ECTS credits ECTS credits: 9
ECTS Hours Rules/Memories Student's work ECTS: 148.5 Hours of tutorials: 4.5 Expository Class: 36 Interactive Classroom: 36 Total: 225
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: Annual
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
1) To know the main methods for solving linear systems.
2) To introduce students to the differential calculus of multivariable functions in order to master the basic problem-solving techniques.
3) To know the basic tools of integration in single variable and multivariable calculus, its definition from a physical and geometric point of view and the calculation techniques.
4) To know line and surface integration tools, as well as their physical meaning.
5) To know some basic methods for the resolution of non-linear equations and for the numerical approximation of single variable definite integrals.
6) To know and handle the basic concepts related to the differential and integral calculus and their applications to real problems and other areas of the degree.
7) To introduce students to the e-learning using the Learning Management System.
1) LINEAR SYSTEMS
1.a) Interpretation of linear systems in terms of matrices and vectors.
1.b) Techniques to compute the determinant of a matrix.
1.c) Numerical methods for solving linear systems: Gauss elimination, Gauss-Seidel iterative method.
2) MULTIVARIABLE FUNCTIONS
2.a) Scalar and vector functions. Domain, image, graph and level set of a multivariable function.
2.b) Limits and continuity.
2.c) Parameterization of curves and surfaces.
3) DIFFERENTIAL CALCULUS FOR MULTIVARIABLE FUNCTIONS
3.a) Partial derivatives.
3.b) Gradient. Tangent plane.
3.c) Newton's method for the resolution of non-linear equations and non-linear systems.
3.d) Jacobian matrix.
3.e) Chain rule.
3.f) Implicit differentiation.
3.g) Directional derivatives.
3.h) Higher order derivatives. Hessian matrix.
3.i) Taylor's theorem for multivariable functions.
3.j) Maxima and Minima.
4) SINGLE VARIABLE INTEGRAL CALCULUS
4.a) The definite integral: geometrical meaning and properties.
4.b) Fundamental theorem of integral calculus.
4.c) The indefinite integral: calculation of primitives.
4.d) Improper integrals.
4.e) Numerical integration.
5) MULTIVARIABLE INTEGRAL CALCULUS.
5.a) Integration over rectangular parallelepipeds and elementary regions. The geometric meaning.
5.b) Iterated integrals. Fubini's theorem.
5.c) Integrals in polar, cylindrical and spherical coordinates.
6) LINE AND SURFACE INTEGRATION.
6.a) Parameterization of regular curves in space. The tangent vector to a curve. Integral of a scalar function over a curve. Integral of a vector function over a curve.
6.b) Parameterized surfaces in space. The tangent plane and the normal vector to a surface. The orientation of a surface. Integral of a scalar function over a surface. Integral of a vector function over a surface.
Basic bibliography:
- THOMAS, G.B., 2015. Cálculo: Una variable [on line]. 13ª edición. México: Pearson. ISBN 9786073233293.
- THOMAS, G.B., 2015. Cálculo: Varias variables [on line]. 13ª edición. México: Pearson. ISBN 9786073233392.
- Notes and slides available in the Learning Management System.
Complementary bibliography:
- KOLMAN, B., 1999. Álgebra lineal con aplicaciones y Matlab. 6ª edición. México: Pearson Educación. ISBN 970-17-0265-4
- LAY, D. C., 2001. Álgebra lineal y sus aplicaciones. 3ª edición. México: Pearson-Prentice Hall. ISBN 970-26-0080-4
- ADAMS, R.A., 2009. Cálculo. 6ª edición. Madrid: Pearson-Addison Wesley. ISBN 9788478290895
- MARSDEN, J. E. y TROMBA, A. J., 2004. Cálculo vectorial. 5ª edición. Madrid: Pearson. ISBN 84-7829-069-9
- CAMPOS, B., CHIRALT, C., 2011. Cálculo integral [on line]. Publicación de la Universitat Jaume I. Servei de Comunicació i Publicacions. Licencia Creative Commons. Notes available in the Learning Management System.
Specific competences:
FB.1 .- Ability to solve mathematical problems that may arise in engineering. Ability to apply the acquired concepts on:
FB.1.1. Linear algebra, geometry, differential geometry, differential and integral calculus;
FB.1.3. Numerical methods, numerical algorithms.
Basic and general competences:
CB.1. Knowledge and understanding in a field of study that parts of the basis of general secondary education, and it is typically at a level which, although it is supported by advanced textbooks, includes some aspects which require knowledge from the forefront of their field of study.
CG.3. Knowledge in basic and technological topics enabling to learn new methods and theories. Ability to adapt to new situations.
CG.4. Ability to solve problems with initiative, decision making, creativity, critical thinking. Ability to communicate and transmit knowledge and skills in the field of chemical engineering industry.
Transversal competences: achieve the competences included in the BSc in Chemical Engineering report: CT.1, CT.2, CT.4-.T.7, CT.12-CT.15, CT.19.
1) The theoretical contents of the course will be introduced during the lectures. Slides will be used as support. Related competences: CB.1, CG.3, FB.1.1 e FB.1.3.
2) The students will have a problem set of each chapter. These problems will be solved during the corresponding seminars. Related competences: CG.3, CG.4, FB.1.1, CT.1, CT.2, CT.4, CT.5, CT.6 ,CT.7, CT.13, CT.19.
3) The tutorial sessions with small groups will be used to answer questions formulated by the students and related to the contents of the course. Competences: CG.4, CT.1, CT.2, CT.5-CT.7, CT.12-CT.15, CT.19.
4) In the course created in the Learning Management System the student will have all the material of the course, as well as a forum of news and a virtual support to ask questions to the teachers via e-mail.
Students will take a theoretical exam at the end of each semester on the dates fixed by the center. The theoretical exam will provide 70% of the grade, and it will be made up of theoretical questions and problems related to the subject. The remaining 30% will correspond to four short tests on theory issues and problems that will be performed during the course (two by semester).
Specifically:
The overall grade of the first semester is defined as C1=máx(EF1,0.7xEF1+0,3xPC1), being:
a) EF1: grade of the final exam on theory and problems.
b) PC1: grade of the tests taken throughout the course.
In the same way, the overall grade of the second semester is defined as: C2=máx(EF2,0.7xEF2+0,3xPC2).
Based on these ratings, the final CF rating is calculated as:
a) If C1 >=4 and C2 >= 4 then CF=(C1+C2)/2.
b) Otherwise CF = min(4,(C1+C2)/2).
If CF >=5 then the subject has been passed obtaining the corresponding qualification. Otherwise the subject is failed.
In the case that the student fails, he/she may recover it in the second opportunity exam. This will consist of two parts corresponding to the first and second semester. The student could take the parts of the exam with global qualification less than five. The grades of the tests taken during the course shall be kept for the second opportunity. To pass the course in the second opportunity it is mandatory to reach the minimun qualifications established for each part of the course.
Grades PC1 and PC2 will be communicated to the student before the exam.
Those students not attending any of the exams will be qualified as "absent" (no presentado).
Assesment tools evaluate 100% of the basic, general, specific and transversal competences previously described. In particular, in the final exam (EF) and in the tests taken throughout the course (PC) the competences CB.1, CG.3, CG.4, FB.1.1, F.B.1.3, CT.1, CT.2, CT.4, CT.5, CT.6, CT.7, CT.12, CT.13, CT.14, CT. 15 e CT.19 will be evaluated.
In cases of fraudulent performance of exercises or tests, the provisions of the "Regulations for the evaluation of the academic performance of students and the review of grades" will apply.
Lectures: 57 hours + 80.4 hours of work = 5.5 ECTS
Exercise classes: 16 hours + 22.6 hours of work = 1.5 ECTS
Small group classes: 4 hours + 8 hours of work = 0.5 ECTS
Individualized tutoring: 4 hours + 2 hours of work = 0.4 ECTS
Assessment of the acquired skills: 9 hours (exams) + 22 hours of work = 1.1 ECTS
Total: 90 hours + 135 hours of work = 9 ECTS
1) The student should attend the lectures and the practical classes.
2) The effort concerning the preparation of the course should be uniformly distributed in time.
3) The student should check the assimilation of concepts and the acquisition of computational techniques solving the exercises proposed during the lectures as well as the problem sets.
Patricia Barral Rodiño
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813213
- patricia.barral [at] usc.es
- Category
- Professor: University Lecturer
Maria Luisa Seoane Martinez
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813230
- marialuisa.seoane [at] usc.es
- Category
- Professor: University Lecturer
Saray Busto Ulloa
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- saray.busto.ulloa [at] usc.es
- Category
- Researcher: Ramón y Cajal
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| 11:00-12:00 | Grupo /CLIS_01 | Spanish | Classroom A2 |
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| 10:00-11:00 | Grupo /CLIS_02 | Spanish | Classroom A2 |
| 01.11.2024 09:15-14:00 | Grupo /CLE_01 | Classroom A3 |
| 01.11.2024 09:15-14:00 | Grupo /CLIS_01 | Classroom A3 |
| 01.11.2024 09:15-14:00 | Grupo /CLIS_03 | Classroom A3 |
| 01.11.2024 09:15-14:00 | Grupo /CLIS_02 | Classroom A3 |
| 01.11.2024 09:15-14:00 | Grupo /CLIS_02 | Classroom A4 |
| 01.11.2024 09:15-14:00 | Grupo /CLE_01 | Classroom A4 |
| 01.11.2024 09:15-14:00 | Grupo /CLIS_01 | Classroom A4 |
| 01.11.2024 09:15-14:00 | Grupo /CLIS_03 | Classroom A4 |
| 06.06.2024 09:15-14:00 | Grupo /CLE_01 | Classroom A3 |
| 06.06.2024 09:15-14:00 | Grupo /CLIS_02 | Classroom A3 |
| 06.06.2024 09:15-14:00 | Grupo /CLIS_01 | Classroom A3 |
| 06.06.2024 09:15-14:00 | Grupo /CLIS_03 | Classroom A3 |
| 06.06.2024 09:15-14:00 | Grupo /CLIS_01 | Classroom A4 |
| 06.06.2024 09:15-14:00 | Grupo /CLIS_03 | Classroom A4 |
| 06.06.2024 09:15-14:00 | Grupo /CLE_01 | Classroom A4 |
| 06.06.2024 09:15-14:00 | Grupo /CLIS_02 | Classroom A4 |
| 06.25.2024 09:15-14:00 | Grupo /CLIS_01 | Classroom A1 |
| 06.25.2024 09:15-14:00 | Grupo /CLIS_03 | Classroom A1 |
| 06.25.2024 09:15-14:00 | Grupo /CLE_01 | Classroom A1 |
| 06.25.2024 09:15-14:00 | Grupo /CLIS_02 | Classroom A1 |