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: Applied Physics
Areas: Optics
Center Faculty of Physics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
General objectives:
This course is part of the module "Mathematical Methods of Physics", which aims to equip students with the mathematical tools necessary for the development and understanding of the different branches of physics. The specific objectives of the course are:
- Introduce the concept of differential equation
- Provide students with strategies for solving equations and systems of differential equations most basic, including power series solutions.
Learning outcomes:
- To understand the concept of differential equation
- To know the strategies of solving the equations and the most basic differential equations systems, including solutions in series
of powers.
- To acquire skill in the use of calculation techniques to solve physical problems.
BLOCK 1
INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS
INTEGRATION METHODS OF FIRST ORDER DIFFERENTIAL EQUATIONS. Separable differential equations. Homogeneous Equations. Linear Equations. Exact differential equations.
BLOCK 2
LINEAR DIFFERENTIAL EQUATIONS. Linear dependence and independence. Differential equations with constant coefficients. Systems of linear equations.
BLOCK 3
RESOLUTION OF DIFFERENTIAL EQUATIONS BY POWER SERIES. Regular points and singular points of the second order equations. Frobenius series and indicial equation.
SPECIAL FUNCTIONS. Bessel functions. Gamma Function. Legendre, Hermite and Laguerre polynomials. Hypergeometric functions.
Basic bibliography:
- G.F. Simmons, " Ecuaciones diferenciales Ordinarias ", Ed. McGraw-Hill, 1993.
- E.A. Coddington, "An Introduction to Ordinary Differential Equations", Dover Pu. New York, 1989.
- G.D. Zill, “Ecuaciones diferenciales con aplicaciones”, Grupo Editorial Iberoamérica, cop.1988.
Supplementary bibliography:
• L. Elsgoltz, “Ecuaciones diferenciales y Calculo Variacional”, Editorial MIR.
• Y. Ayant y M. Borg, “Funciones Especiales” Ed. Alhambra
• Q. KONG, A Short Course in Ordinary Differential Equations, Universitext, Springer, 2014.
• H. LOGEMANN, E.P. RYAN, Ordinary Differential Equations: Analysis, Qualitative Theory and Control, Springer Undergraduate Mathematics Series, Springer, 2014.
• W. WALTER, Ordinary Differential Equations, Graduate Texts in Mathematics 182, Springer, 1998.
Internet resources:
• Wikipedia
• http://mathworld.wolfram.com
BASIC AND GENERAL
CB1 - That students demonstrate to possess and understand knowledge in a study area that starts from the base of general secondary education, and they are generally at a level that, although supported by advanced textbooks, also includes some aspects that imply the knowledge of the vanguard of its field of study.
CB2 - That the students know how to apply their knowledge to their work or vocation in a professional way and possess the competences that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.
CB3 - The student develop the necessary learning skills to carry out studies with a high degree
of autonomy
CG3 - To apply the theoretical and practical knowledge acquired, as well as the capacity for analysis and abstraction in the definition and
Addressing problems and finding solutions both in academic and professional contexts.
TRANSVERSALS
CT1 - Acquire the ability to analyze and synthesize.
CT2 - Have the ability to organize and plan.
CT5 - Develop critical thinking.
SPECIFIC
CE5 - To be able to perform the essential elements of a process or situation and establish a working model of it, as well as carry out the necessary approaches to reduce the problem to a manageable level. Demonstrate critical thinking to build physical models.
CE6 - To understand and master the use of the most common mathematical and numerical methods in Physics
CE8 - To manage, search and use bibliography, as well as any source of relevant information and apply it to the research work
and technical development of projects.
The general methodological indications established in the Report of the Degree in Physics of the USC will be followed.
A Moodle platform course will be available in the Virtual Campus in order to upload important information for the students, as well as teaching material.
The evaluation system consists of two complementary parts:
a) Continuous evaluation, which is optional
b) Evaluation through a written exam to be held on the official dates set by the center.
The continuous evaluation will consist of several tests that will take place during class time. They may be proposed without prior notice, once a topic or a set of related topics has been completed. Students who do not attend a control will not have the right to repeat it.
The final exam will consist of two distinct parts:
a) A first part containing brief issues and questions related to the basics concepts of the course. This part will be eliminatory, that is, in case of fail, the second part will not be counted.
b) A second part for troubleshooting.
The final grade will be the weighted average of the grades obtained in the continuous evaluation (39%) and in the final exam (61%). However, if there is no grade for a control or it is lower than that of the final exam, the latter will be taken as the control grade:
Qualification = ControlWeight1 * max(Control1,ExamFinal)+ ControlWeight2 * max(Control2,ExamFinal)+...+0.61*ExamFinal
with ControlWeight1+ControlWeight2+... =0.39
The weight of each control will be according to the quantity and difficulty of the subject evaluated.
Study time and individual work
Work in the Classroom Hours
--------------------------------
Teaching to large classes (expository) 32
Teaching to small classes (interactive) 24
Tutorials in very small or individualized groups 4
TOTAL 60
Personal work of the student
--------------------------------
It is recommended the one indicated in the Memory of the Degree in Physics of the USC: about 90 hours; classroom classes time excluded.
- Review of basic mathematical concepts: derivatives, integrals, limits, etc.. and the skillful management of elementary functions such as polynomial and trigonometric functions, logarithmic function or exponential function.
- Attendance at lectures and participative classes.
- It is advisable to study Mathematical Methods I and II previously, as well as to study Mathematical Methods III simultaneously.
In case of fraudulent behaviour, the University Regulations for the evaluation of the academic performance of students will be applied:
Article 16. Fraudulent performance of exercises or tests.
The fraudulent performance of any exercise or test required in the evaluation of a subject will imply the qualification of failure in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. It is considered fraudulent, among others, the performance of plagiarized work or work obtained from sources accessible to the public without reworking or reinterpretation and without citation of the authors and sources.
Maria Elena Lopez Lago
- Department
- Applied Physics
- Area
- Optics
- Phone
- 881813518
- elena.lopez.lago [at] usc.es
- Category
- Professor: University Professor
Xesus Prieto Blanco
- Department
- Applied Physics
- Area
- Optics
- Phone
- 881813506
- xesus.prieto.blanco [at] usc.es
- Category
- Professor: University Lecturer
Eva Maria Acosta Plaza
Coordinador/a- Department
- Applied Physics
- Area
- Optics
- Phone
- 881813511
- eva.acosta [at] usc.es
- Category
- Professor: University Professor
Yago Arosa Lobato
- Department
- Applied Physics
- Area
- Optics
- yago.arosa.lobato [at] usc.es
- Category
- Xunta Post-doctoral Contract
Alejandro Doval Casas
- Department
- Applied Physics
- Area
- Optics
- alejandrodoval.casas [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Tuesday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_02 | Spanish, Galician | Classroom 6 |
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 130 |
| Wednesday | |||
| 10:00-11:00 | Grupo /CLE_02 | Galician, Spanish | Classroom 6 |
| 11:00-12:00 | Grupo /CLE_01 | Spanish, Galician | Classroom 130 |
| Thursday | |||
| 10:00-11:00 | Grupo /CLE_02 | Galician, Spanish | Classroom 6 |
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 130 |
| Friday | |||
| 10:00-11:00 | Grupo /CLE_02 | Spanish, Galician | Classroom 6 |
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 130 |
| 05.27.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 0 |
| 05.27.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 130 |
| 05.27.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 6 |
| 05.27.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 830 |
| 06.26.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 0 |
| 06.26.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 6 |
| 06.26.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 830 |