Mathematics

1) To introduce students to the differential calculus of multivariable functions in order to master the basic problem-solving techniques.
2) 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.
3) To know some basic methods for the resolution of equations, system of equations and single variable definite integrals.
4) To know and handle the basic concepts related to the differential and integral calculus to other areas of the degree.

1) MULTIVARIABLE FUNCTIONS
1.a) Scalar and vector functions. Domain, image, graph and level set of a multivariable function.
1.b) Limits and continuity.

2) DIFFERENTIAL CALCULUS FOR MULTIVARIABLE FUNCTIONS
2.a) Partial derivatives.
2.b) Gradient. Tangent plane.
2.c) Newton's method for the resolution of non-linear equations.
2.d) Numerical methods for solving linear and non-linear systems of equations.
2.e) Jacobian matrix.
2.f) Chain rule.
2.g) Implicit differentiation.
2.h) Directional derivatives.
2.i) Higher order derivatives. Hessian matrix.
2.j) Taylor's theorem for multivariable functions.
2.k) Maxima and Minima.

3) SINGLE VARIABLE INTEGRAL CALCULUS
3.a) The definite integral: geometrical meaning and properties.
3.b) Fundamental theorem of integral calculus.
3.c) The indefinite integral: calculation of primitives.
3.d) Improper integrals.
3.e) Numerical integration.

4) MULTIVARIABLE INTEGRAL CALCULUS.
4.a) Integration over rectangular parallelepipeds and elementary regions. The geometric meaning.
4.b) Iterated integrals. Fubini's theorem.
4.c) Integrals in polar, cylindrical and spherical coordinates.

5) MATLAB PRACTICE.

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:

- ADAMS, R.A., 2009. Cálculo. 6ª edición. Madrid: Pearson-Addison Wesley. ISBN 9788478290895
- 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.

Knowledge and contents:
Con18: Knowledge in basic and technological subjects, enabling them to learn new methods and theories, and giving them the versatility to adapt to new situations.

Skills or abilities:
H/D05: Ability to apply knowledge in practice.

Competences:
Comp03: Ability to solve mathematical problems that may arise in engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial derivative equations; numerical methods; numerical algorithms; statistics and optimisation.

1) The theoretical contents of the course will be introduced during the lectures. Slides will be used as support.
2) The students will have a problem set of each chapter. These problems will be solved during the corresponding seminars.
3) The practical lessons will be used to solve problems with MATLAB.
4) The tutorial sessions with small groups will be used to answer questions formulated by the students and related to the contents of the course.
5) 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 the course on the date 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 two short tests on theory issues and problems that will be performed during the course.

The overall grade is defined as C=máx(CF,0.7xCF+0,3xCP), being:
a) CF: grade of the final exam on theory and problems.
b) CP: grade of the tests taken throughout the course, which will be communicated to the student before the final exam.

In the case that the student fails, he/she may recover it in the second opportunity exam. The grades of the tests taken during the course shall be kept for the second opportunity.

Those students not attending any of the exams will be qualified as "absent" (no presentado).

Assesment tools evaluate 100% of the knowledge, skills and competences previously described.

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: 40 hours
Exercise classes: 8 hours
MATLAB classes: 3 hours
Group tutoring: 1 hour
Exam and review: 4 hours
Hours of personal work by students: 94
Total: 150 hours = 6 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.