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Study of the fundamental Mathematical Analysis of one variable.

1. REAL VARIABLE FUNCTIONS 1.1 The real line: sets of numbers, properties, absolute values 1.2 Elementary functions and curves 1.3 Polar coordinates 2. LIMITS AND CONTINUITY 2.1 Limits of functions. Properties and fundamental theorems 2.2 Continuity of functions 2.3 Fundamental theorems 3. DERIVATIVES AND THEIR APPLICATIONS 3.1 Definition, properties, and derivatives of elementary functions. 3.2 Meaning of the derivative. Extrema. 4 LOCAL STUDY OF A FUNCTION 4.1 Graphic representation 4.2 Taylor polynomial and its applications 5. SEQUENCES AND SERIES OF REAL NUMBERS 5.1 Sequences of numbers 5.2 Series of positive numbers 5.3 Absolute and conditional convergence 6. SEQUENCES AND SERIES OF FUNCTIONS 6.1 Sequences and series of functions. 6.2 Taylor series 7. INTEGRATION IN ONE VARIABLE 7.1 Calculus of primitives 7.2 Fundamental Theorem of Calculus 7.3 Applications

THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.76 ECTS] Knowledge and concepts students must acquire. They receive course notes and will have basic reference texts to facilitate the follow-up of the classes and the development of subsequent work. Exercises will be solved, they will be practised with problems by the student and there will be workshops and tests of evaluation to acquire the necessary skills. TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.16 ECTS] Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher. STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.92 ECTS] FINAL EXAM. [4 hours with 100% on-site, 0.16 ECTS] Global assessment of knowledge, skills and capacities acquired throughout the course. METHODOLOGIES THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support in which the subject`s main concepts are developed while providing material and bibliography to complement student learning. PRACTICAL CLASS. Resolution of practical cases and problems, posed by the teacher, and carried out individually or in a group. TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with a teacher as a tutor.