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
Center Faculty of Physics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Teach the students the fundamentals of mathematical calculus in one and several variables, together with the theorems and basic analysis for vector fields and Fourier series. This topic is complementary and is a continuation of Metodos Matematicos I. The lessons are divided into three main groups: the first one devoted to the differential calculus of real functions in one and several variables. The second one dedicated to the integral theorems of vector calculus. The third one focused into the introduction to Fourier series. The overall goal of the course is the acquisition of concepts and practice to achieve the necessary skills needed to analyse and handle the mathematical equations of Physical laws. This aim covers the calculus of one and several variable functions in the real domain altogether with vector and scalar field calculus.
Learning results
Calculus of derivatives and integrals of several variable real functions.
Development of skills for vector and scalar field calculus according to their use in Physical sciences.
Computation of Fourier expansion of a real function.
Understanding the concepts of mathematical calculus.
Scalar and vector fields
- Graphics and contour levels
Limits and continuity
Differentiation
- Directional derivative and partial derivatives
- The differential. Gradient and Jacobian matrix
- The chain rule
Directional derivatives and tangent planes
Extremes of scalar fields
- Taylor second order formula
- Minima, maxima, saddle points. The Hessian
- Lagrange multipliers, conditioned extremes
Riemann Integrals
- Sums and integral of Riemann
- Fundamental theorems of calculus
- Criterion of Lebesgue
Integration methods
- Integration by parts and by substitution
- Integration of rational and trigonometric functions
Improper integrals
Double and triple integrals
- Volumes and principle of Cavalieri
- Double integrals and Fubini theorem
- Integrals in elementary regions
- Change of variables: polar, spherical, cylindrical coordinates
- Triple integrals
Path integrals
- Parameterization of trajectories
- Path integral of scalar and vector fields
- Green theorem
- Divergence theorem
Gradient, rotational and divergence
- Conservative fields
Surface integrals
- Parameterization of surfaces
- Stokes theorem
- Gauss theorem
Fourier analysis
- Trigonometric series
- Convergence conditions
- Odd and even functions
- Fourier series
- Complex Fourier series
Basic bibliography
- J. E. Marsden, A. J. Tromba, Cálculo vectorial, 2004 Pearson, Addison Wesley.
- R. Larson, B. H. Edwards. Cálculo 2 de varias variables, 2010 McGraw-Hill.
- S. J. Colley, Vector Calculus, 2012 Pearson.
- Juan de Burgos, Cálculo infinitesimal de varias variables, 2008 McGraw-Hill.
- W. Kaplan, Advanced Calculus, 2003 Pearson.
- J. Hass, M. D. Weir, G. B. Thomas, University calculus, 2012 Addison-Wesley.
- E. Aranda y P. Pedregal, Problemas de cálculo vectorial, 2004 Septem Ediciones.
- Uña, J. San Martín, V. Tomeo, Problemas resueltos de cálculo en varias variables, 2007 Paraninfo.
Complementary bibliography
- T. M Apostol, Calculus, vol 1 y 2, 1992 Reverte.
- J. Stewart, Cálculo diferencial e integral, 1999 International Thomson Editores.
- N. Piskunov, Calculo diferencial e integral, 1991 Limusa.
- J. A. Fernandez-Viña, Ejercicios y complementos de análisis matemáticos, 1992 Tecnos.
- Demidovich, Problemas y ejercicios del análisis matemáticos, 1993 Paraninfo.
General and basic competences
CG3 - Apply both the theoretical-practical knowledge acquired as well as the capacity for analysis and abstraction in the definition and approach of problems and in the search for their solutions both in academic and professional contexts.
CB1 - Students should demonstrate to possess and understand knowledge in an area of study that starts from the basics of secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that involve knowledge from the frontier of the field of study.
CB2 - Students should know how to apply their knowledge to their work or vocation in a professional way and possess the competencies that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.
CB5 - Students shoud developed the learning skills necessary to undertake further studies with a high degree of autonomy.
Transversal competences
CT1 - Acquire analysis and synthesis skills.
CT2 - Have the ability of organizeing and planning.
CT5 - Develop critical reasoning.
Specific competences
CE5 - Be able to carry out the essentials of a process or situation and establish a working model of it as well as carry out the required approximations in order to reduce the problem to a manageable level. Demonstrate critical thinking to build physical models.
CE6 - Understand and master the use of the mathematical and numerical methods most commonly used in Physics.
CE8 - Be able to handle, search and use bibliography, as well as any source of relevant information and apply it to research and technical development of projects.
The foundations of each section of the subject will be initially exposed. The corresponding course will be activated on the Moodle platform of the Virtual Campus, to which information of interest to students will be uploaded, as well as diverse teaching material.
The general methodological indications established in the USC Degree Physics Report will be followed. Classes will be presential and the distribution of expository and interactive sessions follows that specified in the Grade Report. During the interactive classes, worksheets will be proposed in order to develop the skills and strengthen the concepts of the subject. A part of the sessions will be devoted to carrying out assigned exercises in the classroom and the rest to the students explaining the solution to their classmates. In each sheet, a more complex exercise will be proposed that students can submit as homework on the virtual campus. The office hours require an appointment and may be presential or telematic.
Continuous evaluation will be applied (through the resolution of exercises and controls, attendance and participation in classrooms) as well as the final exam.
Continuous evaluation
- Assistance to interactive classrooms
- Attitude in the classroom
- Delivery of problems and proposed assignments through the virtual campus
- Control exams
Exams
- Final exam of the contents of the subject
The grade will be obtained as 30% continuous evaluation 70% final exam grade. In case the weight with the continuous evaluation is lower than the final exam grade, the latter will be assigned.
In case of fraudulent filing of assignments or tests, the provisions of the "Regulations for evaluating the students academic performance and grades review" will apply:
"Article 16. Fraudulent filing of assignments or tests.
The fraudulent filing of any exercise or test required in the grading of an individual will imply the fail qualification in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. It is considered fraudulent, among others, the realization of plagiarized works obtained from sources accessible to the public without re-elaboration or reinterpretation and without citations to the authors or sources."
The course has a total of 6 ECTS credits distributed throughout the semester. The total workload is 150 hours, distributed as follows:
Teaching:
Lectures: 32 h
Interactive classes: 24 h
Tutorials: 4 h
Individual work:
Individual self-study or group study: 75h
Writing exercises, conclusions and other work: 15h
It is essential to consolidate the concepts of mathematical analysis by performing multiple exercises that will allow us to gain confidence and practice in differential and integral calculus.
Pablo Vazquez Regueiro
Coordinador/a- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- Phone
- 881813973
- pablo.vazquez [at] usc.es
- Category
- Professor: University Lecturer
Cibran Santamarina Rios
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- Phone
- 881814012
- cibran.santamarina [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
- Professor: University Lecturer
Emilio Xosé Rodríguez Fernández
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- emilioxoserodriguez.fernandez [at] usc.es
- Category
- Xunta Pre-doctoral Contract
Iris Garcia Rivas
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- irisgarcia.rivas [at] usc.es
- Category
- Predoutoral_Doutoramento Industrial
David Palacios Suárez-Bustamante
- Department
- Particle Physics
- Area
- Atomic, Molecular and Nuclear Physics
- david.palacios.suarez-bustamante [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Tuesday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom 130 |
| 11:00-12:00 | Grupo /CLE_02 | Galician | Classroom 6 |
| Wednesday | |||
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom 130 |
| 11:00-12:00 | Grupo /CLE_02 | Galician | Classroom 6 |
| Thursday | |||
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom 130 |
| 11:00-12:00 | Grupo /CLE_02 | Galician | Classroom 6 |
| Friday | |||
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom 130 |
| 11:00-12:00 | Grupo /CLE_02 | Galician | Classroom 6 |
| 05.21.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 0 |
| 05.21.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 130 |
| 05.21.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 6 |
| 05.21.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 830 |
| 07.03.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 0 |
| 07.03.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 6 |
| 07.03.2025 09:00-13:00 | Grupo /CLE_01 | Classroom 830 |