Solve the mathematical problems that can arise in the degree they are studying. 
Understand the concept of sequences and the computation of limits. 
Know and work intuitively, geometrically and formally the notions of limit, continuity, derivative and integral.
Understand and know how to make Taylor's developments of functions of one real variable. 
Acquire basic notions of numerical series and power series. Know the construction of the integral, know how to solve integrals and 
its applications to solving problems where the integral approach is necessary. Improper integrals will be also studied.

1. Sequences of real numbers.
										
											
										
											Limit of a sequence and algebraic properties.
										
											Monotone sequences.
										
											Accumulation points. Subsequences.
										
											Bolzano-Weierstrass theorem.
										
											Cauchy sequences.
										
											Computation of limits.

										
											2. Real functions.
										
											
										
											Domain of a function.
										
											Elementary functions.
										
											Limit of a function at a point. One-sided limits. Properties of the limits. Asymptotes. Limits of functions.
										
											Continuity of a function.
										
											Bolzano's theorem.
										
											Mean value theorem and Weierstrass theorem.
										
											
3.Derivatives.
										
											
										
											Derivatives of a function at a point.
										
											Calculation of some derivatives.
										
											Tangent line equation.
										
											Chain rule. Inverse functions and differentiation. Logarithmic differentiation.
										
											Absolute and relative extreme values of a function.
										
											Rolle's theorem. Mean value theorem.
										
											Hôpital Rule.
										
											Newton's method for finding numerical solutions of functions.

										
											4. Approximation by Taylor polynomials.
										
											
										
											Order of contact between functions.
										
											Taylor polynomial. Properties
										
											Taylor's formula. Taylor's residue.
										
											Approximate calculations. Application to the computation  of limits.
										
											Local study of functions.

										
											5. Integration
										
											
										
											Primitives of a function.
										
											Immediate integrals. Integrals by change of variable. Integrals by parts.
										
											Integration of rational functions. Integration of irrational functions.
										
											The fundamental theorem of calculus.
										
											Applications of integration:  flat areas,  length of a curve, areas and volumes of solids of revolution.
										
											Improper integrals Convergence criteria. Absolute convergence

										
											6. Numerical series and power series.
										
											
										
											Numerical series. Necessary condition of convergence.
										
											Criteria of: comparison, quotient, root, integral.
										
											Alternate series. Absolute convergence
										
											Power series.Radius of Convergence.
										
											Derivation and integration of power series.

Assessment

Continous Assessment Activities

Title	Weighting	Hours	ECTS	Learning Outcomes
First delivery	15%	1	0.04	CM01, CM03, CM04, KM01, SM01, SM02
First partial exam	40%	2	0.08	CM01, CM03, CM04, KM01, SM01, SM02
Second partial exam	40%	2	0.08	CM01, CM03, CM04, KM01, SM01, SM02
delivery	5%	1	0.04	CM01, CM03, CM04, KM01, SM01, SM02

Traducció del català efectuada per "Google Translate"

There will be an evaluable test / delivery of the practical part of the course, with computer, which will be worth 15% of the final grade. This part of the note will not be recoverable.

The delivery of solved exercises, as the teacher indicates, complements (5%) the course evaluation. This part will not be recoverable either.

There will be an exam (First Partial = P_1) in the middle of the semester in which the work done up to that point will be evaluated. The mark of this exam will provide 40% of the final grade. All students who take this exam can no longer be graded as NON-EVALUABLE. A student who has not taken this exam will be listed as NON-EVALUABLE for academic purposes and will not have the right to retake it (except for a duly justified reason, in which case the retake exam will be allowed).

At the end of the semester there will be a second partial exam (called P_2) in which the knowledge of the subjects that have not been evaluated in the first partial will be evaluated. The mark of this exam will provide another 40% of the final grade. A student who has not taken this exam will not be entitled to retake it (except for a duly justified reason, in which case the resit exam will be allowed).

If the average of the marks (out of 10) of the two partial ones (P_1 + P_2) / 2 is inferior to 3,5 the student must go to the examination of recovery, that is an global examination of all the asignatura . If the mean M = (P_1 + P_2) / 2 is greater than or equal to 3.5, then the final grade is NF = 0.8 M + 0.15 P + 0.05 Ll, where P is the practical part of the course (out of 10) and Ll is the grade for deliveries (out of 10). If NF is higher than 5 the student has passed and has NF as a final grade. If not, the student must go to the recovery exam and in this case the final gradewill be 0.8 R + 0.15 S + 0.05 Ll, where R is the grade of the exam recovery (about 10).

5% of the students will be able to obtain the qualification of Honorary Enrollment. They will necessarily have to have a grade equal to or higher than 9. The final decision on the MH grade will be made by the teacher.

In the partial exams and in the one of recovery it will not be allowed to use calculator.

For each evaluation activity, a place, date and time of review will be indicated in which the student will be able to review the activity with the teaching staff. In this context, claims may be made on the grade of the activity, which will be evaluated by the teacher responsible for the subject. If the student does not appear for this review, this activity will not be reviewed later. Dates of problem deliveries and midterm exams will be posted on the Virtual Campus (CV) and may be subject to possible scheduling changes for reasons of adaptation to possible incidents; these changes will always be reported to the CV as the CV is understood to be the usual mechanism for exchanging information between teacher and students.

Without prejudice to other disciplinary measures deemed appropriate and in accordance with current academic regulations, irregularities committed by a student that may lead to a variation in the grade will be graded with a zero (0). For example, plagiarizing, copying, copying, having communication devices (such as cell phones, smart watches, etc.) in an evaluation activity will involve suspending that evaluation activity with a zero (0). Assessment activities qualified in this way and by this procedure will not be recoverable. If it is necessary to pass any of these assessment activities to pass the course, this course will be suspended directly, without the opportunity to retake it in the same course. The numerical mark of the transcript will be the lower value between 3.0 and the weighted average of the marks in case the student has committed irregularities in an act of evaluation (and therefore it will not be possible to pass it by compensation).