ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 97 Hours of tutorials: 3 Expository Class: 25 Interactive Classroom: 25 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Higher Technical Engineering School
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 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.
Due to the COVID-2019 developed material for the subject that is facilitated in the virtual campus.
- 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 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
Total, course: 100 + 10 x 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.
Carmen Rodriguez Iglesias
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813178
- carmen.rodriguez [at] usc.es
- Category
- Professor: University Lecturer
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 | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom A3 |
| 17:30-19:30 | Grupo /CLIL_01 | Galician | Computer Room I5 |
| Tuesday | |||
| 10:00-11:00 | Grupo /CLE_01 | Galician | Classroom A3 |
| 17:30-19:30 | Grupo /CLIL_02 | Galician | Computer Room I5 |
| Wednesday | |||
| 17:30-19:30 | Grupo /CLIL_03 | Galician | Computer Room I5 |
| Thursday | |||
| 17:30-19:30 | Grupo /CLIL_04 | Galician | Computer Room I5 |
| 01.19.2023 09:15-14:00 | Grupo /CLE_01 | rest room / dining room |
| 01.19.2023 09:15-14:00 | Grupo /CLIL_03 | rest room / dining room |
| 01.19.2023 09:15-14:00 | Grupo /CLIL_02 | rest room / dining room |
| 01.19.2023 09:15-14:00 | Grupo /CLIL_04 | rest room / dining room |
| 01.19.2023 09:15-14:00 | Grupo /CLIL_01 | rest room / dining room |
| 05.23.2023 09:15-14:00 | Grupo /CLE_01 | Classroom A3 |
| 05.23.2023 09:15-14:00 | Grupo /CLIL_01 | Classroom A3 |
| 05.23.2023 09:15-14:00 | Grupo /CLIL_03 | Classroom A3 |
| 05.23.2023 09:15-14:00 | Grupo /CLIL_02 | Classroom A3 |
| 05.23.2023 09:15-14:00 | Grupo /CLIL_04 | Classroom A3 |
| 05.23.2023 09:15-14:00 | Grupo /CLIL_02 | Classroom A4 |
| 05.23.2023 09:15-14:00 | Grupo /CLIL_04 | Classroom A4 |
| 05.23.2023 09:15-14:00 | Grupo /CLE_01 | Classroom A4 |
| 05.23.2023 09:15-14:00 | Grupo /CLIL_01 | Classroom A4 |
| 05.23.2023 09:15-14:00 | Grupo /CLIL_03 | Classroom A4 |
| 07.06.2023 16:00-20:45 | Grupo /CLIL_03 | Classroom A1 |
| 07.06.2023 16:00-20:45 | Grupo /CLIL_02 | Classroom A1 |
| 07.06.2023 16:00-20:45 | Grupo /CLIL_04 | Classroom A1 |
| 07.06.2023 16:00-20:45 | Grupo /CLE_01 | Classroom A1 |
| 07.06.2023 16:00-20:45 | Grupo /CLIL_01 | Classroom A1 |