The subject of Algebra is part of the basic training module. It is taught in the first semester of the first year of the following degrees: Bachelor's Degree in Automotive Engineering, Bachelor's Degree in Industrial Electronic Engineering and Automation, Bachelor's Degree in Mechanical Engineering, Bachelor's Degree in Industrial Chemical Engineering and Bachelor's Degree in Computer Engineering Management and Information Systems. And also in the first semester of the second year of the following degrees: Double Degree in Business Administration and Management and in Computer Engineering of Management and Information Systems, and Double Degree in Mechanical Engineering and Business Administration and Management.





Given its basic and applied nature, it should serve as a support for other subjects that require simple or more complex mathematical knowledge.



To tackle this subject, it is essential to master the Mathematics syllabus of the second year of Baccalaureate in its Technology modality.



Algebraic training contributes fundamentally to the acquisition of a rigorous habit of thinking in accordance with formal-logical reasoning and the rigor inherent in the different disciplines of Mathematics. Also to the resolution of practical problems of Engineering that are modeled by algebraic methods and techniques and, in particular, by means of the procedures of Linear Algebra.

Read and interpret mathematical texts related to Linear Algebra, express in writing in a precise and rigorous way their logical-deductive reasoning and be able to transmit them to other people.



Use matrices, determinants and techniques for solving systems of linear equations in the different areas of Linear Algebra application within Engineering.



Accurately employ the mathematical elements related to vector spaces and Euclidean vector spaces, understanding them as an abstraction of the properties of the free vectors of plane and space. Build the most convenient basis that simplifies the solution of the problem at hand, make the best approximation of a vector in a subspace and apply it to the approximate solution of incompatible systems.



Handle the fundamental concepts of linear applications, appreciating their importance in different areas of Linear Algebra in the field of Engineering.



Perform the diagonalization of a real matrix and the orthogonal diagonalization of a real and symmetric matrix, understanding what they mean as simplification of a transformation, apply it to the calculation of the inverse, of matrix powers, evaluation of a polynomial function in a square matrix and to the classification of quadrics.





Identify and use quadratic forms as basic for the geometric study in the affine space of conics and quadrics.

- Vector Spaces: Definition. Subspaces. Linear Dependence/Independence. Bases.



- Matrix calculus and systems of linear equations: Matrices. Determinants. Systems of linear equations.



- Linear Applications: Definition. Classification. Associated matrix.



- Euclidean vector space: Scalar product. Orthogonality. Gram-Schmidt method. Orthogonal projection. Better approximation.



- Diagonalization: Eigenvalues and vectors. Diagonalization. Orthogonal diagonalization.



- Quadratic shapes. Conical. Quadraic.

The methodology used in this subject, in order to achieve learning and the acquisition of skills by the students, will be carried out through various teaching methods, among which we highlight the expository method and the resolution of exercises and problems.



In the face-to-face sessions of the expository method, the teacher will develop, in a clear and accessible way, the theoretical contents of the different topics, showing their need and relationship between them. An attempt will be made to stimulate the participation of students by asking questions during the theoretical presentation.



In the face-to-face sessions of practical work in the classroom, problems will be solved by applying theoretical knowledge. Debate and student participation will be encouraged. To do this, they will have a list of problems that they will have to solve on their own for later discussion in the classroom.



There will be a virtual classroom on the eGela platform that will allow permanent contact between teachers and students. In it, material and information about the subject will be available.



Students will have the opportunity to attend personalised tutorials with the teacher, at a time set aside for this purpose, which can be consulted at GAUR or on the School's website. During these hours, any academic issue related to the subject can be discussed.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 80
  • Actividades durante el curso y prueba escrita. (%): 20

(I) CONTINUOUS EVALUATION SYSTEM



The final grade will be distributed as follows:

The activities carried out during the course will account for 20% of the final grade. The remaining 80% will correspond to the written exam to be taken during the examination period of the call.



To pass the subject, a minimum may be required in each part assessed.



If the part of the previous activities carried out during the course in the continuous assessment is not approved, it will be considered that the continuous assessment is waived (and that the final assessment is chosen) and it will not be necessary to expressly request the waiver.



If you approve this part of the previous activities carried out during the course and you wish to waive the continuous assessment, you must request in writing to the teacher the waiver of the continuous assessment (and that the final evaluation is chosen) before the end of the last week of classes.



If this part of the previous activities carried out during the course is approved and remains in the continuous assessment, the final grade of the ordinary call will be the sum of the grade of the previous activities plus the mark of the written exam of the ordinary call.

(II) FINAL EVALUATION SYSTEM



In the final evaluation system, 100% of the grade will correspond to the written exam to be taken in the exam period of the call.



In either of the two evaluation systems, those who do not take the final written exam will obtain a final grade of "Not Presented" regardless of whether or not they have completed the rest of the tasks.



The use of a calculator will not be allowed in the written tests.

In the extraordinary call, 100% of the grade will correspond to a final test that will consist of a written exam to be taken during the examination period of the call.



Those who do not appear for the final written exam will obtain a final grade of "Not Presented" regardless of whether or not they have completed the rest of the tasks.



The use of a calculator will not be allowed in the written tests.

Material published in eGela.

Basic bibliography

Beitia, M.B.; Besga, M. C.; Cabezas, J. M. y Pastor, E. "Fundamentos Matemáticos de la Ingeniería II: Álgebra Lineal. Resumen teórico y problemas".

Servicio editorial de la U.P.V. / E.H.U.



J.L. Malaina y otros. "Lecciones Básicas de Álgebra Lineal".

Servicio editorial de la U.P.V. / E.H.U.

In-depth bibliography

Blanco M. F. y Reyes M. E. "Problemas de Álgebra Lineal y Geometría".
Ed. Universidad de Valladolid

De Burgos, J. "Álgebra Lineal".
Ed. Mc. Graw-Hill

Iglesias Martín, M.A. "Trigonometría Esférica. Teoría y problemas resueltos".
Ed. UPV/ EHU

Rojo, J. y Martín, I. "Ejercicios y problemas de Álgebra Lineal".
Ed. Mc. Graw-Hill

Strang, G. "Álgebra Lineal y sus aplicaciones".
Ed. Addison-Wesley

De la Villa, A. "Problemas de Álgebra".
Ed. CLAGSA

Web addresses

http://www.vc.ehu.es/matematicaaplicada/
http://thales.cica.es/rd/Recursos/rd99/ed99-0289-02/ed99-0289-02.html
http://www.matematicastyt.cl/Algebra_Lineal/Inicio.htm
http://www.walter-fendt.de/m14s/index.html