Syllabus Information

1. General information

One of the objectives of this subject is that the student consolidates the basic aspects of Mathematics and learns to relate them in order to acquire the ability to develop and adapt them to the resolution of the problems of Telecommunications Engineering. The student must be able to face a problem in a rigorous way, analyzing the techniques and strategies available to select the most effective one and know how to analyze the results obtained. 

These approaches and objectives are aligned with the Sustainable Development Goals (SDGs) of the 2030 Agenda of United Nations (https://www.un.org/sustainabledevelopment/es/) and certain specific goals, so that the acquisition of the learning results of the subject provides training and knowledge, skills and competencies to contribute to some extent to their achievement. In a problem class, an example will be proposed in the context of engineering whose approach is related to the following SDGs:  Goal 6 (Target 6.3), Goal 7 (Target 7.2), and Goal 13 (Target 13.3).

To follow this subject it is essential to have a clear understanding of the concepts and to know how to apply the corresponding techniques from both the Mathematics subjects of the two years of High School (Science and Technology) and from the Calculus and Algebra subjects taught in the first four-month period. In particular, it will be essential to know and master the calculation of limits of functions, as well as differential and integral calculus of one variable. You must also be able to work with matrixes (apply properties and perform operations) and it is also essential to know how to solve systems of linear equations. 

2. Learning results

- Know the techniques of polynomial interpolation to fit a data set or approximate a function.

- Know how to use numerical integration methods to solve integrals.

- Know and knows how to apply the results of differential and integral calculus of real functions of several variables.

- Know how to calculate surfaces of plane regions and volumes of enclosures in the usual coordinate systems.

- Understand and know how to solve line and surface integrals.

- Know how to apply the theorems relating surface integrals to triple integrals and line integrals. 

3. Syllabus

1. Interpolation

2. Numerical integration 

3. Continuity

4. Differentiability 

5. Differential operators 

6. Double and triple integrals 

7. Line integrals.

8. Surface integrals

4. Academic activities

Lectures: 37 h

Two and a half hours per week will be dedicated to the whole group. Theoretical contents and results will be presented and complemented by the resolution of examples and practical exercises.

Problems and cases: 11 h

One hour per week will be dedicated. In these sessions the students (separated in subgroups) will work on problems related to the content of the subject.

Laboratory practices: 12 h

Six 2-hour sessions will be held every two weeks. In these sessions the students (separated in subgroups) will have to program the mathematical algorithms necessary to solve the proposed exercises, using symbolic and numerical programming software installed in the EINA computer laboratories

Assessment tests. 6 h

5. Assessment system

Continuous assessment and Global assessment.

- In the continuous assessment, the student must demonstrate that they have achieved the intended learning results through the following assessment activities:

• Open-response written test on the theoretical-practical contents of the subject with exercises andquestions of a level of difficulty similar to that of the exercises and problems posed throughout the term. Its grade (E) will be between 0 and 10 and will represent 70% of the final grade (F) of the subject.
• Problems and Tutored Activities. The grade obtained (PyAT) will be between 0 and 10 and will represent 10% of the final grade (F) of the subject.
• A test in which the student will have to solve problems similar to those performed and proposed in the practical sessions. It will be graded with a score (P) between 0 and 10 and will represent 20% of the final grade (F) off the subject.

If a grade is obtained in the written test E ≥4 then the final grade (F) will be obtained:

- If PyAT ≥5 then F=0.70*E+0.10*PyAT+0.20*P
- If PyAT ≤5 then F=0.80*E+0.20*P

- In the global assessment, there will be a final exam containing two blocks, one with theoretical-practical questions and problems corresponding to the topics developed in the lectures and problem sessions (E), which will account for 80% of the final grade. Another block with questions dealt with in the practicals (P) and that will represent the remaining 20% of the final grade. With this global evaluation system, 100% of final grade (F) can be obtained.

In order to pass the subject, a grade in the written test must be obtained, both in the continuous assessment and in the global assessment E≥4 and a final grade of F≥5.