General information


Subject type: Basic

Coordinator: Rosa Herrero Antón

Trimester: Second term

Credits: 6

Teaching staff: 

Cristina Steegmann Pascual
Aïda Varea Espelt 

Teaching languages


  • Catalan

Skills


Basic skills
  • B1_That students have demonstrated knowledge and understanding in a field of study that is based on general secondary education, and is accustomed to finding at a level that, although with the support of advanced textbooks, also include some aspects that involve knowledge from the forefront of your field of study

  • B3_Students have the ability to gather and interpret relevant data (usually within their area of ​​study), to make judgments that include reflection on relevant social, scientific or ethical issues

  • B4_That students can convey information, ideas, problems and solutions to both specialized and non-specialized audiences

Specific skills
  • EFB1_Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge about: linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics and optimization

Transversal competences
  • T1_That students know a third language, which will be preferably English, with an adequate level of oral and written form, according to the needs of the graduates in each degree

Description


The subject enables the student to understand and / or solve mathematical problems, which may arise in engineering, related to linear algebra.

The classroom (physical or virtual) is a safe space, free of sexist, racist, homophobic, transphobic and discriminatory attitudes, either towards students or teachers. We trust that together we can create a safe space where we can make mistakes and learn without having to suffer the prejudices of others. 

Contents


Topic 1: Sets and applications 

  1. Sets
  2. Applications
  3. Laws of internal composition
  4. Functions

Topic 2: Principle of induction and complex numbers 

  1. Introduction to numbers
  2. Principle of induction
  3. Complex numbers: Origin and operations
  4. Polar form of complexes
  5. Trigonometric and exponential form
  6. Complex roots of an equation

Topic 3: Vectors, matrices and determinants

  1. arrays
  2. Operations with matrices
  3. determinants
  4. inverse matrix
  5. Gauss method
  6. Cramer's method
  7. Discussion and resolution of systems

Topic 4: Vector spaces and linear applications 

  1. Generalization of the vector concept
  2. Linear dependence of vectors. Bases
  3. Linear applications
  4. Diagonalization of a matrix

Topic 5: Affine geometry 

  1. affine space Linear varieties
  2. Parallelism and intersection 1
  3. Parallelism and intersection 2

 

Evaluation system


90% Tests
There will be two exams during the course (45% each exam), a first partial (first 3 topics) and a final exam made up of two parts. Those who have failed the first exam must take both parts in the final exam. Those who have passed the first part will only need to be evaluated for the second part in the final exam (the first part is subject-free, as long as a minimum grade of 5 points is obtained). A minimum grade of 4/10 is required on the second exam in order to average with the grade on the first exam. Students who fail the final exam will go to recovery with all or that part of the subject they have failed. The maximum grade for recovery is 6 points.

10% Presentation of deliverable individual exercises, non-refundable.

 

 

REFERENCES


Basic

Lay, David C; Murrieta Murrieta, Jesús Elmer (2007). Linear algebra and its applications. 3ª ed. Pearson Education

Holt, Jeffrey (2013). Linear Algebra with Applications. Freeman

Complementary

Castellet, M .; Llerena, I. (1988): Linear algebra and geometry. Bellaterra: Publications of the Autonomous University of Barcelona

Queysanne, Michel (1990). Basic Algebra. Vicens-Vives