Course code: 240101 |
Subject title: MATHEMATICS I |
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Credits: 6 |
Type of subject: Basic |
Year: 1 |
Period: 1º S |
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Department: Estadística, Informática y Matemáticas |
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Lecturers: |
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ASIAIN OLLO, MARÍA JOSÉ (Resp) [Mentoring ] | MILLOR MURUZABAL, NORA [Mentoring ] |

Vector spaces

Linear applications

Matrices and systems of linear equations

Diagonalization of square matrices

Euclidean vector space

Diagonalization of symmetric matrices

Aproximate solutions

Decompositions based of eigenvalues

**G8**Knowledge of basic and tecnological subjects to have the ability to learn new methods and theories, and versatility to adapt to new situations**G9**Problem solving proficiency with personal initiative, decision making, creativity and critical reasoning. Ability to elaborate and communicate knowledge, abilities and skills in computer engineering**T1**Analysis and synthesis ability**T3**Oral and written communication**T4**Problem solving**T8**Self-learning

**FB1**Ability to solve mathematical problems in engineering. Ability to apply theoretical knowledge on linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics and optimization

**FB3**Ability to understand and master the basic concepts of discrete matemathics, logic, algorithmics and computational complexity, and their applications to problem solving in engineering

- RA1 - Solve systems of linear equations using different methods based on Matrix decompositions (LU, QR, generalized inverse).
- RA2 - Make matrix representations of plane and space transformations, proyections, and orthogonal proyections onto subspaces
- RA3 - Diagonalize matrices through fundamental subspaces.
- RA4 - Use matrix diagonalization to study stochastic processes (Markov chains).
- RA5 - Find the singular value descomposition of a given matrix and use it to approximate systems of linear equations by the pseudo-inverse matrix.
- RA6 - Find the least-squares polynomial approximation to a function.
- RA7 - Use some symbolic computation software such as Matlab or Mathematica.

Methodology - Activity | Attendance | Self-study |

A-1 Lectures | 46 | |

A-2 Practical clases | 14 | |

A-3 Self-study | 75 | |

A-4 Exam, evaluation tests | 5 | |

A-5 Office hours | 10 | |

Total | 75 | 75 |

Learning outcome |
Assessment activity |
Weight (%) |
It allows test resit |
Minimum required grade |
---|---|---|---|---|

RA1 - RA7 | Theoretical and practical exam concepts of vectorial space, linear application, matrices and systems of equations | 55 | Yes | |

RA1 - RA7 | Theoretical and practical exam concepts of values and eigenvectors, diagonalization and approximation of solutions | 35 | Yes | |

RA1 - RA7 | Tests at home and class | 10 | Yes |

**Lesson 1**.- Sets, applications and relationships. Operations. Consistencies. Definitions of ring and body.

**Lesson 2**.- Vector spaces. Linear combinations. Linear dependence and independence. Vector subspaces. Bases and dimensions.

**Lesson 3**.- Linear applications. Core and image. Construction of linear applications.

**Lesson 4**.- Matrices. Elemental operations, range and form of Hermite. Matrix equivalence. Systems of linear equations: Rouché-Frobenius theorem. Generalized inverse.

**Lesson 5**.- Eigenvalues and eigenvectors. Diagonalization of square matrices.

**Lesson 6**.- Scalar product. Norm of a vector. Angle between two vectors. Euclidean vector space. Orthogonal and orthonormed bases. Orthogonal projection. Orthogonal matrices. Diagonalization of symmetric matrices.

**Lesson 7**.- Approximate solutions of a system of equations. Applications.

**Access the bibliography that your professor has requested from the Library.**

- J. Hefferon,
*Linear Algebra,*Virginia Commonwealth University Mathematics 2009 - D. C. Lay,
*Linear Algebra and its applications*, Pearson Education 2006 - D. J. S. Robinson,
*A course in Linear Algebra with applications*, World Scientific - R. A. Adams:
*Calculus. A complete course.*Addison Wesley - Larson,
*Calculus of a Single Variable,*10th Edition, Brooks/Cole, Cengage Learning 2014 - S.L. Salas, E. Hille and Etgen,
*Calculus*, Reverté