ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Particle Physics
Areas: Atomic, Molecular and Nuclear Physics, Condensed Matter Physics
Center Faculty of Physics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Within the context of the curriculum of the Degree in Physics, Mathematical Methods I belongs to module 4 (Mathematical Methods for Physics), which has been allocated with 40.5 ECTS. The study and command of mathematics is of fundamental importance in science, specially for a physicist. Almost all branches of mathematics are relevant to physics, but if we had to highlight one due to its high horizontal impact in all areas of physics, that would be differential calculus.
Mathematical Methods I is an introductory course to differential calculus. Its aim is, first, to strengthen the knowledge on the foundations of calculus that the students bring from the high school and, second, to expand it in order to give them access to the concepts and mathematical tools needed in advanced calculus.
Regarding the goals of the learning process, the student should:
o Know the properties of real and complex numbers.
o Master the basic elements of point set topology.
o Be able to evaluate limits and continuity of functions.
o Compute derivatives of functions.
o Understand, both from a rigorous and an intuitive point of view, the limit of sequences and the sum of series.
• Chapter 1: The real and complex numbers systems.
o Axiomatic definition of the real numbers.
o The sets of integers, rational and irrational numbers.
o Finite decimal approximations to real numbers.
o Construction and properties of complex numbers.
•Chapter 2: Elements of point set topology. Topology of the real line and multidimensional spaces.
o Normed, metric and topological spaces.
o Open and closed sets.
o Interior points, points of accumulation and adherent points.
o compact sets.
• Chapter 3: Limits and continuity.
o Convergent sequences and Cauchy sequences.
o Complete metric spaces.
o Limits of functions.
o Continuous functions and homeomorphisms
• Chapter 4: Differential calculus.
o Derivatives of functions of real variable.
o Rolle's theorem. Mean Value Theorem.
o Taylor's formula for real functions of a real variable.
• Chapter 5: Series.
o Infinite series. Alternating series.
o Conditional convergence and absolute convergence.
o Convergence criteria.
o Functional series. Power series.
Basic bibliography:
• T.M. Apostol, Análisis Matemático, 2ª ed., Ed. Reverté, Barcelona.
• J.A. Fernández Viña, Análisis Matemático, Vol. 1,2,3, 2ª ed., Ed. Tecnos, Madrid.
• R.E Larson, R.P. Hostetler, Cálculo y Geometría Analítica. Ed. McGraw-Hill.
• J. de Burgos, Cálculo Infinitesimal de una Variable. Ed. McGraw-Hill.
• K.F. Riley, M.P. Hobson, S.J. Bence, Mathematical methods for physics and engineering: a comprehensive guide. Cambridge University.
Complementary bibliography:
• T.M. Apostol, Calculus, 2ª ed., Vol. 1,2. Ed. Reverté.
• M. Spivak, Calculus, 2ª ed., Ed. Reverté.
• M. de Guzmán y B. Rubio, Problemas, conceptos y métodos del análisis matemático, Vols. 1, 2 y 3. Ed. Pirámide.
• W. Rudin, Principios de Análisis Matemático. Ed. McGraw-Hill.
Exercise Books:
• B. Demidovich, Problemas y Ejercicios de Análisis Matemático. Ed. Mir, Moscú.
• F. Bombal, L. Rodríguez, G. Vera, Problemas de Análisis Matemático, Vols 1,2,3. Ed. AC, Madrid.
• J.A. Fernández Viña, E. Sánchez Mañes, Ejercicios y Complementos de Análisis Matemático, Vols. 1,2, 4ª ed. Ed. Tecnos, Madrid.
• M. Spivak, Suplemento del Calculus. Ed. Reverté.
• BASIC AND GENERAL
The students will:
o CB1 – Have absorbed and understood essential material from a field which is one of the founding stones of high-school and college education. This material is usually found in advanced textbooks, but it includes also some elements coming from forefront research.
o CB2 – Be able to use their newly acquired knowledge to other fields in a professional way. They will show an increase of those skills that come naturally from heavy practice in complex reasoning and problem solving.
o CB5 – Have developed the learning skills needed to undertake further studies with a high degree of autonomy.
o CG3 – Be able to apply the newly acquired theoretical and practical knowledge to solve standard problems and pose original ones. Be able to use their strengthened analysis and abstraction skills as a tool to solve new problems in academic and professional contexts.
• TRANSVERSAL
The students will:
o CT1 – Have increased their analysis and synthesis abilities.
o CT2 - Have developed their skills for planning and organization.
o CT5 - Have developed critical thinking.
• SPECIFIC
The students will:
o CE5 – Be able to evaluate the complexity of a problem. When intractable as originally posed, try to find allowable approximations to make it affordable. They will show enough critical thinking to build simple a physical model to simulate the complexity of the real world.
o CE6 - Understand and master the mathematical and numerical methods most commonly used in Physics
o CE8 - Be able to efficiently handle bibliography as well as any source of relevant information, and use it both in research and technical projects.
The general methodological instructions given in the Report of the Degree in Physics of the USC will be followed. In particular, the teaching will be distributed per week in two master lectures plus another two lectures of interactive type where the students will be divided in small groups. Besides an individualized tutoring agreed with the students will be also given. The basic theoretical aspects of the course will be explained in the master lectures, while the interactive ones will be dedicated to solve problems and exercises with an active participation by the students (although eventually they could also be used to expand the contents of the master lectures). In the tutorials, it will be offered personalized attention to the needs of each student.
It will consist of two parts.
• First, the system will constantly monitor the progress of each student in the assimilation of the matter by short written tests and/or by the resolution of exercises in class (either individually or in groups). It will also promote the discussion with the student on the conceptual aspects of the subject. The qualification of this part will mean, at most, the 25% of the student's final rating, and it will be taken into considartion only if he/she attends to at least 80% of the lectures (master and interactive).
• A final exam consisting of short questions and/or problems with highly practical content.
In any case, the student's overall grade will not be lower than his/her rating in the final exam.
The working time in presence of the teacher is 60 hours, classified as follows:
• 32 hours of master lectures in a large group.
• 24 hours of interactive lectures in small groups.
• 4 hours of tutoring for every student.
The autonomous and individual work time that the student should carry out to achieve the required knowledge on the subject will not exceed 90 hours.
It is of particular importance to acquire a regular habit of study of the subject and to devote a certain percentage of the hours of each working day to this course. It is also necessary for the student to be able to solve all the proposed problems and exercises by himself/herself. To read the solutions proposed by another person is not enough
PLAN DE CONTIXENCIA ante un posible cambio de escenario
1) Obxectivos: sen cambios
2) Contidos: sen cambios
3) Material bibliográfico: sen cambios
4) Competencias: sen cambios
5) Metodoloxía:
Escenario 2
Se as medidas adoptadas polas autoridades sanitarias o permiten, as clases expositivas desenvolveranse telemáticamente e as interactivas presencialmente respectando o horario oficial de clases aprobado polo centro.
Se a limitación de aforo ditado polas autoridades sanitarias non permite que todo o alumnado asista as clases interactivas presenciais, estás se retransmitirán en streaming. Os alumnos asistirán por turnos ás clases presenciais. O número de alumnos por turno estará condicionado ás normas en vigor en cada momento.
Priorizarase á hora de programar a actividade da materia a presencialidade nas probas de avaliación frente ás clases interactivas presenciais. Se debido á unha inevitable rotación do alumnado, as probas de avaliación consumirán un número inasumible de horas, á docencia correspondente se impartiría telemáticamente.
As titorías poderán ser presenciais ou telemáticas, requerirán de cita previa.
Escenario 3
A docencia será telemática e as clases desenvolveranse de forma síncrona no horario oficial de clase. Pode ser que, por causas sobrevidas, algunha das clases se desenvolva de forma asíncrona o que se comunicará ao alumnado con anterioridade.
As titorías serán telemáticas e requerirán de cita previa
6) Sistema de avaliación
Escenarios 2 e 3
As actividades de avaliación que non poidan ser realizadas de xeito presencial, se non poden ser adiadas, realizaranse telemáticamente a través das ferramentas institucionais en Office 365 e Moodle. Neste caso esixirase a adopción dunha serie de medidas que requerirán que o alumnado dispoña dun dispositivo con micrófono e cámara mentres non se dispoña dun software de avaliación axeitado. O alumnado pode ser chamado a unha entrevista para comentar ou explicar unha parte ou o total da proba.
O requisito de asistencia ó 80% das clases contemprado no escenario 1 aplicarase só ás clases presenciais. Polo tanto non se aplica no escenario 3 (as clases son telemáticas) e no escenario 2 só ás clases que, por quenda, lle corresponda asistir ó alumno.
Para os casos de realización fraudulenta de exercicios ou probas será de aplicación o recollido na Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións”.
7) Tempo de estudo e traballo persoal: sen cambios
8) Recomendacións para o estudio da materia: sen cambios
Carlos Carballeira Romero
- Department
- Particle Physics
- Area
- Condensed Matter Physics
- Phone
- 881814015
- carlos.carballeira [at] usc.es
- Category
- Professor: University Lecturer
Pablo Vazquez Regueiro
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- Phone
- 881813973
- pablo.vazquez [at] usc.es
- Category
- Professor: University Lecturer
Xabier Cid Vidal
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- xabier.cid [at] usc.es
- Category
- Researcher: Ramón y Cajal
Abraham Antonio Gallas Torreira
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- Phone
- 881813589
- abrahamantonio.gallas [at] usc.es
- Category
- Professor: Temporary PhD professor
Alexandre Brea Rodríguez
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- alexandre.brea.rodriguez [at] usc.es
- Category
- Xunta Pre-doctoral Contract
Adrián Casais Vidal
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- adrian.casais [at] rai.usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 09:00-10:00 | Grupo /CLIS_03 | Spanish, Galician | Classroom 0 |
| 10:00-11:00 | Grupo /CLIS_04 | Galician, Spanish | Classroom 830 |
| Tuesday | |||
| 11:00-12:00 | Grupo /CLIS_01 | Galician, Spanish | Classroom 0 |
| 12:00-13:00 | Grupo /CLIS_02 | Galician, Spanish | Classroom 830 |
| Wednesday | |||
| 09:00-10:00 | Grupo /CLIS_03 | Galician, Spanish | Classroom 0 |
| 10:00-11:00 | Grupo /CLIS_04 | Galician, Spanish | Classroom 830 |
| Thursday | |||
| 11:00-12:00 | Grupo /CLIS_01 | Galician, Spanish | Classroom 0 |
| 12:00-13:00 | Grupo /CLIS_02 | Spanish, Galician | Classroom 830 |
| 01.11.2021 16:00-20:00 | Grupo /CLE_01 | 3 (Computer Science) |
| 01.11.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 130 |
| 01.11.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 6 |
| 01.11.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 830 |
| 01.11.2021 16:00-20:00 | Grupo /CLE_01 | Corridor |
| 01.11.2021 16:00-20:00 | Grupo /CLE_01 | Main Hall |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | 3 (Computer Science) |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 0 |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 130 |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 140 |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 5 |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 6 |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 830 |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 840 |
| 06.24.2021 09:00-14:00 | Grupo /CLE_01 | Main Hall |