The subject of ALGEBRA is a subject in the first term of the first year and has 6 ECTS credits. The face-to-face classes are divided into four types: lectures (30 hours), classroom practice (8 hours), seminars (7 hours) and computer practice (15 hours). In addition to the classes, students will have to work 45 hours of lectures, 12 hours of classroom practice, 10.5 hours of seminars and 22.5 hours of computer practice.

Knowledge or Content:

RCO1: The graduate will be capable of identifying concepts and techniques from basic and specific subjects that allow the learning of new methods, theories, and modern engineering tools, providing sufficient versatility to adapt to new situations in their professional practice.

RCO5: The graduate will be able to identify concepts and methods related to mathematics that are applicable in the field of engineering.



Competencies:

RC4: The graduate will be capable of applying the strategies inherent to the scientific methodology: analyzing problematic situations both qualitatively and quantitatively, formulating hypotheses and solutions using models specific to renewable energy engineering.



Skills or Abilities:

HE1: The graduate will be capable of solving problems with initiative, decision-making, creativity, and critical reasoning.

HE5: The graduate will be capable of working effectively in a team constructively, integrating skills and knowledge to make decisions.

HE6: The graduate will be capable of acquiring new knowledge and skills for continuous learning, as well as pursuing further studies, with a high degree of autonomy.



Learning outcomes of the subject:

- Analyses and expresses ideas correctly making use of mathematical terminology.

- Knows how to discuss and solve a system of linear equations.

- Calculates the matrix associated to a linear application in different bases.

- Distinguishes a diagonalisable matrix from a non-diagonalisable matrix.

- Performs the diagonalisation process.

- Is able to apply acquired knowledge of geometry.

Topic 1: Matrices.

Matrices. Types of matrices. Operations. Operations. Properties.



Topic 2: Determinants.

Determinant of a square matrix. Properties. Inverse matrix. Orthogonal matrix. Rank of a matrix.



Topic 3: Systems of linear equations.

Systems of linear equations. Equivalent systems. Classification. Cramer's systems. Rouché-Fröbenius theorem. Homogeneous systems.



Topic 4: Vector spaces. Linear applications.

Structure of vector space. Vector subspace. Bases and dimension of a vector space. Coordinates of a vector. Change of basis matrix Linear applications Kernel and image. Classification. Matrix equation of a linear application. Matrices associated in different bases to the same linear application.



Topic 5: Euclidean and affine Euclidean vector space.

The affine space. Scalar product. Euclidean vector space. Orthogonal and orthonormal bases. Expression of the scalar product and the norm in an orthonormal basis. Euclidean affine space. Vector and mixed product. Applications. Equation of the straight line and plane in space. Relative positions. Bundle of planes containing a given line. Angles and distances.



Topic 6: Diagonalisation

Eigenvalue and eigenvector. Characteristic equation. Calculation of eigenvalues and eigenvectors. Diagonalisation of matrices. Diagonalisation of symmetric matrices.



Topic 7: Conics and quadrics.

Conics and quadrics

Geometric places. Calculation of the reduced equation of a conic. Calculation of the reduced equation of a quadric.

The subject will follow a methodology characterised by the following aspects:

Preliminary work: students will carry out the tasks indicated by the teacher, in a non-presential manner.

In class: the teacher will propose various training activities. Among others, doubts that have arisen from the previous work will be resolved.

Deliverables and tests: students will hand in the deliverables and take the tests indicated by the teacher and will be given the corresponding feedback.





In terms of assessment, the tools and grading percentages are as follows:

Final exam: 75%. (It can be advanced by up to 15% through various activities.)

Computer practicals: 25%.

Note: It is necessary to obtain at least a 4/10 in both parts, the final exam and computer practicals.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 75
  • Realization of Practical Work (exercises, cases or problems) (%): 25

Article 8.

In any case, students shall have the right to be assessed by means of the final assessment system, regardless of whether or not they have participated in the continuous or mixed assessment system. To do so, students must submit a written waiver of continuous or mixed assessment to the lecturer responsible for the subject, for which they will have a period of 9 weeks from the beginning of the four-month period, in accordance with the academic calendar of the centre. In this case, the student will be assessed with a single final exam, which will include a theoretical and practical part, and which will comprise 100% of the mark.



Article 12. Waiver of the exam

12.2.- In the case of continuous assessment, if the weight of the final exam is higher than 40% of the grade of the subject, it will be enough not to take the final exam for the final grade of the subject to be no-show or no-show. Otherwise, if the weight of the final exam is equal to or less than 40% of the grade for the subject, students may waive the exam within a period of at least one month before the end of the teaching period for the corresponding subject. This waiver must be submitted in writing to the lecturer responsible for the subject.

Article 9

The assessment of the subjects in the extraordinary exams will be carried out exclusively through the final assessment system.



The final assessment test of the extraordinary call will consist of as many exams and assessment activities as are necessary to be able to assess and measure the defined learning outcomes, in a way that is comparable to how they were assessed in the ordinary call. The positive results obtained by students during the course may be retained.

Workbook

Basic bibliography

J.L. MALAINA Y OTROS. Lecciones de álgebra lineal y geometría. Servicio editorial de la U.P.V.

A. LUZARRAGA. Problemas resueltos de álgebra lineal. Ed. Planograf.

IÑAKI ZURUTUZA. Oinarrizko Aljebra. Elhuyar.

J.L.MALAINA Y A.I.MARTÍN. Fundamentos matemáticos con Mathematica. Servicio editorial de la U.P.V.

M.GOLUBITSKY, M. DELLNITZ (2001). Algebra lineal y ecuaciones diferenciales con uso de Matlab. Madrid. Thomson.

In-depth bibliography

J.V. PROSKURIAKOV. Problemas de álgebra lineal. Ed. Mir.
F.GRANERO. Álgebra y geometría analítica. Ed. Mc. Graw-Hill.
J.ARVESÚ, F. MARCELLÁN, J.SANCHEZ (2005). Problemas resueltos de Algebra Lineal. Madrid, Thomson Paraninfo.

Journals

LA GACETA DE LA REAL SOCIEDAD MATEMATICA ESPAÑOLA.

Web addresses

http://www.divulgamat.net
http://www.hiru.com