The objective of the subject is to provide the fundamentals of matrix algebra, systems of linear equations, vector and normed spaces, and linear applications.



This subject is located within the Basic Training module, and it will apply previous knowledge acquired from the Science Bachelor's subjects on mathematics.

The topics covered within this course will be applied in several subjects of this degree, such as:

- Electric Circuits

- Differential Equations and Numerical Methods

- Statistics

- Fundamentals of Biomedical Image Processing

- Biomedical Image Processing

- Biomedical Equipment

COMPETENCIES



G003: Knowledge in basic and technological subjects, which enable to learn new methods and theories, and provide versatility to adapt to new situations.



T001: Ability to solve problems with initiative, decision making, creativity and critical reasoning, respecting the principles of universal accessibility and design for all people.



M01FB01: Ability to solve mathematical problems in engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; partial differential equations; differential equations; numerical methods; numerical algorithms; statistics and optimization.



LEARNING OUTCOMES



RAG5: The graduate will be able to identify the concepts and methods related to mathematics that are applicable in the field of engineering.



RAT1: The graduate will be able to solve problems with initiative, decision making, creativity and critical reasoning.

Topic 1: Matrix algebra and systems of linear equations

Topic 2: Vector spaces

Topic 3: Normed and Euclidean spaces

Topic 4: Linear transformations and endomorphisms

Topic 5: Diagonalization and triangularization of matrices by similarity transformations

Topic 6: Least squares fitting

LECTURES: During these sessions the main theoretical topics of the programme will be explained and developed, along with solved exercises. In general, there will be no distinction between “Lecture-based sessions” and “Applied classroom-based groups”. In order to further strengthen the understanding of the subject, students will have access to eGela, the official virtual classroom, where several additional media will be uploaded. These include video lectures, solved exercises and notes written by the professor in charge. Lastly, the professor will promote the use of mathematical software such as Wolfram Mathematica in order to integrate the hands-on computer sessions' concepts with the theoretical concepts taught during the lectures. This will also allow the students to solve the exercises proposed in class in an easy and efficient way.



SEMINARS: These sessions will serve a double objective. On the one hand, the most important aspects of each main topic will be reviewed, and several exercises will be proposed in order to strengthen the understanding of these concepts. On the other hand, these classes will also serve to assess teamwork aspects of the subject, either by turning in some exercises proposed by the professor, or by taking part in oral expositions about interesting exercises or related topics proposed beforehand.



COMPUTER LABORATORY SESSIONS: These classes will be used to introduce the students to Wolfram Mathematica. Students will be shown the basic commands of this program, in order to solve Linear Algebra exercises (though other problems from other subjects like Calculus I and II will also be tackled). The main goal of these practice sessions is to allow the student to solve higher difficulty problems with ease and autonomy. In order to do so, we will focus on using the software's documentation properly.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 55
  • Realization of Practical Work (exercises, cases or problems) (%): 30
  • Team projects (problem solving, project design)) (%): 15

ONGOING ASSESSMENT



- Computer-based exam: 15%

- Individual, periodic turn-ins (one per topic): 15%

- Teamwork and oral presentations (including seminars): 15%

- Individual written tests: 55% in total, distributed as follows:

- Topic 1: 10%

- Topic 2: 15%

- Topics 3-6 (during the ordinary examination period): 30%



In order to pass the subject and for the mark to be computed following the guidelines above, students will be required to achieve at least a mark of 2.5/10 in the ordinary examination call. Students who do not meet this criterium will be assessed with a maximum mark of 4.5/10 in GAUR, depending on the rest of the marks obtained throughout the course.



FINAL ASSESSMENT



Regardless of the above, any student may give up on the ongoing assessment. In that case, the subject will be assessed by a single in-person exam, which will be held on the official ordinary examination call. The marks of this final exam will be distributed as follows:



- Computer practice exam: 15%

- Written test corresponding to the topics covered in lectures and seminars: 85%

The subject will be assessed by a single in-person exam whose marks will be distributed as follows:



- Computer practice exam: 15%

- Written test corresponding to the topics covered in lectures and seminars: 85%



Regarding the assessment for the computer practice exam, students may choose to keep the mark they achieved on the computer practice exam for the ordinary call.

Basic bibliography

Linear Algebra: Course Notes. Dept. of Applied Mathematics (UPV/EHU)

In-depth bibliography

- Axler, S. (2015). Linear algebra done right. Springer
- Strang, G. (2016). Introduction to Linear Algebra, 5th Edition, Wellesley-Cambridge Press
- Lay, D. C., Lay, S. R., & McDonald, J. (2016). Linear algebra and its applications. Pearson Education
- Leon, S. J., De Pillis, L. G. (2006). Linear algebra with applications. Pearson Education
- Szabo, F. (2000). Linear Algebra with Mathematica: An Introduction Using Mathematica. Academic Press