To achieve the learning objectives of the subject, knowledge and skills are required that are supposed to be guaranteed in the training prior to access to the University. In particular, it is recommended to have basic knowledge of geometry, algebra and trigonometry, elementary mathematical operations (powers, logarithms, exponentials, fractions...), elementary knowledge of differentiation and integration of real functions of real variables and fundamentals of graphical representation of functions.
The mathematical concepts that are studied in this subject provide an essential tool and constitute a precise language that is later used by most of the basic and advanced subjects of Chemical Engineering. Everything related to matrices, algebraic systems of equations and all the methods studied in this subject appear in the study, synthesis, development, design, operation and optimization of industrial processes that produce physical, chemical and/or biochemical changes in materials. dealing with chemical engineering. Algebra is present in the planning and development of all experimental, academic and professional activities in Chemical Engineering.
Course competences | |
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Code | Description |
CB01 | Prove that they have acquired and understood knowledge in a subject area that derives from general secondary education and is appropriate to a level based on advanced course books, and includes updated and cutting-edge aspects of their field of knowledge. |
CB02 | Apply their knowledge to their job or vocation in a professional manner and show that they have the competences to construct and justify arguments and solve problems within their subject area. |
CB03 | Be able to gather and process relevant information (usually within their subject area) to give opinions, including reflections on relevant social, scientific or ethical issues. |
CB04 | Transmit information, ideas, problems and solutions for both specialist and non-specialist audiences. |
E01 | Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge about: linear algebra; geometry; differential geometry; differential and integral calculation; differential equations and partial derivatives; numerical methods; numerical algorithm; statistics and optimization. |
G03 | Ability to solve problems with initiative, decision making, creativity, critical reasoning and to communicate and transmit knowledge, skills and abilities in the field of Chemical Engineering. |
G12 | Knowledge of Information and Communication Technologies (ICT). |
G13 | Proper oral and written communication |
G14 | ethical commitment and professional ethics |
G17 | Synthesis capacity |
G19 | Ability to analyze and solve problems |
G20 | Ability to learn and work autonomously |
G22 | Creativity and initiative |
G26 | Obtaining skills in interpersonal relationships. |
Course learning outcomes | |
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Description | |
To know the theory of arrays and know how to carry out the corresponding calculations. | |
To know the main approaches for resolution using numerical methods, use at the user level some software packages of statistics, data processing, mathematical calculation and visualization, propose algorithms and program using a high-level programming language, visualize functions, geometric figures and data, design experiments, analyze data and interpret results. | |
To get used to teamwork, express yourself correctly orally and in writing in Spanish and English and behave respectfully. | |
To know the fundamentals of plane and spatial geometry. | |
To know how to use the language of Mathematics. | |
Additional outcomes | |
Description | |
The student will acquire knowledge about the theory of vector spaces, matrices and systems of algebraic equations and will know how to carry out the corresponding calculations. He will also know the fundamentals and applications of optimization. He will know the main approaches for resolution using numerical methods. She will use some mathematical calculation and visualization software packages at the user level, she will propose algorithms and program using a high-level programming language, she will visualize solutions and data and interpret the results. She will know how to apply this knowledge to Chemical Engineering problems. She will acquire the general knowledge of Algebra that will allow her to understand advanced algebraic methods and apply them in chemical engineering situations. She will be able to use, at the user level, some mathematical calculation and visualization software package to visualize solutions, program with a high-level programming language and to perform the necessary numerical calculations and symbolic operations. She will improve her ability to express herself correctly orally and in writing and, in particular, with the language of Algebra to accurately state the relationships, equations and operations that appear in Chemical Engineering, as well as solve and interpret them. She will be able, given a problem, to reason about the model and the mathematical method necessary for its resolution, as well as to interpret the results, which will be a key argument in her decision-making. She will develop her ability to work in a team by solving group problems in practical sessions and in the computer room. You will develop your ability to analyze and solve problems by approaching and solving the problems proposed in the seminar sessions, in the problem sheets, in the evaluations and in the bibliography. You will develop your ability to apply theoretical knowledge to practice by solving problems applied to chemical engineering. Solving problems in groups and with the help of the teacher in the practical and computer sessions by the students will allow them to practice and improve their interpersonal skills. |
Training Activity | Methodology | Related Competences (only degrees before RD 822/2021) | ECTS | Hours | As | Com | Description | |
Class Attendance (theory) [ON-SITE] | Lectures | CB02 CB03 CB04 E01 G03 | 0.72 | 18 | N | N | ||
Problem solving and/or case studies [ON-SITE] | Guided or supervised work | CB01 CB02 CB03 CB04 E01 G03 G13 G14 G17 G19 G20 G22 G26 | 0.94 | 23.5 | Y | N | ||
Computer room practice [ON-SITE] | Practical or hands-on activities | CB01 CB02 CB03 CB04 E01 G03 G13 G14 G17 G19 G20 G22 G26 | 0.32 | 8 | Y | Y | ||
Progress test [ON-SITE] | Assessment tests | CB01 CB02 CB03 CB04 E01 G03 G14 G17 G20 G22 | 0.08 | 2 | Y | N | ||
Progress test [ON-SITE] | Assessment tests | CB01 CB02 CB03 CB04 E01 G03 G14 G17 G20 G22 | 0.12 | 3 | Y | N | ||
Final test [ON-SITE] | Assessment tests | CB01 CB02 CB03 CB04 E01 G03 G13 G14 G17 G20 G22 | 0.12 | 3 | Y | Y | ||
Study and Exam Preparation [OFF-SITE] | Self-study | G12 | 3.6 | 90 | N | N | ||
Project or Topic Presentations [ON-SITE] | CB01 CB02 CB03 CB04 E01 G03 G14 G17 G19 G20 G22 G26 | 0.1 | 2.5 | Y | N | |||
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 |
Assessment of active participation | 1.00% | 0.00% | Attendance and active participation in all presential activities of the subject will be valued positively. |
Theoretical papers assessment | 1.00% | 0.00% | Theoretical team work to be presented in class |
Final test | 0.00% | 90.00% | There will be an exam with all the material or the partial failing. It will be valued: 1. Correction of the problem statement 2. Correction of the solution 3. Correction of written expression Concept errors and errors in basic mathematical operations will imply penalties. The subject will be passed if the final grade is equal to or greater than 5. It is necessary to obtain a minimum grade of 4 for the partial exams and the computer test to be considered compensable. |
Progress Tests | 18.00% | 0.00% | It will be valued 1. Correction of the problem statement. 2. Correction of the solution. 3. Correction of written expression. Concept errors and errors in basic mathematical operations will imply penalties. |
Test | 70.00% | 0.00% | It will be valued 1. Correction of the problem statement. 2. Correction of the solution. 3. Correction of written expression. Concept errors and errors in basic mathematical operations will imply penalties. You need to get a note minimum of 4 for the partial exams and the computer test to be considered compensable. |
Assessment of activities done in the computer labs | 10.00% | 10.00% | It will be valued 1. Attendance and active participation. 2. Correction of the approach to the problem/practice. 3. Solution correction and resolution method. You need to get a note minimum of 4 for the partial exams and the computer test to be considered compensable. |
Total: | 100.00% | 100.00% |
Not related to the syllabus/contents | |
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Hours | hours |
Progress test [PRESENCIAL][Assessment tests] | 4 |
Final test [PRESENCIAL][Assessment tests] | 3 |
Unit 1 (de 6): Algebra foundations | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4 |
Problem solving and/or case studies [PRESENCIAL][Guided or supervised work] | 2 |
Computer room practice [PRESENCIAL][Practical or hands-on activities] | 2 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 12 |
Unit 2 (de 6): Numerical methods in algebra | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 5 |
Problem solving and/or case studies [PRESENCIAL][Guided or supervised work] | 2 |
Computer room practice [PRESENCIAL][Practical or hands-on activities] | 4 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 16 |
Unit 3 (de 6): Vector spaces | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 6 |
Problem solving and/or case studies [PRESENCIAL][Guided or supervised work] | 3 |
Computer room practice [PRESENCIAL][Practical or hands-on activities] | 1 |
Progress test [PRESENCIAL][Assessment tests] | 1 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 20 |
Unit 4 (de 6): Euclidean vector spaces | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4 |
Problem solving and/or case studies [PRESENCIAL][Guided or supervised work] | 2 |
Computer room practice [PRESENCIAL][Practical or hands-on activities] | 1 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 15 |
Unit 5 (de 6): Linear maps and matrices | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4 |
Problem solving and/or case studies [PRESENCIAL][Guided or supervised work] | 2 |
Computer room practice [PRESENCIAL][Practical or hands-on activities] | 1 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 15 |
Unit 6 (de 6): Eigenvalues and eigenvectors | |
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Activities | Hours |
Class Attendance (theory) [PRESENCIAL][Lectures] | 4 |
Problem solving and/or case studies [PRESENCIAL][Guided or supervised work] | 2 |
Computer room practice [PRESENCIAL][Practical or hands-on activities] | 2 |
Progress test [PRESENCIAL][Assessment tests] | 1 |
Study and Exam Preparation [AUTÓNOMA][Self-study] | 12 |
Global activity | |
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Activities | hours |
Author(s) | Title | Book/Journal | Citv | Publishing house | ISBN | Year | Description | Link | Catálogo biblioteca |
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http://matematicas.uclm.es/qui-cr | http://matematicas.uclm.es/qui-cr | ||||||||
http://www.gnu.org/software/octave | http://www.gnu.org/software/octave | ||||||||
A. de la Villa | Problemas de Álgebra | Madrid | CLAGSA | 1998 | |||||
García, J. | Álgebra lineal: sus aplicaciones en Economía, Ingeniería y otras Ciencias | Madrid | Delta Publicaciones | 2006 | |||||
García, J. y López, M. | Álgebra Lineal y Geometría | Alcoy | Marfil | 1989 | |||||
Hernández, E. | Álgebra y Geometría | Madrid | Addison-Wesley | 1994 | |||||
Herrero, H. y Díaz-Cano, A. | Informática aplicada a las Ciencias y a la Ingeniería con Matlab | Ciudad Real | ETSII-Ñ | 2000 | |||||
Lay, D.C. | Álgebra lineal y sus aplicaciones | Madrid | Prentice-Hall | 2001 | |||||
Mathews, J.H. y Fink, K.D. | Métodos Numéricos con Matlab | Madrid | Prentice-Hall | 1999 | |||||
Quarteroni, A. y Saleri, F. | Cálculo Científico con Matlab y Octave | Milán | Springer | 2006 |