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, English
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Higher Technical Engineering School
Call: Second Semester
Teaching: Sin docencia (Extinguida)
Enrolment: No Matriculable | 1st year (Yes)
To connect with the subject "Fundamentos de Matematicas" and to serve to the students for consolidating their mathematical language and to form them in the main analytical and numerical methods on multivariable differential calculus, single variable integral calculus and solution of ordinary differential equations. In the practices, students will learn how to solve the aforementioned problems using numerical methods.
1. Numerical solution of non-linear equations: separation of roots; bisection method; Newton's method.
2. Fundamentals of multivariable functions: domain, image, level sets and graph.
3. Multivariable differential calculus: partial derivatives; gradient vector; Jacobian matrix; chain rule; tangent plane; extreme values of functions; optimization using method of steepest descent.
4. Solution of nonlinear and linear systems: Newton's method for nonlinear systems; method of steepest descent; LU and Cholesky factorizations; analysis of the computational cost.
5. Single variable integral calculus: definite and indefinite integral; fundamental theorems of calculus; primitive calculation; Leibniz rule.
6 Numerical integration: trapezoidal and Simpson's rules.
7. First order ordinary differential equations: notion of ordinary differential equation; initial value problems; separable equations; first order linear differential equations; numerical solution using Euler's method.
Basic:
THOMAS, G. B. Cálculo. Varias variables.. 13ª ed., México: Pearson, 2015. ISBN: 9789702627357
Cálculo Numérico [online]. Universidad de Concepción, Chile [fecha de consulta: 15 junio 2017]. Disponible en: http://www.ing-mat.udec.cl/pregrado/asignaturas/521230/
Complementary:
CHAPRA, S. C. y CANALE, R. P. Métodos numéricos para ingenieros. 7ª ed., México: McGraw-Hill, 2015. ISBN: 9786071512949
ANASTASSIOU, G. A. y MEZEI, R. Numerical Analysis Using Sage. Switzerland, Springer, 2015. ISBN: 978-3-319-16739-8
To contribute to achieve the competences described in the document "Grao de Enxeñaría Informática na USC": G5, G8, G9, G10, TR1, TR2, TR3, FB1 and RI6.
Competences associated to the Mathematics module:
- To expose and argue clearly both hypotheses and methods used in the resolution of problems, and to use a suitable language.
- To develop the ability to analyze the resolution of a problem.
- To have a critical attitude when dealing with different types of solutions.
- To master notation, method and vocabulary for mathematical modeling and case studies.
- Knowledgeable use of the mathematical language.
- To develop capacity for abstraction and formalization using the language of logic to express ideas with precision and rigor.
- To know mathematical techniques that allow to solve problems related to engineering.
This subject has assigned two hours of lectures and two practices a week, and three tutorial shifts.
- In the lectures, the contents will be explained by the teacher, following the matherial shared by the teachers, as a guide. The exposition will partially rely on slides based on the book and partly developing the concepts and exercises on the blackboard, or depending of the scenarios, in videos being made by teaches that will be able to consult asynchronously.
- In the practices, the scientific software Sage will be applied to solve mathematical problems. Three tasks will be proposed, where the understanding of the relationship between the mathematical problem and its scientific context will be important: the first task, presented in writing, will involve a peer review; the last two tasks will be presented by the student (it could be done in groups) in two tutorial shifts.
All course materials will be available in the Virtual Campus of the University; there, students can also access to information on the organization of subject, to contact the teachers or other colleagues to solve doubts.
Continuous assessment:
* To submit three tasks: tasks two and three will be exposed in practices and tutorial hours. Students must assist to the practice hours devoted to that tasks.
* To participate in the subject's blog, posting the summary of one lecture class.
* The continuous assessment can grant up to 30% of the final grade for any opportunity of the current course. It can only be achieve during the regular development of the course.
Exam:
* A written examination will grant up to 60% of the final grade in both opportunities.
* The "no show" grade will be applied to students that do not participate in either of the opportunities.
* Study time and individual work spent by a student per week:
2 hours of lectures + 2 hours of practices + 4 h of personal work devoted to analyze theoretical contents and to solve problems.
Total: 12,5 x 8 = 100 h.
* Preparation of each task: 9 hours per work
Tutorial shifts in small groups: 3h
Total, course: 100 + 9 x 3 + 3 = 130 h
* Exam:
3 h for the exam + 20 h for preparation of final exam.
Total, exam: 23 h.
Total: 153 h
Attendance to the classes with an active participation in the same ones. Use of text book and the recommended material. Accomplishment of the practices and of necessary exercises corresponding to the different subjects to obtain raised objectives.
- To assist to the classes and to have participative attitude.
- To use the recommended material and textbooks.
- To carry out practices and exercises in order to achieve the proposed goals.
Plan de contingencia para la adaptación de esta guía al documento Bases para el desarrollo de una enseñanza presencial segura en el año académico 2020-2021, aprobado por el Consejo de Gobierno de la USC en su sesión ordinaria celebrada el 19 de junio de 2020.
Metodología:
--------------
Las adaptaciones propuestas para la enseñanza en el escenario 2 son:
Las clases expositivas se transmitirán y grabarán por la docente para los estudiantes. Si la docente responsable puede asistir al aula, ella hará las grabaciones de la misma, si no es posible, hará los videos desde el despacho.
Las clases de laboratorio se impartirán desde el aula como en el Escenario 1.
Las adaptaciones propuestas para la enseñanza en el escenario 3 son:
• Las clases expositivas se imparten haciendo grabaciones de diferente duración, atendiendo a las diferentes secciones de los contenidos. Los videos resultantes son provistos desde el Campus Virtual por los enlaces a OneDrive, están en formato mp4. El campus virtual también proporciona los documentos sobre los cuales se dan las explicaciones en los videos.
• En la metodología provista para el tema dentro de la evaluación continua, los estudiantes hicieron un registro de cada sesión expositiva. Para la enseñanza remota, se propone, a partir de los blogs del año pasado, qué material compondría cada clase presencial, y los estudiantes continuarán blogueando en las clases expositivas para definir el plan semanal de la asignatura.
• En las clases de laboratorio se planifican las actividades de cada semana. Se proporcionan las grabaciones en las que se explican las prácticas, con los documentos correspondientes. El software científico Sage de distribución gratuita no tiene restricciones para que los estudiantes lo usen de forma remota.
• Se organizó un Foro de Participación en el Campus Virtual para facilitar la explicación de temas, compartir materiales de forma remota y canalizar dudas.
Evaluación:
------------
Los pesos son los mismos en los tres escenarios.
Las adaptaciones propuestas para la enseñanza en el escenario 2 son:
• Se mantiene la evaluación continua detallada en la sección correspondiente, las tareas 2 y 3 serán presentadas en persona o de forma remota por los estudiantes que utilizan equipos de MS. Los blogs se adaptan como se describe. Si un estudiante no tiene medios electrónicos para hacer las presentaciones, se organizarán presentaciones cara a cara.
Las clases expositivas y de laboratorio se impartirán desde el aula como en el Escenario 1 y se transmitirán y grabarán para los estudiantes que no puedan asistir.
* La prueba final se realizará electrónicamente.
Las adaptaciones propuestas para la enseñanza en el escenario 3 son:
• La evaluación continua detallada en la sección correspondiente se mantiene, las tareas 2 y 3 serán presentadas de forma remota por los estudiantes que utilizan equipos de MS. Los blogs se adaptan como se describe. Si un estudiante no tiene medios telemáticos para hacer las presentaciones, se organizarán presentaciones presenciales, cuando sea posible.
* La prueba final se realizará telemáticamente.
Francisco Jose Pena Brage
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813194
- fran.pena [at] usc.es
- Category
- Professor: Temporary PhD professor
Maria Elena Vazquez Cendon
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813196
- elena.vazquez.cendon [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 15:30-17:30 | Grupo /CLIL_02 | Galician | Computer Room I7 |
| Tuesday | |||
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom A1 |
| 15:30-17:30 | Grupo /CLIL_04 | Galician | Computer Room I7 |
| Wednesday | |||
| 12:00-13:00 | Grupo /CLE_01 | Galician | Classroom A1 |
| 15:30-17:30 | Grupo /CLIL_01 | Galician | Computer Room I7 |
| Thursday | |||
| 15:30-17:30 | Grupo /CLIL_03 | Galician | Computer Classroom I3 |
| 01.14.2021 09:15-14:00 | Grupo /CLE_01 | rest room / dining room |
| 01.14.2021 09:15-14:00 | Grupo /CLIL_01 | rest room / dining room |
| 01.14.2021 09:15-14:00 | Grupo /CLIL_04 | rest room / dining room |
| 01.14.2021 09:15-14:00 | Grupo /CLIL_02 | rest room / dining room |
| 01.14.2021 09:15-14:00 | Grupo /CLIL_03 | rest room / dining room |
| 05.25.2021 16:00-20:45 | Grupo /CLE_01 | Classroom A1 |
| 05.25.2021 16:00-20:45 | Grupo /CLIL_03 | Classroom A1 |
| 05.25.2021 16:00-20:45 | Grupo /CLIL_01 | Classroom A1 |
| 05.25.2021 16:00-20:45 | Grupo /CLIL_04 | Classroom A1 |
| 05.25.2021 16:00-20:45 | Grupo /CLIL_02 | Classroom A1 |
| 05.25.2021 16:00-20:45 | Grupo /CLIL_02 | Classroom A2 |
| 05.25.2021 16:00-20:45 | Grupo /CLE_01 | Classroom A2 |
| 05.25.2021 16:00-20:45 | Grupo /CLIL_03 | Classroom A2 |
| 05.25.2021 16:00-20:45 | Grupo /CLIL_01 | Classroom A2 |
| 05.25.2021 16:00-20:45 | Grupo /CLIL_04 | Classroom A2 |
| 07.02.2021 09:15-14:00 | Grupo /CLIL_03 | Classroom A5 |
| 07.02.2021 09:15-14:00 | Grupo /CLIL_01 | Classroom A5 |
| 07.02.2021 09:15-14:00 | Grupo /CLIL_04 | Classroom A5 |
| 07.02.2021 09:15-14:00 | Grupo /CLE_01 | Classroom A5 |
| 07.02.2021 09:15-14:00 | Grupo /CLIL_02 | Classroom A5 |