## ALGEBRA

### Course

Code: 1226

Degree: Bachelor's in Mechanical Engineering

School of Engineering of Elche

Year: Year 1 of Bachelor's in Mechanical Engineering

Semester: Fall

Type: Core

Language: Spanish

ECTS credits: 6 Lecture: 3 Laboratory: 3 | Hours: 150 Directed: 60 Shared: 15 Autonomous: 75 |

Subject matter: Mathematics

Module: Core

Department: Statistics, Mathematics and Informatics

Area: APPLIED MATHEMATICS

Course instructors are responsible for the course content descriptions in English.

### Description

### Faculty

Name | Coordinator | Lecture | Laboratory |
---|---|---|---|

HERRANZ CUADRADO, MARIA VICTORIA | ■ | ||

SANCHEZ MARTINEZ, JOSE RAFAEL | ■ | ||

GARCIA BARBERA, ANTONIO MANUEL | ■ | ■ |

### Competencies and learning outcomes

#### General competencies

- Knowledge about basic and technological material that enable learning new methods and theories, providing versatility for adapting to new situations.

#### Specific competencies

- Capacity for solving mathematical problems that may arise in engineering. Aptitude for applying knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, differential equations and in partial derivatives, numerical methods, numerical algorithms, statistics, and optimization.

#### Objectives (Learning outcomes)

- 01Know the different kinds of matrices and its properties. Perform operations with vectors and matrices.
- 02Students will be able to use matrix techniques to represent and solve a system of simultaneous linear equations checking its nature previously
- 03Know and find the fundamental subespaces of a matrix.
- 04Understand the extension of vector concepts to abstract vector spaces of arbitrary finite dimension.
- 05Understand linear transformations, theirs matrix representations and applications.
- 06Understand the metric concepts of inner product, norm, orthogonality and orthogonal projection.
- 07Find and interpret the eigenvalues and eigenvectors of a linear transformation.
- 08Identify when a matrix is diagonalizable and find its diagonal form.
- 09Apply spectral techniques to solve engineering problems.

### Contents

#### Teaching units

#### Association between objectives and units

Objective/Unit | U1 | U2 | U3 | U4 | U5 |
---|---|---|---|---|---|

01 | |||||

02 | |||||

03 | |||||

04 | |||||

05 | |||||

06 | |||||

07 | |||||

08 | |||||

09 |

#### Schedule

Week | Teaching units | Directed hours | Shared hours | Autonomous hours | Total hours |
---|---|---|---|---|---|

1 | U1 | 2 | 0 | 8 | 10 |

2 | U1 | 4 | 0 | 6 | 10 |

3 | U1 | 2 | 0 | 8 | 10 |

4 | U2 | 6 | 2 | 2 | 10 |

5 | U2 | 4 | 0 | 6 | 10 |

6 | U2 | 4 | 2 | 4 | 10 |

7 | U2,U3 | 6 | 1 | 3 | 10 |

8 | U3 | 4 | 2 | 4 | 10 |

9 | U3 | 6 | 0 | 4 | 10 |

10 | U4 | 4 | 2 | 4 | 10 |

11 | U4 | 2 | 0 | 8 | 10 |

12 | U4 | 6 | 2 | 2 | 10 |

13 | U5 | 2 | 0 | 8 | 10 |

14 | U5 | 6 | 0 | 4 | 10 |

15 | 2 | 4 | 4 | 10 |

#### Basic bibliography

- Arvesú Carballo, Jorge. Marcellán Español, Francisco / Sánchez Ruiz, Jorge. "Problemas resueltos de álgebra lineal". Madrid Thomson-Paraninfo D.L. 2005.
- Aversú Carballo, Jorge. Alvarez Nodarse, Renato / Marcellán Español, Francisco. "Algebra lineal y aplicaciones". Madrid Síntesis 1999.
- Barbolla, Rosa. Sanz, Paloma. "Álgebra lineal y teoría de matrices". Madrid [etc.] Prentice Hall 1998.
- Burgos Román, Juan de. "Álgebra lineal". Madrid [etc.] McGraw Hill D.L.1996.
- Kolman, Bernard. Hill, David Ross , col. "Algebra lineal con aplicaciones y matlab". México [etc.] Prentice Hall 1999.
- Merino González, Luis M. Santos Aláez, Evangelina , coaut. "Álgebra lineal con métodos elementales". Granada [.s.n.] D. L. 1999.

#### Complementary bibliography

- Hill, David R. Zitarelli, David E. "Linear algebra labs with MATLAB". Upper Saddle River Prentice Hall [1996].
- McMahon, David (David M.). "Linear algebra demystified [electronic resource] /". New York : McGraw-Hill, c2006.
- McMahon, David (David M.). "MATLAB demystified [electronic resource] /". New York : McGraw-Hill, c2007.

#### Links

#### Software

- MATLAB2012B

### Methodology and grading

#### Methodology

**Lecture:**Pass on knowledge and activate cognitive processes in students, encouraging their participation.**Solving exercises and problems:**Exercise, test, and apply previous knowledge through routine repetition.

#### Grading

In February the student will be able to opt for a system of continuous evaluation or for a final evaluation.

**Continuous evaluation system:**

the final mark will be a weighted average according to the following percentages:

1) Continuous evaluation test (10%)

2) Matlab (15%): This takes place in the final practice session in the computer classroom. Consist of solving problems through the Maxima program.

3) Development exam (70%): theoretical and practical exam.

4) Monitoring of the tutorials (5%): The assistance at the problem workshops and / or participation in the class , seminars, tutorials, etc.**Final evaluation system**:The final mark will be a weighted average according to the following percentages:

1) Test (10%): consists of 10 questions, each with 4 options of which only one is correct. Each successful answer is 1 point of the final mark and each erroneous answer is -0.3 points. Blank questions neither add nor subtract.

2) Development exam (75%): theoretical and practical exam.

3) Matlab exam(15%): This will be done after the development exam.In order to pass the subject are required two conditions:

1) Obtain more than 4 points in the final exam.

2) Obtain a weighted average mark equal or higher than 5.For September and December exams, the evaluation is:

1) Development exam (75%)

2) Test type test (10%)

3) Matlab exam (15%): It will be done immediately after the development exam.

#### Correction criteria

Each problem or issue of both the development exams and the corresponding to practices, will be scored according to the quality of its approach and numerical resolution.