The course has three hours of theory classes per week. These classes will be taught in the traditional way, using chalk and blackboard. In the theory sessions, the main concepts will be developed and the important results of differential and integral calculus in several variables will be stated. We will prove the theorems and provide examples of their applications.

Students will receive lists of exercises and problems, which we will work on in the weekly problem session. Beforehand, as part of their independent study, they should have read and thought about the proposed exercises and problems. This will help ensure their participation in class and facilitate the assimilation of procedural content. There will be one problem session per week.

There will be eight seminar sessions, each lasting two hours. Students will have material previously made available on the Virtual Campus, which they will be expected to have studied. Students will work on a list of activities, asking any questions that may arise throughout the session. At the end of some seminar sessions, which will be announced in advance, there will be an assessment.

The expected progression for students, and the one that ensures better performance, is the following:

(i) Prior reading of the theory notes posted on the Virtual Campus. Identification of the concepts that may be more difficult.

(ii) Attendance at the corresponding theory sessions. Students are expected to participate actively, asking any questions that may arise. Every question is welcome, and encouraged, in the theory sessions.

(iii) Reading and attempting to solve the corresponding problems. It is strongly recommended that students first make an active and individual effort to solve the problems. In a second iteration, working in groups to solve problems is a good idea. Finally, once the problems have been attempted individually and collectively, students may use Artificial Intelligence tools for support, although this is by no means essential. It is important not to alter this order of action and not to start directly with the use of this tool. In fact, in this course it is recommended to avoid generative Artificial Intelligence tools, since current models tend to agree with users and confirm their hypotheses, which may create a false sense of mastery of the content.

(iv) Attendance at the problem and seminar sessions corresponding to this block. Students are expected to participate actively, asking any questions that may arise. Every question is welcome, and encouraged, in the problem and seminar sessions.

The Virtual Campus will be the means of communication between the teaching staff and students. It will be important to check it on a daily basis.

Students will have access to office-hour tutorials. They are encouraged to make use of this support in order to follow the course properly. You may contact the teaching staff by email to arrange a tutorial session.

Note: 15 minutes of one class will be set aside, within the calendar established by the centre/degree programme, so that students can complete the surveys evaluating the teaching staff’s performance and the course itself.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

There will be continuous assessment consisting of a first midterm exam (P1) and two compulsory assessed seminars (S1, S2). The marks for the assessed seminars cannot be retaken. At the end of the course there will be a second midterm exam (P2) and a resit exam (R).

The final mark is obtained in two steps. We denote by P1, P2, S, R, respectively, the marks for the first midterm exam, the second midterm exam, the average of the seminars S1, S2, and the resit exam, all out of 10.

First sitting. If min(P1, P2)<3.5, the student must take the resit exam. Otherwise, the mark for the first sitting is computed as

C1=0.45P1+0.45P2+0.1*S.

If C1>=5, the student has passed the first sitting and has passed the course with final mark C1+V, where V is a variable component that will be detailed below.

Second sitting. Students who have not passed the first sitting, as well as those who wish to improve their mark, may take the resit exam. The mark C2 for the second sitting is

C2=min(7, 0.9R+0.1S)

and replaces C1. If C2>=5, the student has passed the second sitting and has passed the course with final mark C2+V.

If C1<5 and the student does not take the resit exam, their final mark will be C1. If C1<5 and C2<5, the student’s final mark will be C2.

The variable component V may range from 0 to 0.5 points. It will depend mainly on participation in the Virtual Campus forums, but it may also be complemented by the completion of extra assignments and exercises. Under no circumstances will the variable component be taken into account if the final mark C1 or C2 is lower than 5.

Remark 1: If the teaching staff considers it appropriate, students may be asked to attend interviews in order to further clarify the marks.

Remark 2: Possible honours distinctions will be awarded before the resit exam, since this exam does not allow the mark to be raised above 7.

Remark 3: A student will be considered “Not assessable” if they have not taken part in any exam, that is, if they have no P1, P2 or R mark.

Students who have chosen the single-assessment modality must take a final assessment consisting of an oral theory exam, in which they will have to present a topic and respond to the teaching staff’s questions and comments. In addition, on the day of the final exam they must take a problem-solving test, in which they will have to solve a series of exercises similar to those worked on in the Practical Classroom sessions. The theory exam will account for 50% of the mark and the problem-solving exam for the remaining 50%. If the final mark does not reach 5, the student will have another opportunity to pass the course through the resit exam, which will have the same structure. Single-assessment students who have not taken part in either of these two exams will be considered “Not assessable”.

Without prejudice to any other disciplinary measures that may be deemed appropriate and in accordance with the current academic regulations, any irregularities committed by a student that may lead to a change in the final mark will be graded with a zero (0).

For example, plagiarism, copying, allowing others to copy, or having communication devices —such as mobile phones, smart watches, etc.— during an assessment activity will result in failing that assessment activity with a zero (0).

Assessment activities graded in this way and through this procedure will not be eligible for reassessment. If passing any of these assessment activities is required in order to pass the course, the course will be failed directly, with no opportunity for reassessment during the same academic year.

The numerical mark recorded in the student’s academic transcript will be the lower value between 3.0 and the weighted average of the marks if the student has committed irregularities in an assessment activity.

This teaching guide has been translated from the original Catalan version. In the event of any discrepancy, difference in interpretation, or contradiction between this translation and the Catalan version, the original Catalan version shall always prevail.