ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Hours of tutorials: 1 Expository Class: 30 Interactive Classroom: 20 Total: 51
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: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
- Know the basic fundamentals of mathematics on which the rest of the subjects of the degree will be based.
- Know how to identify, model and solve problems specific to differential and integral calculus.
- Acquire the conceptual basis of the mathematical instruments that are the skeleton of the methods of analysis and modelling of artificial intelligence.
- Master the concepts of function of several real variables, gradient of a function and approximation of functions and their application to real problems.
In the practical part, students will learn to solve numerically the problems posed with the different numerical methods studied.
1. Introduction to mathematical analysis and numerical calculation.
Real numbers. Functions and their graphs. Elementary functions. Review of basic concepts of numerical calculus.
2. Differential calculus of one variable. Numerical derivation.
Derivation. Derivation rules. Chain rule. Implicit derivation Mean value theorem Taylor's polynomial Numerical derivation Extremes of functions.
3. Numerical solution of non-linear equations.
Separation of roots. Bisection method. Newton's method.
4. Integral calculus in one variable
Indefinite integral Fundamental theorems of integral calculus. Calculus of primitives. Leibniz's rule.
5. Numerical resolution of linear systems.
Rapid descent method. LU and Cholesky factorisations. Computational cost analysis.
6. Basic concepts of functions of several variables.
Domain, image, contour lines, graph of a function of several variables.
7. Derivation in several variables.
Partial derivatives, gradient, Jacobian matrix.
Maximum and minimum of scalar functions of several variables.
Basic:
THOMAS, G. B. Calculus: several variables. Pearson Educación, Mexico, D.F., 13th ed., 2015. ISBN: 9786073233361.
CHAPRA, S. C. and CANALE, R. P. Numerical Methods for Engineers. McGraw-Hill, Mexico, 7th ed., 2015. ISBN: 9786071512949.
Complementary:
ATKINSON, K. E. An introduction to Numerical Analysis. Wiley, New York, 2nd ed., 1989. ISBN: 0-471-62489-6.
ISAACSON, E. and KELLER, H. B. Analysis of Numerical Methods. John Wiley and Sons, New York, 2nd ed. 1994. ISBN: 0-486-68029-0
ANASTASSIOU, G. A. and MEZEI, R. Numerical Analysis Using Sage. Springer, Switzerland, 2015. ISBN: 978-3-319-16739-8.
Basic and general:
GC2 - Ability to solve problems with initiative, decision-making, autonomy and creativity.
GC4 - Ability to select and justify the appropriate methods and techniques to solve a specific problem, or to develop and propose new methods based on artificial intelligence.
CB2 - That students know how to apply their knowledge to their work or vocation in a professional manner and possess the competences that are usually demonstrated through the elaboration and defence of arguments and the resolution of problems within their area of study.
CB3 - Students have the ability to gather and interpret relevant data (usually within their area of study) in order to make judgements that include reflection on relevant social, scientific or ethical issues.
CB5 - That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy.
Transversal:
TR3 - Ability to create new models and solutions autonomously and creatively, adapting to new situations. Initiative and entrepreneurial spirit.
Specific:
CE1 - Ability to use mathematical concepts and methods that may arise in the modelling, approach and resolution of artificial intelligence problems.
The lecture hours will be used to present the basic contents of this subject, in which the competences CG2, CG4, CB2, CB3 and CE1 will be worked on.
In the interactive classes in small groups, exercises and computer exercises will be carried out, in which the competences CB2, CB3 and TR3 will be worked on.
Likewise, study topics and problems will be proposed to be solved by the students, who will have to present these results, in which support will also be offered. These tasks will work on the competences CB5 and TR3.
The presentation of the contents will be supported by the use of transparencies provided by the teachers and the development of the concepts and exercises on the blackboard. All course material will be available on the USC Virtual Campus.
Assessment First opportunity (January / February)
A continuous assessment method will be followed, through directed academic activities, taking into account the work done both individually and in groups, including work done on the computer, in which students must demonstrate their knowledge of the subject; and a final exam.
(60% of the mark) Final exam on theoretical-practical contents, which will include some questions related to the practical work with the computer. In this part the competences CG2, CG4, CB2 and CB5 will be assessed.
(40% of the mark) Continuous assessment of the work, throughout the course, which may include the following elements:
- Preparation of group work to be presented in front of the class, and any member of the group may be questioned. Competences CB3 and CE1 will be assessed.
- Individual resolution of problems and/or computer practices with an author control on some part of it. The competences CG2, CB5 and TR3 will be assessed.
- Response to questionnaires in class and / or in the virtual course. The competences CG2, CB5, CE1 and TR3 will be assessed.
4 tests will be proposed, each of them with the same weight: 1 written test at the end of topic 2, 1 computer test at the end of topic 4, 1 computer test in the last laboratory session and 1 written test at the end of topic 7.
Second opportunity (June / July)
The evaluation of students will be based on a final exam with the following percentages:
- Final theoretical-practical exam which may include questions on computer practices: 70%.
- Continuous assessment, carried out at the first opportunity: 30%.
Although attendance to the different teaching activities helps to improve the understanding of the subject and the acquisition of competences, it will not have any assessment in terms of evaluation (see article 1 of the regulations on class attendance in official USC bachelor's and master's degree courses).
All students will be considered "presented" if they take part in any assessable activity.
In the case of fraudulent performance of exercises or tests, the rules set out in the Regulations for the evaluation of students' academic performance and revision of grades shall apply.
For repeat students, the continuous assessment mark obtained in the previous year will be maintained for the current year. The rest of the activities will be assessed in the same way as for ordinary students.
Face-to-face:
30 hours of theory classes
20 hours of laboratory work in small groups
1 hour of individual tutorials
3 hours of final written exam
3 hours of final computer exam.
Non-attendance:
48 hours of self-study related to the classes (24 hours for theory, 10 for problems, 14 for computer practice)
25 hours to work on the proposed problems
20 hours to program solutions to proposed problems on computer
Total workload: 150 hours
- Attendance at classes with active participation in them.
- Use of the basic bibliography and recommended material.
- Carrying out the necessary practices and exercises corresponding to the different subjects in order to achieve the established objectives.
The Virtual Campus is used.
The language of instruction is the one that appears on the official website of the USC for this subject.
José Luis Ferrín González
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813191
- joseluis.ferrin [at] usc.es
- Category
- Professor: University Lecturer
Daniel Paraje Ordás
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- daniel.paraje [at] rai.usc.gal
- Category
- Predoutoral_Doutoramento Industrial
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLE_01 | Spanish | IA.11 |
| 12:00-14:00 | Grupo /CLIL_02 | Spanish | IA.13 |
| Tuesday | |||
| 11:00-12:00 | Grupo /CLE_01 | Spanish | IA.11 |
| Thursday | |||
| 09:30-11:30 | Grupo /CLIL_03 | Spanish | IA.13 |
| Friday | |||
| 11:00-12:00 | Grupo /CLE_01 | Spanish | IA.11 |
| 12:00-14:00 | Grupo /CLIL_01 | Spanish | IA.13 |
| 01.09.2026 09:15-14:00 | Grupo /CLE_01 | IA.S1 |
| 01.09.2026 09:15-14:00 | Grupo /CLIL_02 | IA.S1 |
| 01.09.2026 09:15-14:00 | Grupo /CLIL_01 | IA.S1 |
| 01.09.2026 09:15-14:00 | Grupo /CLIL_03 | IA.S1 |
| 01.09.2026 09:15-14:00 | Grupo /CLE_01 | IA.S2 |
| 01.09.2026 09:15-14:00 | Grupo /CLIL_02 | IA.S2 |
| 01.09.2026 09:15-14:00 | Grupo /CLIL_01 | IA.S2 |
| 01.09.2026 09:15-14:00 | Grupo /CLIL_03 | IA.S2 |
| 06.26.2026 16:00-20:30 | Grupo /CLE_01 | IA.01 |
| 06.26.2026 16:00-20:30 | Grupo /CLIL_02 | IA.01 |
| 06.26.2026 16:00-20:30 | Grupo /CLIL_01 | IA.01 |
| 06.26.2026 16:00-20:30 | Grupo /CLIL_03 | IA.01 |