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: With teaching
Enrolment: Enrollable
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. 8 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. (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. 5 lectures)
8. Applications of ordinary differential equations. (approx. 2 lectures)
Basic bibliography
W.E. BOYCE - R.C. DI PRIMA, Ecuaciones Diferenciales y Problemas con Valores de Frontera, Limusa, 1996.
S. NOVO - R. OBAYA - J. ROJO, Ecuaciones y Sistemas Diferenciales, McGraw-Hill, 1995.
R. PRECUP, Ordinary Differential Equations, Example-driven, Including Maple Code, De Gruyter Textbook, De Gruyter, 2018.
G.F. SIMMONS, Ecuaciones Diferenciales, McGraw-Hill, 1993.
D.G. ZILL, Ecuaciones diferenciales con aplicaciones de modelado, novena edición, Paraninfo, 2009.
Complementary bibliography
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.
J. 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.
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.
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). 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. Students will be encouraged to use software packages that allow symbolic computation and graphic representations concerning the contents of the subject.
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.
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 mainly presential and they could be partially virtual through 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, which will be similar for all the groups in the subject, will consist of the completion of three activities:
- an intermediate test (representing the 40% of C),
- monitoring of learning during interactive classes through two or three small tasks to be completed with the use of class notes (30%), and
- the submission of one activity in groups with presentation (30%).
The proposed activities will be related to practical, theoretical, or applicability aspects of the concepts of the subject.
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, presential, 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. The final written test will be the same for all the groups. 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.
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,0.3*C+0.7*F}
Those students who do not take the final exam will be considered as NOT PRESENTED.
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, and the same for all the groups of the subject.
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.
Rosana Rodríguez López
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813368
- rosana.rodriguez.lopez [at] usc.es
- Category
- Professor: University Professor
Jorge Rodríguez López
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- jorgerodriguez.lopez [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
| Tuesday | |||
|---|---|---|---|
| 15:00-16:00 | Grupo /CLE_02 | Galician | Classroom 03 |
| 16:00-17:00 | Grupo /CLE_01 | Spanish | Classroom 02 |
| Wednesday | |||
| 15:00-16:00 | Grupo /CLIL_06 | Galician | Classroom 07 |
| 16:00-17:00 | Grupo /CLIS_02 | Spanish | Classroom 03 |
| 16:00-17:00 | Grupo /CLIL_05 | Galician | Classroom 07 |
| 17:00-18:00 | Grupo /CLIS_01 | Spanish | Classroom 02 |
| 18:00-19:00 | Grupo /CLIL_04 | Galician | Classroom 07 |
| Thursday | |||
| 15:00-16:00 | Grupo /CLIL_01 | Spanish | Classroom 07 |
| 15:00-16:00 | Grupo /CLIS_03 | Galician | Classroom 08 |
| 16:00-17:00 | Grupo /CLIL_03 | Spanish | Classroom 07 |
| 16:00-17:00 | Grupo /CLIS_04 | Galician | Classroom 09 |
| 18:00-19:00 | Grupo /CLIL_02 | Spanish | Classroom 08 |
| 05.23.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 07.08.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |