Gestión Académica

This course is part of the mathematical education included in the basic training module. Since it is taught in the second semester of the first year, the students have already studied Linear Algebra and Calculus. The subject covers multivariable integral calculus, vector calculus, ordinary differential equations and functions of a complex variable. These topics are important for future engineers.

Moreover, after completing this course, the students should be able to use mathematical language properly and to analyze mathematical models. They should also be fluent in the advanced calculus software used during the computer sessions.

It is advisable that the students are familiar with integral calculus in one variable, differential calculus in simple and multiple variables, and vector spaces. All of these contents are included in the subjects Calculus and Linear Algebra taught in the first semester of the first year.

General competences:
CG03. Knowledge of basic subjects and technologies, which enables the student to learn new methods and technologies, as well as giving the student great versatility to adapt to new situations.
CG04. Ability to solve problems with initiative, decision making, creativity, and to communicate and transmit knowledge, skills and abilities, understanding the ethical and professional responsibility of the activity of the Telecomunication Engineer.
CG05. Knowledge for the realization of measurements, calculations, valuations, appraisals, surveys, studies, reports, task planning and other analogous works in the specific field of telecommunications.

Specific competences:
CB01. Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge about: linear algebra; geometry; vector calculus; differential and integral calculation; differential equations.

CB02. Basic knowledge about the use and programming of computers, operating systems, databases and computer programs with application in engineering.

Learning results:

RA-2.11. State and apply the basic properties of functions of a complex variable, and represent them through serial developments.

RA-2.12. Calculate and classify the singularities of a function of complex variable.

RA-2.13. Compute integrals of functions of two and three variables, and apply them to solve problems related to telecommunications.

RA-2.14. Use the parameterizations of the main curves and surfaces, and apply these parametrizations in integration problems.

RA-2.15. Describe and analyze differential equations and initial value problems ​​related to telecommunications engineering, and calculate their solutions and understand their behavior.

1. Functions of a complex variable.
   1. Analytic functions.
   2. Elementary functions.
   3. Taylor series.
   4. Laurent series and Singularities.
2. Ordinary differential equations.
   1. First order differential equations.
   2. Differential equations of order n.
3. Multiple Integrals
   1. Double and triple integrals.
   2. Changing variables.
4. Vector calculus.
   1. Curves and surfaces.
   2. Vector fields
   3. Line integrals.
   4. Surface integrals.
   5. Green's, Stokes' and Gauss' theorems.

Under exceptional circumstances (e.g. if sanitary conditions require it), online teaching and evaluation methods may be used, and students will be kept informed of any changes.

Ordinary calls:
TE grade:
- A continuous assessment model is used. There will be two written controls, one at the end of units 1 and 2, and another at the end of units 3 and 4. In case the grade at each control is at least 3 points out of 10, the arithmetic mean of the two will be taken. Students can retake each part of the course (either because they have not reached a 3 in that part or because they want to improve their grade) by going to the final exam which will take place at the end of the course; by doing so, the student waives the previous grade.
- The final exam of the ordinary call will be a global test where the grade of each of the two controls can be saved as long as it is greater than or equal to 3 points out of 10.
- A total TE grade of at least 5 points is required, and its weight in the total grade is 70%.
PL grade:
- The laboratory practices are evaluated during the practice sessions and an examination is also carried out. The grade of the practices will be the average of the grades achieved during the sessions and the grade earned at the exam.
- To pass this part of the course it is necessary to obtain at least 4 points out of 10 and to attend at least 80% of the sessions. The weight in the total grade is 15%.
PA grade:
- Individual and group activities are evaluated throughout the course and weight 15% in the total grade.
TOTAL grade:
- The total grade can be calculated with the following criterium: TOTAL grade = 70% TE grade + 15% PL grade + 15% PA grade.
- To pass the course, the total grade must be equal or greater than 5, and it is mandatory to have a minimum of 5 points out of 10 in the TE grade and 4 points in the PL grade (otherwise, the final grade will be suspended with 4 points maximum).

Extraordinary calls:
- In the extraordinary calls, both a written exam and a practical exam are carried out. Their weights are 70% and 15%, respectively; the grade of the activities evaluated during the course (PA grade) will be kept and cannot be retaken.
- To pass the course, the total grade must be equal or greater than 5, and it is mandatory to have a minimum of 5 points out of 10 in the TE grade and 4 points in the PL grade (otherwise, the final grade will be suspended with 4 points maximum).

Under exceptional circumstances (e.g. if sanitary conditions require it), online evaluation methods may be used and students will be kept informed of any changes.

Resources:

• Theory classroom with a projector device.
• Classrooms with computers for the laboratory sessions.
• Virtual Campus of the University of Oviedo.

References:

• J. Stewart, Calculus.  Cengage Learning.  7th Edition, International Edition, 2012 or 8th Edition, Metric Version, 2015.
• M. Spivak, Calculus. Cambridge University Press, corrected 3rd ed.  2006.
• D.G. Zill, M.R. Cullen, Advanced Engineering Mathematics. Jones & Bartlett, 2nd edition, 2000.