Competencies / Study results |
Code
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Study programme competences / results
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A3 |
CE3 - Reconocer y analizar problemas físicos, químicos, matemáticos, biológicos en el ámbito de la Nanociencia y Nanotecnología, así como plantear respuestas o trabajos adecuados para su resolución, incluyendo el uso de fuentes bibliográficas. |
A7 |
CE7 - Interpretar los datos obtenidos mediante medidas experimentales y simulaciones, incluyendo el uso de herramientas informáticas, identificar su significado y relacionarlos con las teorías químicas, físicas o biológicas apropiadas. |
B2 |
CB2 - Que los estudiantes sepan aplicar sus conocimientos a su trabajo o vocación de una forma profesional y posean las competencias que suelen demostrarse por medio de la elaboración y defensa de argumentos y la resolución de problemas dentro de su área de estudio |
B4 |
CB4 - Que los estudiantes puedan transmitir información, ideas, problemas y soluciones a un público tanto especializado como no especializado |
B5 |
CB5 - Que los estudiantes hayan desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía |
B6 |
CG1 - Aprender a aprender |
B7 |
CG2 - Resolver problemas de forma efectiva. |
B8 |
CG3 - Aplicar un pensamiento crítico, lógico y creativo. |
B9 |
CG4 - Trabajar de forma autónoma con iniciativa. |
B10 |
CG5 - Trabajar de forma colaborativa. |
B11 |
CG6 - Comportarse con ética y responsabilidad social como ciudadano/a y como profesional. |
B12 |
CG7 - Comunicarse de manera efectiva en un entorno de trabajo. |
C3 |
CT3 - Utilizar las herramientas básicas de las tecnologías de la información y las comunicaciones (TIC) necesarias para el ejercicio de su profesión y para el aprendizaje a lo largo de su vida |
C7 |
CT7 - Desarrollar la capacidad de trabajar en equipos interdisciplinares o transdisciplinares, para ofrecer propuestas que contribuyan a un desarrollo sostenible ambiental, económico, político y social. |
C8 |
CT8 - Valorar la importancia que tiene la investigación, la innovación y el desarrollo tecnológico en el avance socioeconómico y cultural de la sociedad |
C9 |
CT9 - Tener la capacidad de gestionar tiempos y recursos: desarrollar planes, priorizar actividades, identificar las críticas, establecer plazos y cumplirlos |
Learning aims |
Learning outcomes |
Study programme competences / results |
Remember sets of numbers and especially handle complex numbers. Know and handle with ease the differential calculus in a variable: successive derivatives, chain's rule, Taylor expansion, calculation of
extremes and local study of functions. Know how to apply knowledge to real problems |
A3 A7
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B2 B4 B5 B6 B7 B8 B9 B10 B11 B12
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C3 C7 C8 C9
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Know and acquire fluency in the techniques of integration of functions of a variable. Improper integrals. Know how to apply knowledge to real problems. |
A3 A7
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B2 B4 B5 B6 B7 B8 B9 B10 B11 B12
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C3 C7 C8 C9
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Know the numerical and functional sequences and series, determine their convergence and acquire fluency in the calculation of limits. Know and handle the Fourier series. Know how to apply knowledge to real problems. |
A3 A7
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B2 B5 B6 B7 B8 B9 B10 B11 B12
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C3 C7 C8 C9
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Know and handle matrix calculus, systems of linear equations and vector spaces with ease. Know how to apply knowledge to real problems. |
A3 A7
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B2 B5 B6 B7 B8 B9 B10 B11 B12
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C3 C8 C9
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Manage software tools that implement the methodologies studied and know how to analyze the results. |
A3 A7
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B2 B4 B5 B6 B7 B8 B9 B10 B11 B12
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C3 C7 C8 C9
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Contents |
Topic |
Sub-topic |
Unit 0: Sets of numbers. |
Real numbers.
Complex numbers. |
Unit 1: Differential calculus of one variable. |
Differentiable functions. Chain's rule.
Increasing and decreasing functions. Local extrema.
Concavity and convexity. Inflection points.
Graph representation of functions.
Newton's method.
Taylor's polynomial.
Applications. |
Unit 2: Integral calculus of one variable. |
Definite integral.
Fundamental theorem of Calculus.
Integration rules.
Computation of flat areas and volumes.
Numerical integration: trapezoid's method.
Improper integrals.
Applications. |
Unit 3: Vector spaces. Linear algebra. |
Matrix algebra.
Solving linear system equations.
Gauss' method.
Vector spaces.
Diagonalization. Eigenvalues and eigenvectors.
Applications. |
Unit 4: Sequences and series. |
Numerical sequences.
Numerical series.
Function sequences.
Function series.
Series of Taylor.
Series of Fourier.
Applications. |
Planning |
Methodologies / tests |
Competencies / Results |
Teaching hours (in-person & virtual) |
Student’s personal work hours |
Total hours |
Guest lecture / keynote speech |
A3 A7 B6 B7 B8 C3 |
28 |
56 |
84 |
ICT practicals |
B2 B4 B5 B6 B7 B9 B10 B11 B12 C7 C8 C9 |
12 |
25 |
37 |
Mixed objective/subjective test |
A3 B2 B4 B7 |
3 |
0 |
3 |
Problem solving |
A3 A7 B6 B7 C3 |
8 |
16 |
24 |
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Personalized attention |
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2 |
0 |
2 |
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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 |
Guest lecture / keynote speech |
Exhibition of the contents specified in the program of the subject, for this, audiovisual media or blackboard will be used. |
ICT practicals |
Interactive practices in which relevant problems in the field of Science and Engineering will be solved, for this the Python programming language will be used |
Mixed objective/subjective test |
Development of issues and problems of the subject. |
Problem solving |
Sessions where relevant problems in the field of Sciences and Engineering will be presented, which will be solved both analytically and numerically. The student must be able to reach the solution of any problem by hand or alternatively using computer tools, and compare the results. |
Personalized attention |
Methodologies
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Problem solving |
ICT practicals |
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Description |
a) During practical and solving problems lessons, professors will help students to develop purposed problems as well as applications to problems outside the scope of Science and Engineering.
b) The specific personalized attention measures for "Students with recognition of part-time dedication and academic waiver of attendance exemption" for the study of the subject, the continuous evaluation of the practices through ITC and the resolution of problems carried out attending, as far as possible, to your particular circumstances.
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Assessment |
Methodologies
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Competencies / Results |
Description
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Qualification
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Mixed objective/subjective test |
A3 B2 B4 B7 |
Proba que inclúe a resolución de cuestións e problemas da materia |
60 |
Problem solving |
A3 A7 B6 B7 C3 |
Resolución de problemas de carácter práctico. |
20 |
ICT practicals |
B2 B4 B5 B6 B7 B9 B10 B11 B12 C7 C8 C9 |
Resolución de problemas de carácter práctico empregando o lenguaxe de programación Python |
20 |
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Assessment comments |
The final qualification of the subject consists of three parts: - Qualification of internships through ICT (CP): between 0 and 2 points
- Problem Solving Qualification (CR): between 0 and 2 points
- Mixed test qualification (CE):
- If CP+CR is equal or greater to 2 points, the qualification of the mixed test (CE) will be E=10-(CP+CR).
- If CP+CR is smaller than 2 points, the qualification of the mixed test (CE) will be CE=8-(CP+CR).
The final qualification will be the sum of three parts: Final_Note= CP + CR + CE, if the qualification of the mixed test (CE) is greater than 2 (over 10 points). In other case, the final qualification will be the mark obtained on the mixed test, CE.
The qualification of the practices through ICT (CP) + the resolution of problems (CR), constitute the note of Continuous Evaluation (EV), EV = CP + CR. The qualifications of practices through ICT (CR) and problem solving (CP) will be kept on the second opportunity of the evaluation, that is, the EV note will be kept for the second opportunity. The evaluation of CP + CR will be carried out by solving four small mixed tests, in which the student will have to solve problems of the subject by hand and with Python. The qualifications of practices through ICT (CR) and problem solving (CP) will be retained in the second opportunity of the evaluation. Students who do not show up for the final mixed test will be considered as "Not presented". All previous observations are applicable to students who request the early December call. All aspects related to “academic dispensation”, "dedication to study", "permanence" and "academic fraud" are governed in accordance with the current academic regulations of the UDC.
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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 |
Advanced Calculus /610G04009 |
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Other comments |
It is recommended to have knowledge of the second year of high school. In particular, differential and integral calculus. Daily study of the contents treated in the classroom, complementing them with the recommended bibliography. - Gender perspective: as stated in the transversal competences of the title (C4), the development of a critical, open and respectful citizenship with diversity in our society will me promoted, highlighting the equal rights of students without discrimination based on gender or sexual condition. An inclusive language will be used in the material and during the development of the lessons. Work will be done to identify and modify prejudices and sexist attitudes and influence the environment to modify them and promote values of respect and equality.
Green Campus Program of the Faculty of Science
In order to achieve an inmediate and sustainablem and to fullfill the point 6 of the "Declaración
Ambiental da Facultade de Ciencias (2020)", the work carried out in this subject will be requested in virtual format or computer support.
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