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: Statistics, Mathematical Analysis and Optimisation
Areas: Mathematical Analysis
Center Faculty of Mathematics
Call: Second Semester
Teaching: Sin docencia (Extinguida)
Enrolment: No Matriculable
To introduce students into the field of the ordinary differential equations, to show the importance of its applications to the study of real-life problems. More precisely, to provide the theoretical foundations, techniques and applications relating to the existence of solution, solving some differential equations by applying certain elementary methods of integration and specially the study of the linear systems and higher order linear equations, both from the theoretical and practical point of view.
1. Motivations, generalities and examples of ordinary differential equations. Concept of solution. The Cauchy problem.
(approx. 2 lectures)
2. Existence and uniqueness of solution. (approx. 7 lectures)
3. Prolongation of solutions. Maximal solutions. Continuous dependence on initial conditions. (approx. 3 lectures)
4. Elementary methods of integration for first order differential equations. Power Series to solve ordinary differential equations.
(approx. 3 lectures)
5. Systems of linear equations. Properties of solutions. Fundamental matrix. (approx. 3 lectures)
6. Systems of linear differential equations with constant coefficients. (approx. 2 lectures)
7. Linear differential equation of higher order. Equations with constant coefficients. (approx. 4 lectures)
8. Applications of ordinary differential equations. (approx. 2 lectures)
W.E. BOYCE - R. C. DI PRIMA, Ecuaciones Diferenciales y Problemas con Valores de Frontera, Limusa, 1996.
M. BRAUN, Ecuaciones Diferenciales y sus Aplicaciones, Grupo Editorial Iberoamérica, 1990.
Y.A. CENGEL. Ecuaciones diferenciales para ingeniería y ciencias. McGraw-Hill, 2013.
E. A. CODDINGTON - N. LEVINSON, Theory of Ordinary Differential Equations, McGraw-Hill, 1955.
C.H. EDWARDS - D.E. PENNEY, Ecuaciones Diferenciales, Prentice Hall, 2001.
C. FERNÁNDEZ PÉREZ, Ecuaciones Diferenciales, vol.1, Pirámide, 1992.
C. FERNÁNDEZ PÉREZ - J. M. VEGA MONTANER, Ecuaciones Diferenciales, vol. 2, Pirámide, 1996.
M. M. GUTERMAN - Z. H. NITECKI, Differential Equations. A first Course, Saunders College Publishing, 1992.
Q. KONG, A Short Course in Ordinary Differential Equations, Universitext, Springer, 2014.
G. LEDDER, Ecuaciones Diferenciales. Un enfoque de modelado. McGraw-Hill, 2006. H. LOGEMANN, E.P. RYAN, Ordinary Differential Equations: Analysis, Qualitative Theory and Control, Springer Undergraduate Mathematics Series, Springer, 2014
R. K. NAGLE - E. B. SAFF, Fundamentos de Ecuaciones Diferenciales, Addison Wesley Iberoaméricana, 1992.
S. NOVO - R. OBAYA - J. ROJO, Ecuaciones y Sistemas Diferenciales, McGraw-Hill, 1995.
G. F. SIMMONS, Ecuaciones Diferenciales, McGraw-Hill, 1993.
SOTOMAYOR, Liçoes de Equaçoes Diferenciais Ordinarias, I.M.P.A., 1979.
W. WALTER, Ordinary Differential Equations, Graduate Texts in Mathematics 182, Springer, 1998.
D. ZILL, Ecuaciones Diferenciales con Aplicaciones, Grupo Editorial Iberoamérica, 1988.
In this course, our aim is to contribute to prepare the students in the competences mentioned for the Degree in Mathematics at USC: the basic and general competences CB1, CB2, CB3, CB4, CB5, CG1, CG2, CG3, CG4, CG5, the transversal competences CT1, CT2, CT3, CT5, and the specific competences CE1, CE2, CE3, CE4, CE5, CE6, CE7, CE8 and CE9.
Furthermore, being a subject part of the block of Differential Equations, the formative activities will be oriented to:
- To understand, to assimilate and to be able to express with rigor, the concepts and techniques developed in the program. In particular, to be able to apply the results related to the existence and uniqueness of solution of an ordinary differential equation, to solve some differential equations by applying some elementary methods and to solve linear systems and equations of high order, both with constant coefficients.
- To apply the techniques studied to elementary problems of Physics, Chemistry, Biology, Sociology, etc.
- To use a software package to deal with the previous concepts in the computer.
The students will work in a special way the following aspects: The rigorous expression and clarity, both oral and written, logical reasoning and identification of errors in procedures, abstraction, creativity, development of analysis ability in problem solving and critical attitude towards different solutions.
It will be followed the general methodological indications established in the Title of Degree in Mathematics of the USC.
Teaching is programmed in theoretical and interactive classes, some of which will consist in computer-based practices.
The lectures will be devoted to the presentation and development of the essential contents of the subject.
Interactive classes will be devoted to the presentation of examples and problems' resolution (Combining both theory and applications).
In some interactive laboratory classes, students will handle software packages that allow symbolic computation and graphic representations concerning the contents of the subject.
It will be promoted the maximum participation of students on the various classes of interactive teaching laboratory, where the discussion and debate with students on aspects of the subject and the resolution of the proposed tasks will aim to practice and improve their knowledge, and to work to achieve some of the competences mentioned.
The tutorials in small groups are specially designed to stimulate the student's activity outside the classroom, so that the students who are interested can examine their learning process, and teachers can make a direct monitoring of this learning process to detect difficulties and correct them when they occur.
SCENARIO 1 (adapted normality):
The theoretical and interactive classes will be presential and will be complemented with the virtual course of the subject, in which the students will find bibliographic materials, problem bulletins and other didactic materials.
The tutorials will be presential.
SCENARIO 2 (distancing):
Partially virtual teaching, if necessary, according to the distribution organized by the Faculty of Mathematics. For this, the virtual course will be used with bibliographic materials, problem bulletins and other didactic materials, provided by the teachers and, if so established, synchronous virtual classes using MS Teams or the available telematic tools.
The tutorials will be attended by email or through MS Teams.
SCENARIO 3 (closure of the facilities):
Fully remote teaching through the virtual course of the subject and MS Teams. For this, the virtual course will be used with bibliographic materials, problem bulletins, and other didactic materials, provided by the teachers and synchronous virtual classes using MS Teams (or, if it was not possible, asynchronous virtual classes through the available telematic tools).
Tutoring by email or MS Teams.
The evaluation will be carried out by combining a continuous formative evaluation with a final test.
Continuous assessment (C)
The continuous assessment will consist of the completion of a minimum of 3 intermediate tasks, either through the virtual campus or as delivery of work that will be specified throughout the course. The proposed activities will be related to practical, theoretical or applicability aspects of the concepts of the subject, which may be individual or in groups.
Through the proposed activities, the acquisition of skills, such as CB2, CB3, CB4, CG2, CG3, CG4, CT2, CT3, CE7, CE8, will be evaluated, of course, contextualizing the subject in the second year of the Degree. The qualification obtained in the continuous assessment will be applied in both opportunities of the same academic year.
Final test (F)
A final, written test will be carried out, which allows to check the knowledge attained by the students in relation to the concepts and results of the subject and the ability to apply it to specific cases, both from a theoretical and practical point of view, also evaluating the clarity and logical rigor shown in their exposition. With the final written test, which will consist of theoretical and practical questions, the competences CB1, CB2, CB4, CB5, CG1, CG3, CG4, CE1, CE2, CE3, CE4, CE5, CE6, CE7 will be evaluated.
Regarding the final test and the second opportunity, the difference between the three scenarios will consist in the way it will be carried out: presential in the case of scenario 1 and telematic in scenarios 2 and 3.
Final grade
With the mark of the continuous formative assessment (C) and the mark of the final test (F), the final mark in the subject (NF) will be calculated according to the following formula:
NF = max {F, 0.4 * C + 0.6 * F}
It will be understood as NOT PRESENTED those who does not take the final test.
In the second opportunity, the same evaluation system will be used but with the test corresponding to the second opportunity, which will be of the same type as that of the first opportunity.
SCENARIO 1 (adapted normality):
The continuous assessment tasks will be presential unless, for some of them, its preparation is recommended in another way.
The final test will be done presentially.
SCENARIO 2 (distancing):
Same procedure as that described for SCENARIO 1, with the only difference that the final test will be telematic and the delivery of work will be also carried out by telematic means.
SCENARIO 3 (closure of the facilities):
Both the continuous evaluation and the final test will be telematic.
Warning. In cases of fraudulent performance of exercises or tests (plagiarism or improper use of technologies), the provisions of the “Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións” will be applied.
ON-SITE WORK AT CLASSROOM (58 hours):
Lectures (28 hours)
Interactive Seminar classes (14 hours)
Interactive Laboratory classes (14 hours, some of them with the use of computer)
Tutorials in very small groups or individualized (2 hours)
PERSONAL WORK OF THE STUDENT (92 hours):
Autonomous individual study or in group (57 hours)
Writing exercises, conclusions or other works (20 hours)
Programming / experimentation or other works with computer (10 hours)
Recommended readings, activities at the library or similar (5 hours)
It is recommended that students handle with fluency the topics studied in the subjects "Introduction to Mathematical Analysis", "Continuity and Derivability of Functions of a Real Variable", "Integration of Functions of a Real Variable" and "Differentiation of Functions of several Real Variables". Departing from this situation, they will have to work regularly (daily) and with rigor. It is basic to take part actively in the learning process of the subject: to attend regularly to classes both theoretical and practical, to come to classes on a participative way, specially at classes and tutorials in small groups, and to formulate the appropriate questions that allow them to clarify all the doubts that could arise in relation to the subject.
Contingency plan:
Adaptation of the methodology to Scenarios 2 and 3:
SCENARIO 2 (distancing):
Partially virtual teaching, if necessary, according to the distribution organized by the Faculty of Mathematics. For this, the virtual course will be used with bibliographic materials, problem bulletins and other didactic materials, provided by the teachers and, if so established, synchronous virtual classes using MS Teams (or, if it was not possible, asynchronous virtual classes through the available telematic tools).
The tutorials will be attended by email or through MS Teams.
SCENARIO 3 (closure of the facilities):
Fully remote teaching through the virtual course of the subject and MS Teams. For this, the virtual course will be used with bibliographic materials, problem bulletins, and other didactic materials, provided by the teachers and synchronous virtual classes using MS Teams or the available telematic tools.
Tutoring by email or MS Teams.
Adaptation of the evaluation system to Scenarios 2 and 3:
SCENARIO 2 (distancing):
Same procedure as that described for SCENARIO 1, with the only difference that the final test will be telematic and the delivery of work will be also carried out by telematic means.
SCENARIO 3 (closure of the facilities):
Both the continuous evaluation and the final test will be telematic.
Maria Victoria Otero Espinar
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813170
- mvictoria.otero [at] usc.es
- Category
- Professor: University Professor
Rosana Rodríguez López
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813368
- rosana.rodriguez.lopez [at] usc.es
- Category
- Professor: University Lecturer
Cristina Lois Prados
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881821048
- cristina.lois.prados [at] usc.es
- Category
- Ministry Pre-doctoral Contract
Érika Diz Pita
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813202
- erikadiz.pita [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 15:00-16:00 | Grupo /CLE_01 | Galician | Classroom 07 |
| 16:00-17:00 | Grupo /CLE_02 | Galician | Classroom 08 |
| Tuesday | |||
| 15:00-16:00 | Grupo /CLE_01 | Galician | Classroom 07 |
| 16:00-17:00 | Grupo /CLE_02 | Galician | Classroom 08 |
| Wednesday | |||
| 15:00-16:00 | Grupo /CLIS_04 | Galician | Classroom 06 |
| 19:00-20:00 | Grupo /CLIL_01 | Galician, Spanish | Classroom 06 |
| Thursday | |||
| 15:00-16:00 | Grupo /CLIS_03 | Galician | Classroom 06 |
| 16:00-17:00 | Grupo /CLIL_04 | Galician, Spanish | Computer room 2 |
| 16:00-17:00 | Grupo /CLIS_02 | Galician | Ramón María Aller Ulloa Main Hall |
| 17:00-18:00 | Grupo /CLIL_05 | Galician, Spanish | Classroom 03 |
| 19:00-20:00 | Grupo /CLIL_06 | Galician, Spanish | Classroom 03 |
| Friday | |||
| 15:00-16:00 | Grupo /CLIS_01 | Galician | Ramón María Aller Ulloa Main Hall |
| 16:00-17:00 | Grupo /CLIL_03 | Galician, Spanish | Classroom 03 |
| 17:00-18:00 | Grupo /CLIL_02 | Spanish, Galician | Classroom 06 |
| 05.28.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 02 |
| 05.28.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 03 |
| 05.28.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |
| 05.28.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 07 |
| 05.28.2021 10:00-14:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 07.07.2021 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |