Guías Docentes Electrónicas
1. General information
Course:
ALGEBRA
Code:
57704
Type:
BASIC
ECTS credits:
6
Degree:
344 - CHEMICAL ENGINEERING
Academic year:
2022-23
Center:
1 - FACULTY OF SCIENCE AND CHEMICAL TECHNOLOGY
Group(s):
21 
Year:
1
Duration:
First semester
Main language:
Spanish
Second language:
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer: HENAR HERRERO SANZ - Group(s): 21 
Building/Office
Department
Phone number
Email
Office hours
Margarita Salas/341
MATEMÁTICAS
926295412
henar.herrero@uclm.es
Wednesday from 6:00 p.m. to 8:00 p.m. Thursday from 4:00 p.m. to 8:00 p.m. Other hours by appointment

2. Pre-Requisites

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.

3. Justification in the curriculum, relation to other subjects and to the profession

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.


4. Degree competences achieved in this course
Course competences
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.
5. Objectives or Learning Outcomes
Course learning outcomes
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.
6. Units / Contents
  • Unit 1: Algebra foundations
    • Unit 1.1: Complex numbers
    • Unit 1.2: Matrices and determinants
    • Unit 1.3: Systems of linear euqtions
    • Unit 1.4: Computer practice. Scientific and technological applications
  • Unit 2: Numerical methods in algebra
    • Unit 2.1: Numerical solution of nonlinear equations
    • Unit 2.2: Numerical solution of systems of linear equations
    • Unit 2.3: Numerical solution of systems of nonlinear equations
    • Unit 2.4: Linear programming
    • Unit 2.5: Computer practice. Scientific and technological applications
  • Unit 3: Vector spaces
    • Unit 3.1: Vector space concept
    • Unit 3.2: Vector subspaces
    • Unit 3.3: Linear combination. Generator sets
    • Unit 3.4: Linear dependence and independence
    • Unit 3.5: Base, dimension and coordinates
    • Unit 3.6: Subspace equations. Operations with subspaces
    • Unit 3.7: Base change
    • Unit 3.8: Computer practice. Introduction to programming
  • Unit 4: Euclidean vector spaces
    • Unit 4.1: Scalar product. Euclidean vector space
    • Unit 4.2: Norms and angles
    • Unit 4.3: Orthogonality. Gram-Schmidt method. Orthogonal projection
    • Unit 4.4: Computer practice. Introduction to programming
  • Unit 5: Linear maps and matrices
    • Unit 5.1: Linear application
    • Unit 5.2: Kernel and image
    • Unit 5.3: Matrix representation
    • Unit 5.4: Operations
    • Unit 5.5: Base change
    • Unit 5.6: Computer practice. Introduction to programming
  • Unit 6: Eigenvalues and eigenvectors
    • Unit 6.1: Eigenvalues and eigenvectors of a matrix
    • Unit 6.2: Eigenvector subspaces
    • Unit 6.3: Diagonalization of matrices
    • Unit 6.4: Computer practice. Scientific and technological applications
7. Activities, Units/Modules and Methodology
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).

8. Evaluation criteria and Grading System
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%  
According to art. 4 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 12.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).

Evaluation criteria for the final exam:
  • Continuous assessment:
    There will be two progress tests, two partial exams and a computer test. 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. Midterm exams serve as recovery tests for progress. 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 so that the partial exams and the computer test are considered compensable.
  • Non-continuous evaluation:
    There will be an exam with all the material. The exam will consist of solving a series of exercises, which will constitute 90% of the grade, and a computer test for the remaining 10%. 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.

Specifications for the resit/retake exam:
If the student has not passed the subject in the ordinary call, he/she must take the exam in the extraordinary call with all the material or the partial fails. The exam will consist of solving a series of exercises, which will constitute 90% of the grade, and a computer test for the remaining 10%. 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 so that the partial exams and the computer test are considered compensable.
Specifications for the second resit / retake exam:
Evaluation criteria not defined
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
Hours hours
Progress test [PRESENCIAL][Assessment tests] 4
Final test [PRESENCIAL][Assessment tests] 3

Unit 1 (de 6): Algebra foundations
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
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
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
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
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
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
Activities hours
10. Bibliography and Sources
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
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  



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