Study programme competencies |
Code
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Study programme competences
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A1 |
Capacidade para a resolución dos problemas matemáticos que se poden presentar na enxeñaría. Aptitude para aplicar os coñecementos sobre: álxebra linear; cálculo diferencial e integral; métodos numéricos; algorítmica numérica; estatística e optimización. |
B3 |
Capacidade de análise e síntese |
Learning aims |
Learning outcomes |
Study programme competences |
Being able to analyze functions of a real variable:
- Limits , continuity, differentiation, optimization and graphical representation
- Definite and indefinite integration and its application to the calculation of areas and volumes , as well as solving differential equations. |
A1
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B3
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Being able to use a computer application of symbolic and computational calculus for the development of the contents of the subject |
A1
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B3
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Contents |
Topic |
Sub-topic |
Sets of numbers |
Classic sets of numbers
Complex numbers |
Real valued functions of one real variable |
Basic definitions
Elementary functions
Limits
Continuity
Bisection method
Lagrange interpolation polynomial |
Derivation |
Definition of derivative and basic properties
Newton-Raphson method
Higher order derivatives
Applications of derivatives
Convexity and concavity
Taylor's theorem |
Integration |
Indefinite integration
Riemann integration
Fundamental Theorem of Calculus
Numerical integration
Improper integration
Applications of integration
Differential equations |
Pyhton for one variable calculus |
SymPy introduction
Limits and continuity in Sympy
NumPy introduction
Graphics with Matplotlib
Derivation in Python
Integration in Python |
Planning |
Methodologies / tests |
Competencies |
Ordinary class hours |
Student’s personal work hours |
Total hours |
Laboratory practice |
A1 B3 |
18 |
18 |
36 |
Guest lecture / keynote speech |
A1 B3 |
30 |
60 |
90 |
Seminar |
A1 B3 |
9 |
9 |
18 |
Objective test |
A1 B3 |
0 |
3 |
3 |
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Personalized attention |
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3 |
0 |
3 |
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(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. |
Methodologies |
Methodologies |
Description |
Laboratory practice |
- The use of the software package Octave, which will be used in the subject for symbolic and numerical computation, will be taught .
- Problems related to the subject will be solved using Octave |
Guest lecture / keynote speech |
- Presentations in (previously provided to students) containing the basic notes to follow the development of the subject, will be maid using a projector
- Short videos will be used to illustrate some key points in the development of the subject, both in the theoretical and practical parts. |
Seminar |
- Doubts of the students will be resolved, as well as works and exercises from the problem sets, previously available, or others proposed by the teacher or the students. For this, when necessary, the software explained in the laboratory practices will be used.
- In some seminars the possibility of carrying out, on a voluntary basis, a project linked to the Sustainable Development Goals (SDGs) will be offered. In this educational task, the student will link the contents of the Calculus subject with some of the SDGs, proposing and solving mathematical problems related to them.
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Objective test |
- A quiz consisting of a collection of theoretical and/or practical questions will be done |
Personalized attention |
Methodologies
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Seminar |
Laboratory practice |
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Description |
- The diversity of the students and their background recomends giving an orientation, that should be carried out in the framework of a personalized tutorial action.
- In the laboratory sessions the teacher, who will be present in the clasroom, will guide and help students to develop the practises, teaching them in the use of a software package, helping them to understand some theoretical and practical aspects of the subject.
- During the seminars (TGR) the teacher will help the students in the resolution of theoretical and applied exercises.
- Tutorials will be held through the Teams platform to students who request it.
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Assessment |
Methodologies
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Competencies |
Description
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Qualification
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Seminar |
A1 B3 |
Throughout the course there will be two test-type tests with a maximum grade, each one, of 10% of the grade. Those students who do not reach the maximum grade in these written tests will be able to recover the remaining part by taking the mixed test.
Eventually and with prior agreement with the teacher, the student will be able to obtain this 20% of the grade by completing a project linked to the Sustainable Development Goals (SDGs). |
60 |
Guest lecture / keynote speech |
A1 B3 |
There will be no evaluation practices during these sessions. |
0 |
Laboratory practice |
A1 B3 |
Up to 4 assessment tests will be carried out during the laboratory classes that will account for 40% of the final grade.
Only students enrolled part-time who have not been evaluated in the laboratory practical part will be able to take a specific test to recover 40% of the mark corresponding to this part. |
0 |
Objective test |
A1 B3 |
The final exam, with a value between 40 and 100% (depending on the grade obtained in the seminar part) will consist of taking a written test. |
40 |
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Assessment comments |
The students will finish the class period with a maximum of 60% of the grade, which will be obtained through four quizzes that will be conducted during seminar sessions (each quiz carrying a weight of 15%). In each of these quizzes, each student will solve one or several practical problems using their laptop and Python software, as explained in the laboratory practices. Note: If any illicit activity is detected in any of these quizzes (such as copied exercises, inappropriate use of online resources, etc.), all students involved will receive a grade of 0 for the respective quiz, and, depending on the severity of the incident, the teachers may decide to assign a global grade of 0 for the entire "Seminar" section. On dates determined by the Faculty Board, students will take a written final exam for the course. The grade obtained in the final exam will be scaled so that each student has the opportunity to recover the portion lost in the evaluation corresponding to the seminars. Thus, the final exam will account for 40% to 100% of the final grade for the course. It is necessary to obtain a grade equal to or higher than 2.50 out of 10 in the final exam to pass the course. The final exam for the second opportunity (June or July 2023) will follow the same principles as the first opportunity. The evaluation of the seminars and laboratory practices for part-time students will be conducted taking into account their specific circumstances, as far as possible. Regarding the extraordinary December session, the evaluation process will include: a) An objective test worth a maximum of four points. b) An exam to assess the knowledge acquired in the laboratory practices, worth a maximum of six points.
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Sources of information |
Basic
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Bibliografía básica: |
Complementary
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Complementary bibliography: |
Recommendations |
Subjects that it is recommended to have taken before |
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Subjects that are recommended to be taken simultaneously |
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Subjects that continue the syllabus |
Numerical Methods for Computing/614G01064 |
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Other comments |
Daily work is recommended for getting optimal profit from the seminars (TGR) and laboratory practices. Also assistance to the master classes is recommended. |
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