In order to achieve the learning objectives, the students should have the knowledge and skills that their previous education provides to their access to the University training:
- Knowledge: geometry, basic trigonometry, basic mathematical operations (power, logarithms, fractions, etc.), polinomials, matrices, derivation, integration and graphical
representation of elementary functions.
- Basic skills in the managment of instrumentation: elementary use of computers and mathematical software.
Industrial engineers are professionals who use knowledge of physical and mathematical sciences and engineering techniques to develop his professional activity in aspects such as control, instrumentation an automation of processes and equipment, as well as design, construction, operation and maintenance of industrial products. This training allows them to participate succesfully in the different branches integrated in industrial engineering, such as mechanics, electricity, electronics, etc. It also make them adopt the changes of technologies in these areas, where appropriate, to respond to the needs that arise in the productive branches and services, so achieving the welfare of society.
Within the mathematical knowledge, the methods developed in the course of Algebra have revealed as the most adequate for the modern treatment of many disciplines including in the curriculum. Such disciplines will allow industrial engineers to face real problems that they can find at work.
Therefore, this subject is an essential part of the basic training of future engineers. Its main purpose is to provide students the algebraic and geometric resources to solve problems concerning maths and engineering. In this sense, this subject will help them to enhance the capacities of abstraction, understanding, analysis, implementation and synthesis that are common in mathematics and neccesary to any other scientific discipline or branch of engineering.
| Course competences | |
|---|---|
| Code | Description |
| A01 | To understand and have knowledge in an area of study that moves on from the general education attained at secondary level and usually found at a level that, while supported in advanced text books, also includes some aspects that include knowledge found at the cutting edge of the field of study. |
| A02 | To know how to apply knowledge to work or vocation in a professional manner and possess the competences that are usually demonstrated by the formulation and defence of arguments and the resolution of problems in the field of study. |
| A03 | To have the capability to gather and interpret relevant data (normally within the area of study) to make judgements that include a reflection on themes of a social, scientific or ethical nature. |
| A07 | Knowledge of Information Technology and Communication (ITC). |
| A08 | Appropriate level of oral and written communication. |
| A12 | Knowledge of basic materials and technologies that assist the learning of new methods and theories and enable versatility to adapt to new situations. |
| A13 | Ability to take the initiative to solve problems, take decisions, creativity, critical reasoning and ability to communicate and transmit knowledge, skills and abilities in Mechanical Engineering. |
| A17 | Ability to apply principles and methods of quality control. |
| B01 | Ability to solve mathematical problems that occur in engineering. Aptitude to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial differential equations; numerical methods; numerical algorithms; statistics and optimization. |
| Course learning outcomes | |
|---|---|
| Description | |
| Be able to express yourself correctly both orally and in writing, and, in particular, to know how to use mathematical language to express with precision quantities and operations that appear in industrial engineering. Become accustomed to working in a team and behaving respectfully. | |
| To know the theory of matrices and determinants and to know how to carry out the corresponding calculations. Know the fundamentals and applications of Lineal Algebra and Euclidean Geometry | |
| To know how to use and carry out elementary operations with complex numbers. | |
| Know the main approaches for resolution through using numerical methods, to use some statistical software packages at user level, data processing, mathematical calculus and vizualization, set out algorithms and program through programming language of a high level, vizualize functions, geometric figures and data, design experiments, analyze data and interpret results | |
| Additional outcomes | |
| Description | |
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Unit 1: COMPLEX NUMBERS
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Unit 1.1: The complex numbers system.
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Unit 1.2: Geometric representation of the complex numbers: modulus and arguments
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Unit 1.3: Trigonometric and polar form of a complex number
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Unit 1.4: Powers and roots of a complex number
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Unit 2: MATRICES AND DETERMINANTS
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Unit 2.1: Matrices: some related definitions
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Unit 2.2: Rank of a matrix
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Unit 2.3: Non-singular matrices. Calculation of the inverse matrix.
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Unit 2.4: Determinant of a matrix
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Unit 2.5: Properties of the determinants
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Unit 2.6: Application to the calculation of the rank and the inverse matrix
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Unit 3: SYSTEMS OF LINEAR EQUATIONS
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Unit 3.1: Systems of linear equations: some related definitions
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Unit 3.2: Rouché-Frobenius theorem.
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Unit 3.3: Solving systems of linear equations with algebraic and direct methods
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Unit 3.4: Numerical algebra
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Unit 3.5: Iterative methods
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Unit 3.6: Jacobi method
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Unit 3.7: Gauss-Seidel method
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Unit 4: VECTOR SPACES
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Unit 4.1: The algebraic structure of a vector space
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Unit 4.2: Vector subespaces. Subespaces operations
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Unit 4.3: Linear dependence and independence
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Unit 4.4: Basis and dimension of a vector space
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Unit 4.5: Rank of a vector system
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Unit 4.6: Vector varieties
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Unit 4.7: Equations of subespaces and varieties
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Unit 4.8: Equations of a change of basis
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Unit 5: LINEAR MAPS
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Unit 5.1: Linear maps and related concepts
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Unit 5.2: Linear maps operatiions
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Unit 5.3: Kernel, Image and character of a linear map
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Unit 5.4: Rank of a linear map
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Unit 5.5: Equations and matrices associated with a linear map
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Unit 5.6: Equations and matrices associated with a change of basis in linear map
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Unit 6: DIAGONALIZATION
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Unit 6.1: Eigenvalues and Eigenvectors
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Unit 6.2: Characteristic Polinomial
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Unit 6.3: Diagonalization of an endomorphism
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Unit 6.4: Digonalization of a square matrix
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Unit 6.5: Application to the calculation of a power of matrix
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Unit 6.6: Jordan canonical form
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Unit 7: EUCLIDEAN SPACES AND ORTHOGONAL TRANSFORMATIONS
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Unit 7.1: Inner products and Euclidean spaces
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Unit 7.2: Euclidean norm
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Unit 7.3: Euclidean distance
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Unit 7.4: Orthogonality and orthonormality: orthogonal and orthonormal basis
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Unit 7.5: Gramm-Schmidt orthogonalization
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Unit 7.6: Orthogonal projections
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Unit 8: GEOMETRY. AFFINE SPACES
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Unit 8.1: Geomtry in affine spaces
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Unit 8.2: Geometry in affine and Euclidean spaces
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Unit 9: DIFFERENCE EQUATIONS
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Unit 9.1: Introduction
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Unit 9.2: Classification
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Unit 9.3: Solving difference equations
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Unit 9.4: Modeling with difference equations
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| Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | Description | |
| Class Attendance (theory) [ON-SITE] | Lectures | A01 A02 A03 A07 A12 B01 | 1 | 25 | Y | N | ||
| Problem solving and/or case studies [ON-SITE] | Problem solving and exercises | A02 A07 A13 B01 | 0.6 | 15 | Y | N | ||
| Computer room practice [ON-SITE] | Practical or hands-on activities | A02 A07 B01 | 0.3 | 7.5 | Y | N | ||
| Progress test [ON-SITE] | Assessment tests | A01 A12 B01 | 0.1 | 2.5 | Y | N | ||
| Writing of reports or projects [OFF-SITE] | Group Work | A01 A02 A03 A07 A08 A12 A13 A17 B01 | 0.54 | 13.5 | Y | N | ||
| Study and Exam Preparation [OFF-SITE] | Self-study | A02 A08 A12 A13 A17 B01 | 3.06 | 76.5 | Y | N | ||
| Group tutoring sessions [ON-SITE] | Group tutoring sessions | 0.2 | 5 | Y | N | |||
| Workshops or seminars [ON-SITE] | Workshops and Seminars | A01 A02 A03 A08 A13 A17 B01 | 0.1 | 2.5 | Y | N | ||
| Final test [ON-SITE] | Assessment tests | A01 A02 A03 A07 A08 A12 A13 A17 B01 | 0.1 | 2.5 | Y | Y | ||
| Total: | 6 | 150 | ||||||
| Total credits of in-class work: 2.4 | Total class time hours: 60 | |||||||
| Total credits of out of class work: 3.6 | Total hours of out of class work: 90 | |||||||
As: Assessable training activity Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).
| Evaluation System | Continuous assessment | Non-continuous evaluation * | Description |
| Progress Tests | 40.00% | 0.00% | |
| Final test | 50.00% | 90.00% | |
| Theoretical papers assessment | 10.00% | 10.00% | |
| Total: | 100.00% | 100.00% |
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Continuous assessment:Evaluation criteria not defined
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Non-continuous evaluation:Evaluation criteria not defined
| Not related to the syllabus/contents | |
|---|---|
| Hours | hours |
| Class Attendance (theory) [PRESENCIAL][Lectures] | 25 |
| Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] | 15 |
| Computer room practice [PRESENCIAL][Practical or hands-on activities] | 7.5 |
| Progress test [PRESENCIAL][Assessment tests] | 2.5 |
| Writing of reports or projects [AUTÓNOMA][Group Work] | 13.5 |
| Study and Exam Preparation [AUTÓNOMA][Self-study] | 76.5 |
| Group tutoring sessions [PRESENCIAL][Group tutoring sessions] | 5 |
| Workshops or seminars [PRESENCIAL][Workshops and Seminars] | 2.5 |
| Final test [PRESENCIAL][Assessment tests] | 2.5 |
| Global activity | |
|---|---|
| Activities | hours |
