K3: Know the fundamental definitions and results of real, complex and functional mathematical analysis, including both the statements and their proofs. 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. C4: Understand the need to prove new mathematical results, as well as appreciate rigor in demonstrations, identify gaps in demonstrations, and use counterexamples to demonstrate the falsity of propositions. C5: Abstract complex problems from real life or other sciences and formulate them in terms of mathematical equations, using variables, constants and parameters to make them understandable and solvable.

Metric spaces. Uniform continuity and Cauchy sequences. Sequences and series of functions and uniform convergence. Fourier series and their convergence. Parametric integrals, Laplace and Fourier transforms.

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.