| Study programme competencies |
|
Code
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Study programme competences
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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 |
| Conocer y manejar con soltura las funciones en varias variables escalares y vectoriales: su representación espacial, su necesidad en el modelado de problemas reales, el cálculo de límites y la continuidad |
A3
A7
|
B2
B4
B5
B6
B7
B8
B9
B10
B11
B12
|
C3
C7
C8
C9
|
| Conocer y manejar con soltura el cálculo diferencial en varias variables: derivadas parciales y direccionales, operadores diferenciales, desarrollo de Taylor y cálculo de extremos y extremos condicionados. Saber aplicar los conocimientos
a problemas reales, especialmente relacionados con la titulación. |
A3
A7
|
B2
B4
B5
B6
B7
B8
B9
B10
B11
B12
|
C3
C7
C8
C9
|
| Conocer y adquirir soltura en las técnicas de integración en varias variables, aplicándolo a problemas reales. |
A3
A7
|
B2
B4
B5
B6
B7
B8
B9
B10
B11
B12
|
C3
C7
C8
C9
|
| Conocer y adquirir soltura en la integración sobre curvas y superficies. Saber aplicar las fórmulas de Green y Stokes, aplicándolo a problemas relacionados con la titulación |
A3
A7
|
B2
B4
B5
B6
B7
B8
B9
B10
B11
B12
|
C3
C7
C8
C9
|
| Manejar herramientas de software que implementen las metodologías estudiadas y saber analizar los resultados. |
A3
A7
|
B2
B4
B5
B6
B7
B8
B9
B10
B11
B12
|
C3
C7
C8
C9
|
| Contents |
| Topic |
Sub-topic |
| Unit 1: Topology in R^n |
Scalar product, norm and distance.
Classification of points and sets.
Topology in R: bounded sets, supreme, infimo, maximum and minimum.
Polar, cylindrical and spherical oordinates.
Applications. |
| Unit 2: Functions of more than one variable |
Scalar and vector functions.
Level sets.
Continuity.
Applications. |
| Unit 3: Differentiation of functions of more than one variables and applications |
Directional derivative.
Partial derivatives: properties and practical computations.
Differerential of a function.
Relationship between the differential and the partial derivatives.
Gradient vector, relationship with the directional derivatives.
Jacobian matrix.
Higher order partial derivatives.
Introduction to vector calculus.
Taylor's theorem for scalar functions.
Critical points, classification.
Hessian matrix.
Extremos condicionados: reducción de la dimensión, método de los multiplicadores de Lagrange.
Aplicaciones. |
| Unit 4: Integration of functions of one and more variables |
Double integrals.
Triples integrals.
Change of variables in double and triple integrals.
Applications of integrals. |
| Unit 5: Integration in curves and surfaces |
Parameterized curves.
Integral line.
Gradient function and conservative field.
Green's theorem.
Parameterized surfaces.
Integral of surface. Sotkes theorem. Divergence's theorem.
Applications. |
| Planning |
| Methodologies / tests |
Competencies |
Ordinary class hours |
Student’s personal work hours |
Total hours |
| Guest lecture / keynote speech |
A3 A7 B6 B11 C8 |
28 |
56 |
84 |
| ICT practicals |
B2 B4 B5 B7 B12 C3 C7 C8 |
12 |
25 |
37 |
| Mixed objective/subjective test |
A3 B2 B6 B7 B9 |
3 |
0 |
3 |
| Problem solving |
B2 B4 B5 B7 B8 B9 B10 B12 C3 C7 C9 |
8 |
16 |
24 |
| |
| Personalized attention |
|
2 |
0 |
2 |
| |
| (*)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
|
| Problem solving |
| ICT practicals |
|
| 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) As specific personalized attention measures for "Students with partial time dedication recognition and academic exemption from attendance exemption" for the study of the subject, the continuous assessment of practical lessons through ICT and problem solving will be carried out through online tests.
b)As medidas de atención personalizada específicas para o “Alumnado con recoñecemento de dedicación a tempo parcial e dispensa académica de exención de asistencia” para o estudo da materia, a avaliación continua das prácticas a través de TIC e da resolución de problemas realizarase mediante probas parciais online.
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| Assessment |
|
Methodologies
|
Competencies |
Description
|
Qualification
|
| Problem solving |
B2 B4 B5 B7 B8 B9 B10 B12 C3 C7 C9 |
Resolución de problemas de carácter práctico. |
20 |
| ICT practicals |
B2 B4 B5 B7 B12 C3 C7 C8 |
Resolución de problemas de carácter práctico empregando o linguaxe de programación Python |
20 |
| Mixed objective/subjective test |
A3 B2 B6 B7 B9 |
Proba que inclúe a resolución de cuestións e problemas da materia
|
60 |
| |
|
Assessment comments |
The final qualification of the subject consists of three parts: The
final qualification will be the sum of the three parts CP + CR + CE, if
the qualification of the objective test is greater than 2 (over 10
points). In other situation, the final qualification will be the
qualification of the objective test, CE. The qualifications of the
practical lessons by ITC (CR) and solving problems (CP) will be kept
for the second opportunity of the assessment. In the proceedings, the students who do not attend the final test will be considered as "Not presented". |
| Sources of information |
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Basic
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|
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Bibliography: Jerrold Marsden. " Cálculo Vectorial". Pearson. Edición 6ª. 2018. Ron Larson, Bruce Edwards. "Cálculo. Tomo II". Cengage Learning, Edición 10ª.2018. - Claudia Neuhauser, "Calculus for Biology and Medicine", Prentice Hall.Edición 2ª. 2004.
Robert G. Mortimer. "Mathematics for Physical Chemistry". Pearson. Edición 4ª. 2013. Saturnino L. Salas, Finar Hille, Garret J. Etgen. "Calculus II. Una y varias varialbles" (Vol. nº 2). Reverté. Edición 4ª. 2018. Edward Jen Herman, Gilbert Strang. "Calculus. Volumen 3". OpenStax. Rice University. Disponible gratuitamente en :https://openstax.org/details/books/calculus-volume-3
Bibliography for practical lessons by ITC: Jeffrey J. Heys. "Chemical and Biomedical Engineering Calculations using Python". Wiley. 2017. Svein Linge, Hans P. Langtangen. "Programming for Computations - Python. A Gentle Introduction to Numerical Simulations with Python". Springer. Texts in Computational Science and Engineering. Edición 1ª. 2017. Anders Mathe-Sorenssen."Elementary Mechanics Using Python: A Modern Course Combining Analytical and Numerical Techniques (Undergraduate Lecture Notes in Physics)". Springer. 2015. Robert Johansson. "Numerical Python: Scientific Computing and Data Science Applications with Numpy, Scipy and Matplotlib". Apress. . Edición: 2ª. 2018.Rubin H. Landau, Manuel J. Paez, Christian C. Bordeiany. "Computational Physics: Problem Solving with Computers". Wiley VCH Verlag GmbH. Edición 2ª. 2007.
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Complementary
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| Recommendations |
| Subjects that it is recommended to have taken before |
| Fundamentals of Mathematics/610G04001 | | Physics: Mechanics and Waves/610G04002 |
|
| Subjects that are recommended to be taken simultaneously |
| Fundamentals of Computing Science/610G04010 |
|
| Subjects that continue the syllabus |
| Numerical and Statistical Methods/610G04013 | | Differential Equations/610G04016 |
|
| Other comments |
It is recommended to have knowledge of the second year of high school 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.
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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