Linear algebra is the branch of mathematics concerning vector spaces, linear transformations between such spaces, systems of linear equations and matrices.



Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science and social sciences.



In this course we are going to develop some concepts that will be assumed to be known by the students.

Algebra.

1. Develop the knowledge in Algebra to solve problemas related to Engineering.

2. Apply algebraic procedures to solve Engineering problemas such as cuantitative analysis, employ mathematical terminology, make abstraction, construct hypothesis, apply and interpret mathematical results and writing a mathematical proof.

3. Employ computer sources based on the Algebraic knowledge to solve Engineering problems.

4. Follow the right steps to solve problems applying the algebraic procedures, concepts and results.

5. Have a responsible behaviour, being organized and self-sufficient.

1 lesson: Vector subspaces.

Subspaces. Linear Independence. Basis and dimension. Coordinates and change of basis. Operations between vector spaces.

2 lesson: Linear transformations.

The null space and range. Special linear transformations. Construction of a linear transformation.

3 lesson: Matrices.

Operations with Matrices. Change of basis matrix. Matrix representation of a linear transformation.

4 lesson: Determinants.

Determinants properties. Calculus of a determinant. Rank of a matrix.The inverse of a square matrix.

5 lesson: systems of linear equations.

Solution Sets of Linear Systems. Methodologies for solving llinear systems. Applications.

6 lesson: Inner Product spaces.

Norm and Orthogonality. Orthogonal basis.

7 lesson: Diagonalization of square matrices..

Diagonalization of Symmetric Matrices.Orthogonal diagonalization.

8 lesson: Conics and quadric surfaces

Reduced equations.

Master classes, classroom practices and computer lessons will be the followed methodology. The timetable will be fixed by the School.



Computer lessons will take place in the Faculty of Engineering (Gipuzkoa) labs.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 70
  • Realization of Practical Work (exercises, cases or problems) (%): 10
  • Individual works (%): 20

The evaluation will be carried out according to the article number 8 of the "Normativa reguladora de la evaluación del alumnado en las titulaciones oficiales de grado". The evaluation will be continous with tasks and activities carried out along the term. This evaluation will be completed with a final exam that will be held in the exams period.



The tasks and activities will be the following:

Computer lab:

A computer exam will be done for evaluating the computer lessons carried out along the term.



Occasional evaluation of the learning process:

Suggested exercises will be collected by the professor. Exercises will be individual, and if a student does not give the exercise to the professor the mark will be a 0.



Writing exam:

The exam will consist of theorical questions and with issues related to computer lessons.



Marks:

%10 computer lessons.

%20 occasional evaluation of the learning process.

%70 writting exam.



According to the article 8.3, if a student wants to be evaluated by the system of final evaluation, regardeless his participation in the continuous evaluatiaon, he must give to the responsible lecturer a resignation letter during. For that, the students have a period of 9 weeks starting from the beginning of the term. In this case, the final evaluation will consist of a writing exam (85%) and a computer exam (15%).



The students that does not take the exam will have a "NO PRESENTADO".



During the development of an evaluation test, the use of books, notes, as well as phones, electronic devices, computer, calculator or other devices is forbidden for students. If necessary, the places where unauthorized materials can be deposited can be signaled so that they are out of reach of students.

Writing exam: The exam will consist of theorical questions and with issues related to computer lessons(100%).

The lecturer will give to the students the necessary material.

Basic bibliography

S. Lang (1990). Algebra Lineal. México, Addison-Wesley Iberoamericana.

J.C. Del Valle Sotelo (2012). Álgebra lineal para estudiantes de ingeniería y

ciencias. Mexiko: McGraw-Hill.

D.C. Lay (2001). Álgebra lineal y sus aplicaciones.

Addison-Wesley/Longman/Pearson.

G. Nakos, D. Joyner (1999). Álgebra lineal con aplicaciones. Barcelona, Thomson.

J. Rojo, I. Martin (1994). Ejercicios y problemas de álgebra lineal. Madrid.

McGraw-HIll.

C. Alcalde, M. C. Caballer (1994). Algebra Lineala. Azterketetako Problema

Ebatziak. Donostia, Elkar

J. Arvesú, F. Marcellán, J. Sánchez (2005). Problemas resueltos de Algebra

Lineal. Madrid, Thomson/Paraninfo.

J. Burgos (1999). Álgebra Lineal. Madrid: MCGraw-Hill.

S. I. Grossman (1996). Álgebra Lineal con aplicaciones. México: McGraw-Hill.

E. Hernández (1994). Álgebra y Geometría. México: Addison-Wesley/UAM.

In-depth bibliography

T. Garcia, A. Ruiz, M. Sainz (1993). Álgebra. Teoría y ejercicios. Madrid,
Thomson.
W. K. Nicholson (2003). Álgebra lineal. Madrid, McGraw-Hill.
B. Kolman (1997). Introductory linear algebra with applications. Prentice-Hall.
I. Kostrikin (1992). Introducción al Álgebra Lineal. Madrid, McGraw-Hill.
J.L. Malaina, A. Gallego, M. L. González, E. Martín (1992). Lecciones básicas de
Álgebra Lineal. Bilbo, EHUko Argitalpen Zerbitzua.
D. Poole (2004). Álgebra Lineal. Una introducción moderna. Madrid, Thomson.
G. Williams (1999). Álgebra Lineal y sus aplicaciones. México, Wm. C. Brown
Publishers.

Web addresses

http://sourceforge.net/projects/wxmaxima/
http://maxima.sourceforge.net/es/documentation.html
http://www.telefonica.net/web2/biomates/maxima/max.pdf
http://www.moodle.ehu.es/moodle
http://mathworld.wolfram.com/topics/LinearAlgebra.html