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: Theoretical Physics
Center Faculty of Physics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable
1st situation
Basic and general:
- That the students have showed to possess knowledge in an area of study that starts from secondary education, and is used to reach a level that, although supported in advanced textbooks, also includes the most recent findings in the field.
- That the students know to apply their knowledge to their professional work or their vocation and possess the relevant competences through the preparation and defence of arguments and the resolution of problems inside their area of study.
- That the students have developed those skills require to continue their studies with a high degree of autonomy.
- That they are able to apply both the theoretical and the practical knowledge like the capacity of analysis and of abstraction in the definition and approach to problems, and in the search of solutions both in and outside academia.
Transversal:
- Acquire capacity of analysis and synthesis.
- Acquire capacity of organisation and planning.
- Develop critical reasoning.
Specific:
- Be able to capture the essentials of a process or situation and develop a model, as well as perform the approximations required to reduce the problem to a handy level. They will show to possess critical thought to build physical models.
- Comprise and dominate the use of the mathematical and numerical methods more commonly used in Physics.
- Be able to search and use bibliography, as well as any source of relevant information, and apply it to research and technical development of projects.
2nd and 3rd situations
No changes (depending on the situation)
1st situation
The course will be developed in accordance with the following syllabus:
THE COMPLEX PLANE. The field of complex numbers. Polar form and
complex exponentials. Roots of complex numbers. Topology of
the complex plane.
FUNCTIONS OF COMPLEX VARIABLE. Single-valued and multivalued functions:
Branches and Riemann surfaces. Analytic functions and Cauchy-
Riemann equations. Poles and branch cuts.
THE COMPLEX INTEGRAL. Cauchy's Theorem. Application to the calculation of real valued
integrals. Sum of series.
CAUCHY INTEGRAL FORMULAS. Theorems of Morera and Liouville. Fundamental
theorem of algebra. Argument Theorem. Laurent series.
INTEGRAL TRANSFORMS. Fourier Transform and its inverse.
Convolutions. Laplace transform. Application to solving differential and integral
equations.
GENERALIZED FUNCTIONS. The Dirac delta function and its derivatives.
Generalized Fourier transforms.
2nd and 3rd situations
No changes (depending on the situation)
Basic Bibliography (includes the signature of the books in the library of the Department of Physics).
- M.R. Spiegel, Variable compleja, Ed. McGraw Hill (3 A02 59).
-R. V. Churchill, J. W. Brown, Variable compleja y aplicaciones, Ed. McGraw Hill (3 A02 163).
-R. Seely, Introducción a las series e integrales de Fourier, Ed. Reverte (3 A02 164).
-M.J. Lighthill, Introduction to Fourier análisis and generalizad functions, Ed. Cambrigde University Press.
Online Resources
There are many complex variables courses online. Some of them are:
http://math.fullerton.edu/mathews/complex.html
(Complex Analysis Project for Undergraduate Students, California State Univ., USA)
http://web.me.com/paulscott.info/CA2/contents.html
(Complex Analysis notes and interactive quizzes, University of Adelaide, Australia).
http://faculty.gvsu.edu/fishbacp/complex/complex.htm
(Grand Valley State University, Allendale, Michigan, USA)
The videos of the classes at Stanford University and MIT on Fourier transforms can be viewed at the following addresses:
http://www.cosmolearning.com/courses/the-fourier-transforms-and-its-app…
http://www.cosmolearning.com/video-lectures/filters-fourier-integral-tr…
http://www.cosmolearning.com/video-lectures/fourier-integral-transform-…
Informatio on Laplace trasforms can be found in
http://sites.science.oregonstate.edu/math/home/programs/undergrad/Calcu…
Information on sums of series can be found in
http://www.supermath.info/InfiniteSeriesandtheResidueTheorem.pdf
Information on generalized functions can be found in
https://cds.cern.ch/record/1453294/files/978-3-642-23617-4_BookBackMatt…
A useful reference is the website of Wolfram MathWorld:
http://mathworld.wolfram.com
In case of the 2nd and 3rd situations, we will include links to existing web material in the Virtual Campus, together with other material to compensate the loss of access to some USC bibliographic resources.
1st situation
As a basic skill that students should acquire, at a practical level, the mathematical and computational techniques necessary for the analysis and solution of physical problems. The student must acquire sufficient maturity to successfully address mathematical problems needed in studying physics.
2nd and 3rd situations
No changes (depending on the situation)
A course in the Moodle platform in the Virtual Campus will be activated, where useful information and teaching material will be uploaded.
1st situation
There will be lectures and classes of exercises and problems, both being face to face. Individual sessions with the professor will be either remote or in person, if remote they will require booking which is also advised for the ones in person.
2nd situation
See the Contingency Plan in Observations
3rd situation
See the Contingency Plan in Observations
1st and 2nd situations
During the course the student will be evaluated by performing a small number of controls, tests and proposed exercises. A qualification NC will come from this evaluation. At the end of the course, there will be a final exam consisting of solving problems or exercises, leading to qualification NE. The final qualification will be obtained using the formula MAX(0.4*NC+0.6*NE,NE) if NE is greater than or equal to 3.0. If NE is smaller than 3.0, NE will be used as final qualification.
In case of unethical conduct during exercises or exams, the regulations contained in Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións will be applied.
3rd situation
See the Contingency Plan in Observations
1st situation
The on-site classes will be 32 of theory, 24 of practice and 4 of tutorship. It is rather difficult to estimate the study time needed to assimilate the contents of the course, since it strongly depends on the dedication and capabilities of the student. As a general indication, in the report of the grade in physics of the USC the time for the personal work of the student is estimated to 75 hours. To this time we should add 15 hours needed to carry out the work in the lectures and other practical exercises. This will give a total of 90 hours.
2nd and 3rd situations
No changes (depending on the situation)
1st situation
The student needs a good knowledge of mathematical analysis of real variable and ease of use of elementary algebraic methods.
These skills are taught in the Mathematical Methods courses prior to this one.
2nd and 3rd situations
No changes (depending on the situation)
CONTINGENCY PLAN in case of a change of situation
1) Objetives: no changes.
2) Contents: no changes.
3) Bibliography: no changes.
4) Competences: no changes.
5) Methodology:
2nd situation
If the measurements taken by the health authorities allow, lectures will be held remotely (e.g. by Teams) and exercise lessons in person, respecting the timetable approved by the Faculty. If limitations in the attendance established by the health authorities do not allow that all students attend the lessons, they will be broadcasted in streaming. Students will attend the in person lessons in turns. Their number per turn will be dictated by the rules at that moment.
Priority will be given to in person exams over in person exercise sessions. If the exams take too much time due to the limitations in the number of attendees, exercise lessons will turn remote.
Individual sessions with the professor, either in person or remote, must be booked in advance.
3rd situation
All teaching will be remote and during the official time for the lectures and lessons. If delay becomes unavoidable, it will be communicated to the students in advance.
Individual sessions with the professor, either in person or remote, must be booked in advance.
6) Evaluation system
2nd and 3rd situations
Those evaluation activities that cannot be held in person, will be done remotely using institutional USC tools (Office 365 and Moodle) if they cannot be held in person. If so, a series of measurements will be taken that require the student to be equipped with a microphone and a camera while evaluation software is not available. Students can be called for interview to explain or comment part of or the whole exam.
In case of unethical conduct during exercises or exams, the regulations contained in Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións will be applied.
7) Study time and individual work: no changes.
8) Recommendations for the study of the subject: no changes.
Nestor Armesto Perez
Coordinador/a- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881814107
- nestor.armesto [at] usc.es
- Category
- Professor: University Professor
Jose Daniel Edelstein Glaubach
- Department
- Particle Physics
- Area
- Theoretical Physics
- Phone
- 881813975
- jose.edelstein [at] usc.es
- Category
- Professor: University Lecturer
Pedro Augusto Agostini Infante
- Department
- Particle Physics
- Area
- Theoretical Physics
- pedroaugusto.agostini [at] rai.usc.es
- Category
- Xunta Pre-doctoral Contract
Alberto Rivadulla Sánchez
- Department
- Particle Physics
- Area
- Theoretical Physics
- alberto.rivadulla.sanchez [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | 2nd Virtual Classroom |
| 18:00-19:00 | Grupo /CLE_02 | Galician, Spanish | 2nd Virtual Classroom |
| Tuesday | |||
| 11:00-12:00 | Grupo /CLE_01 | Spanish, Galician | 2nd Virtual Classroom |
| 18:00-19:00 | Grupo /CLE_02 | Galician, Spanish | 2nd Virtual Classroom |
| Wednesday | |||
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | 2nd Virtual Classroom |
| 18:00-19:00 | Grupo /CLE_02 | Spanish, Galician | 2nd Virtual Classroom |
| Thursday | |||
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | 2nd Virtual Classroom |
| 18:00-19:00 | Grupo /CLE_02 | Galician, Spanish | 2nd Virtual Classroom |
| Friday | |||
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | 2nd Virtual Classroom |
| 18:00-19:00 | Grupo /CLE_02 | Spanish, Galician | 2nd Virtual Classroom |
| 05.19.2021 10:00-14:00 | Grupo /CLE_01 | 3 (Computer Science) |
| 05.19.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 0 |
| 05.19.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 130 |
| 05.19.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 140 |
| 05.19.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 6 |
| 05.19.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 830 |
| 05.19.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 840 |
| 05.19.2021 10:00-14:00 | Grupo /CLE_01 | Main Hall |
| 07.02.2021 09:00-14:00 | Grupo /CLE_01 | 3 (Computer Science) |
| 07.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 0 |
| 07.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 130 |
| 07.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 140 |
| 07.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 6 |
| 07.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 830 |
| 07.02.2021 09:00-14:00 | Grupo /CLE_01 | Classroom 840 |
| 07.02.2021 09:00-14:00 | Grupo /CLE_01 | Main Hall |