as to understand the importance and necessity of hypotheses in mathematical results. K3: Know the fundamental definitions and results of real, complex and functional mathematical analysis, including both the statements and their proofs. S1: Learn and adapt mathematical techniques and methods from one branch to another (such as algebra, calculus or probability) and apply them to different scientific or industrial problems. S4: Use logical and abstract reasoning to state, demonstrate and verify the validity of mathematical results, as well as to analyze models and design solution strategies.

Differential calculation in several variables Optimization in multi-variable functions Multiple integration. Line and surface integrals. Integral theorems of vector calculus.

A1: CLASSROOM LECTURES. Each subject has two weekly sessions: a lecture session, with more theoretical content, and a reduced session, with more practical content. In this session, the main theoretical content takes place. 100% de presencialidad / A2: FACE-TO-FACE CLASSES: REDUCED (WORKSHOPS, SEMINARS, CASE STUDIES). As indicated above, this session has a more practical content where teachers can carry out some of the examples given. 100% de presencialidad / A3: STUDENT INDIVIDUAL WORK. 0% de presencialidad / A4: LABORATORY SESSION. This is a series of additional hours where teachers reinforce more practical content with students. 100% de presencialidad / A5: FINAL EXAM. 100% de presencialidad M1: SEMINARS AND LECTURES SUPPORTED BY COMPUTER AND AUDIOVISUAL AIDS. / M2: PRACTICAL LEARNING BASED ON CASES AND PROBLEMS, AND EXERCISE RESOLUTION. / M3: INDIVIDUAL AND GROUP OR COOPERATIVE WORK WITH THE OPTION OF ORAL OR WRITTEN PRESENTATION. / M4: INDIVIDUAL AND GROUP TUTORIALS TO RESOLVE DOUBTS AND QUERIES ABOUT THE SUBJECT.