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
Center Higher Technical Engineering School
Call: Annual
Teaching: Sin Docencia (En Extinción)
Enrolment: No Matriculable (Sólo Planes en Extinción)
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.
Subject without face-to-face teaching.
Evaluation through examination in the first and second opportunity.
Patricia Barral Rodiño
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813213
- patricia.barral [at] usc.es
- Category
- Professor: University Lecturer
| 01.08.2025 09:15-14:00 | Grupo de examen | Work Classroom |
| 05.21.2025 09:15-14:00 | Grupo de examen | Classroom A1 |
| 06.23.2025 09:15-14:00 | Grupo de examen | Classroom A1 |