To pass the course, it will be necessary to obtain, added the marks of all the activities, a minimum grade of 50% of the total and 50% of the multiple-choice test. To obtain the grade of not presented, it will be sufficient that the student does not participate in the multiple-choice test and has not been evaluated in the supervised Works in more than 50%. In the second chance test, the criterion to pass the subject will be the previous one or to obtain a grade of not less than 50% in the multiple choice test. With regard to successive academic courses, the teaching-learning process, including assessment, refers to one academic course, and therefore a new course would be restarted, including all assessment activities and procedures that were scheduled for that course; however, it is allowed to request to maintain the practical qualification of a previous course.

Students enrolled in part-time regime and academic exemption from attendance exemption, can be evaluated in a personalized way regarding the methodologies of Maxistral Session, Problem Solving and Tutored Jobs. Students enrolled in part-time regimen are required to sit the multiple-choice test, as well as the partial tests throughout the course. For the first and second opportunity, the evaluation criteria for this student body is the same as for the others and the attendance waiver percentage will be 80%.

Students at the first opportunity have priority in the granting of honors.

Contingency plan (due to Covid19):

Mathematics part (75%): There are no changes in the weights of the grades: 54% Multiple-choice test of the theory part, 21% Multiple-choice test of the practice (or supervised work in case of non-attendance).

Part of the statistic (25%). There are no changes in the weights of the grades: 16% Multiple choice test of the theory part, 9% Multiple choice test of the practice (or supervised work in case of non-attendance).

*Evaluation observations:

They remain the same as above.

REQUIREMENTS TO PASS THE SUBJECT:

1. Regularly attend and participate in class activities.

2. Submit supervised work by the date indicated.

3. Obtain a minimum grade of 50% in the objective test and a minimum final grade of 50% plus the marks of all the activities.

4. The July opportunity will be subject to the same criteria as the June opportunity.

Learning outcomes	Study programme competences
The study, representation and interpretation of elementary functions of one and several variables	A15 A16 A20 A24 A25 A27	B1 B2 B3 B6	C1 C3 C6
Use skilfully the techniques of calculation of primitive and its applications.	A15 A16 A20 A24 A25 A27	B1 B2 B3 B6	C1 C3 C6
Set out and solve simple models that comport equations and systems of differential equations.	A15 A16 A20 A24 A25 A27	B1 B2 B3 B6	C1 C3 C6
Solve problems of basic statistical methods from the descriptive point of view	A15 A16 A20 A24 A25 A27	B1 B2 B3 B6	C1 C3

Topic	Sub-topic
Differentiation of functions of several variables	Functions of several variables. Topological notions. Flat curves and parametric equations. Surfaces in space. Polar, cylindrical and spherical coordinates. Real functions of several variables. Scalar and vector functions. Graphs and level sets. Concept of continuity. Differentiation of functions of several variables. Partial derivatives. Directional derivative. Differential of a function. Higher order partial derivatives. Jacobean Matrix. Chain rule. Taylor's theorem. Plane tangent to a surface. Function ends of two variables. Lagrange multipliers.
Integration of functions of several variables	Multiple integration. Integral line. Iterated integrals. Double integrals. Change of variables: polar coordinates. Triple integrals Change of variables: cylindrical and spherical coordinates. Applications. Line integrals of scalar and vector functions. Applications. Green and Stokes theorem.
Differential Equations	First order differential equations. Separable variables. Homogeneous equations. Exact equations Linear equations. Differential equations as mathematical models. Linear differential equations of order n. Homogeneous linear differential equations. Variation of parameters. Indeterminate coefficients. Linear systems of differential equations. Modeling with systems of differential equations.
Descriptive statistics	Statistical description of a variable Joint statistical description of several variables Regression curves: least squares.

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Guest lecture / keynote speech	A15 A16 A24 A27 B1 B2 B3 B6	32	64	96
Problem solving	A20 A25 B2 B3 C1	8	18	26
Supervised projects	A20 A15 B3 B1 C1 C3 C6	8	16	24
Multiple-choice questions	B2 B3	3	0	3

Personalized attention		1	0	1

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies	Description
Guest lecture / keynote speech	concept development and problem solving Contingency plan (due to Covid19): * Teaching methodologies that change. Master Session: Presence is replaced by material (PDF, explanatory videos) available at moodle.udc.es. and team video conferencing
Problem solving	Questionnaires, bulletins and exams from other courses that will be periodically made available to students on different contents and that students will have to solve. Contingency plan (because of Covid19). * Teaching methodologies that change. Problem solving: Compute in the assessment. Attendance is replaced by material (PDF, explanatory videos) available on moodle.udc.es and group video conferences on Teams
Supervised projects	Working on topics proposed by the teacher, a theoretical summary will be presented along with a bulletin of solved problems on the corresponding topic Contingency plan (because of Covid19): * Teaching methodologies that are maintained Tutored works
Multiple-choice questions	Multiple answer test Contingency plan (because of Covid19): * Teaching methodologies that change Multiple choice test: Compute in the assessment. The following changes will be made: (a) The test relating to the practical part of Statistics is replaced by practical work to be carried out in groups of two students. (b) The tests related to the practical part of Mathematics will be done through online tests at moodle.udc.es (c) The tests related to the theoretical part of the subject will be done through online tests at moodle.udc.es

Methodologies	Competencies	Description	Qualification
Supervised projects	A20 A15 B3 B1 C1 C3 C6	Development of specific aspects with examples and solved problems. Competence B3 will be assessed.	10
Multiple-choice questions	B2 B3	Multiple-choice questions	70
Problem solving	A20 A25 B2 B3 C1	Delivery of exercises and solved exams. Competences A15, B2 and C3 will be assessed.	20

Assessment comments
To pass the course, it will be necessary to obtain, added the marks of all the activities, a minimum grade of 50% of the total and 50% of the multiple-choice test. To obtain the grade of not presented, it will be sufficient that the student does not participate in the multiple-choice test and has not been evaluated in the supervised Works in more than 50%. In the second chance test, the criterion to pass the subject will be the previous one or to obtain a grade of not less than 50% in the multiple choice test. With regard to successive academic courses, the teaching-learning process, including assessment, refers to one academic course, and therefore a new course would be restarted, including all assessment activities and procedures that were scheduled for that course; however, it is allowed to request to maintain the practical qualification of a previous course. Students enrolled in part-time regime and academic exemption from attendance exemption, can be evaluated in a personalized way regarding the methodologies of Maxistral Session, Problem Solving and Tutored Jobs. Students enrolled in part-time regimen are required to sit the multiple-choice test, as well as the partial tests throughout the course. For the first and second opportunity, the evaluation criteria for this student body is the same as for the others and the attendance waiver percentage will be 80%. Students at the first opportunity have priority in the granting of honors. Contingency plan (due to Covid19): Mathematics part (75%): There are no changes in the weights of the grades: 54% Multiple-choice test of the theory part, 21% Multiple-choice test of the practice (or supervised work in case of non-attendance). Part of the statistic (25%). There are no changes in the weights of the grades: 16% Multiple choice test of the theory part, 9% Multiple choice test of the practice (or supervised work in case of non-attendance). *Evaluation observations: They remain the same as above. REQUIREMENTS TO PASS THE SUBJECT: 1. Regularly attend and participate in class activities. 2. Submit supervised work by the date indicated. 3. Obtain a minimum grade of 50% in the objective test and a minimum final grade of 50% plus the marks of all the activities. 4. The July opportunity will be subject to the same criteria as the June opportunity.

Basic	Zill (). Ecuaciones diferenciales con aplicaciones de modelado. Thomson-Learning CAO ABAD, R. y otros (2001). Introducción a la estadística y sus aplicaciones. LARSON (2006). CALCULO. McGrawHill Jon Rogawski (). Cálculo varias variables. Reverté MILLER, J.C. Y MILLER, J.N. (2002). Estadística para Química Analítica. Addison-Wesley Iberoamericana TOMEO PERUCHA V. y UÑA JUÁREZ I. (2003). Lecciones de Estadística Descriptiva. Paraninfo W. Keith Nicholson (2019). Linear Algebra with Applications. Lyryx Learning Team
	Contingency plan (due to Covid 19): Modifications to the bibliography or webography. No changes will be made. They already have all the work materials digitized in Moodle.
Complementary	GONICK, L. Y SMITH, W. (2001). A estatística ¡en caricaturas! . SGAPEIO Bradley (). Cálculo. Prentice Hall Finney (). Cálculo. Addison-Wesley Alfonsa García (). Cálculo I. CLGSA Alfonsa García (). Cálculo II. CLGSA Salas / Hille / Etgen (). Cálculus. Reverté Rainville (). Ecuaciones diferenciales. Prentice Hall Ayres (). Ecuaciones diferenciales. Mcgraw-Hill Quimiometría (2005). MONGAY FERNÁNDEZ, C.. PUV Alegre (). Problemas de funciones de varias variables. PPU GARCÍA ÁLVAREZ-COQUE, C. Y RAMIS RAMOS, G. (2001). Quimiometría. Editorial Síntesis

Other comments
It is convenient to have knowledges of mathematics of 2 bachillerato, if it does not have them recommend do the course of nivelación.