First opportunity:

The evaluation of the students in the first opportunity will be based on the following sections:

Final exam. It will consist of two theoretical-practical tests, corresponding to the subject of each block: Statistics and Calculus.

To pass the subject, it will be necessary to obtain an average grade, between the two blocks, greater than or equal to 5, and not have a grade lower than 4 in any of them. Students who do not meet any of these requirements will have a fail grade on the first opportunity (the numerical grade will be the minimum between 4.5 and the average of the grades obtained in each block).

Evaluation of the continuous follow-up of the matter. The interest and active participation of the student will be valued, both in the expositive and interactive classes, the completion of the work and problems raised, as well as its delivery on time.

The final exam has a weight of 90% and the continuous evaluation has a weight of 10% in the course grade.

Observation of the evaluation of the calculus block: To evaluate the follow-up of the calculus block, two tests will be carried out throughout the semester. The first test will correspond to the subject taught in Topic 4, and the second to the subject taught in Topics 5 and 6. If the grades obtained in these tests are not less than 3, the average grade between the two is considered, with a weighting of 90%, to which would be added the evaluation of the continuous follow-up of the matter, with a weighting of 10%; If the total result is greater than or equal to 5, then the student may choose not to take the final exam, in which case the grade obtained by continuous assessment and partial exams will represent 100% of the final grade for the Calculus block.

Observation of the evaluation of the statistics block: To evaluate the monitoring of the statistics block, two tests will be carried out throughout the semester. The first test will correspond to the matter taught in Theme 1, and the second to the matter taught in Themes 2 and 3. If the grades obtained in these tests are not less than 3, the average grade between the two is considered, with a weighting of 90%, to which would be added the evaluation of the continuous follow-up of the matter, with a weighting of 10%; If the total result is greater than or equal to 5, then the student may choose not to take the final exam, in which case the grade obtained by continuous assessment and partial exams will represent 100% of the final grade for the Statistics block.

Second opportunity (July):

The evaluation of second chance students will be based on the following sections:

- Final exam: It will consist of two theoretical-practical tests, corresponding to the subject of each block: Calculus and Statistics.

Those students who have passed one of the blocks in the first opportunity, may choose not to take the exam in that block, since the grade obtained in the first opportunity is saved.

- Evaluation of the continuous follow-up of the subject, equal to that established for the first opportunity.

The final exam has a weight of 90% and the continuous evaluation has a weight of 10% in the course grade.

To pass the subject on the second chance, it will be necessary to obtain an average grade, between the two blocks, greater than or equal to 5, and not have a grade lower than 4 in any of them. Students who do not meet any of these requirements will have a fail grade on the second chance (the numerical grade will be the minimum between 4.5 and the average of the grades obtained in each block).

Both opportunities:

1) The students with recognition of part-time dedication and academic dispensation of exemption from attendance (which they must communicate to one of the teachers of the subject), will be evaluated, both in the first and on a second opportunity, only for the grade obtained in the final exam. Like the rest of the students, to pass the subject, they will have to have an average grade between the two blocks of the exam, greater than or equal to 5, and not have a grade lower than 4 in any of them.

2) There are no differentiated evaluation criteria for repeating students.

3) Indication referring to plagiarism and improper use of technologies in carrying out tasks or tests: For cases of fraudulent carrying out of exercises or tests, the provisions of the "Regulations for evaluating the academic performance of students" will apply. students and the review of grades" of the USC and in the "Rules for evaluation, review and claim of the grades of Bachelor's and Master's degree studies" of the UDC.

The fraudulent completion of the tests or evaluation activities, once verified, will directly imply the grade of failing "0" in the subject in the corresponding call, invalidating any grade obtained in the tests and/or evaluation activities, as established in the academic regulations at the UDC.

Learning outcomes	Study programme competences
Acquire the ability to: -Organize, summarize and represent data. -Formulate problems in terms of statistical models. -Perform the calculations required by the proposed methods. -Interpret the results of the statistical analysis.	A5 A13	B6 B10	C1 C2 C3 C4 C5 C6 C7 C8
Know and apply numerical calculus and differential and integral calculus: -Know and use the differential calculus of one and several variables. -Know and properly apply the integration methods of functions of one variable. -Establish the basic concepts of the definite integral and know its applications. -Understand the fundamental concepts related to differential equations. -Recognize and integrate equations of first order and higher order than the first. -Know and be able to apply approximate methods for solving first-order differential equations. Know and apply the methods of descriptive statistics to organize, summarize, present and obtain synthetic measures related to a set of data obtained from a population or a sample. - Know the fundamentals of probability calculation and its specific language, as the basis of the statistical inference process, particularly the concepts of random experiment, random variable and probability distribution of a variable, and apply it to problem solving and to identify situations in these concepts are manifested. - Know and apply the basic techniques of statistical inference: sampling, estimation, estimation and precision and uncertainty measurements associated with the inference process.	A13	B1 B2 B3 B4 B5 B6 B10	C1 C2 C3 C4 C5 C6 C7 C8

Topic	Sub-topic
Topic 1. Exploratory data analysis.	Sampling distribution of a variable. Summary measures. Regression and correlation.
Topic 2. Random variables.	Random variables. Population distribution of a variable. Summary measures. Commonly used probability distribution models.
Topic 3. Statistical inference techniques.	Confidence intervals based on one and two samples. Contrast of hypotheses based on one and two samples.
Topic 4. Real functions and vector functions.	Real valued functions and vector functions. Limits and continuity. Derivation. Relative and conditional extremes.
Topic 5. Integration.	Integration. Numerical integration.
Topic 6. Ordinary differential equations.	Ordinary differential equations. Methods of solving ordinary differential equations. Numerical resolution of first order differential equations.

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Introductory activities	B6 C8	1	0	1
Guest lecture / keynote speech	A5 A13 B10 C6 C7	27	30	57
Problem solving	A13 B1 B2 B6 B10 C1 C2 C3 C4 C5 C6	27	60	87
Objective test	A13 B1 B2 B3 B4 B5 C1 C2	4	0	4

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
Introductory activities	In the first class of the course there will be a presentation of the contents, skills and objectives to be achieved with this subject. A brief test may be carried out in order to know the competences that the student possesses.
Guest lecture / keynote speech	Oral presentation complemented by the use of audiovisual media, in which the teacher will present the different topics of the subject, as well as the problems that the student must learn to solve. Throughout it, the student will be able to intervene by asking questions that facilitate her instruction and the teacher will ask questions addressed to the students in order to transmit knowledge and facilitate learning.
Problem solving	As the subject develops, the teacher will propose assignments and/or deliver problem sets that the students must solve. Problem sets are not tests. Its resolution will begin in the classroom, where the students, in small groups, will discuss where their difficulty lies and how their resolution can be faced. The student will finish carrying them out independently and will be able to check if they have done them correctly, in the classroom or on the USC Virtual Campus.
Objective test	Theoretical-practical exam of the subject taught.

Methodologies	Competencies	Description	Qualification
Objective test	A13 B1 B2 B3 B4 B5 C1 C2	Evaluation of the continuous follow-up of the matter. The active participation in the classes, the realization of works and exposed problems, as well as their delivery on time will be taken into account.	90
Problem solving	A13 B1 B2 B6 B10 C1 C2 C3 C4 C5 C6	Final exam, consisting of two theoretical-practical tests corresponding to the two blocks of the subject: Calculus and Statistics.	10

Assessment comments
*First opportunity:* The evaluation of the students in the first opportunity will be based on the following sections: Final exam. It will consist of two theoretical-practical tests, corresponding to the subject of each block: Statistics and Calculus. To pass the subject, it will be necessary to obtain an average grade, between the two blocks, greater than or equal to 5, and not have a grade lower than 4 in any of them. Students who do not meet any of these requirements will have a fail grade on the first opportunity (the numerical grade will be the minimum between 4.5 and the average of the grades obtained in each block). Evaluation of the continuous follow-up of the matter. The interest and active participation of the student will be valued, both in the expositive and interactive classes, the completion of the work and problems raised, as well as its delivery on time. The final exam has a weight of 90% and the continuous evaluation has a weight of 10% in the course grade. Observation of the evaluation of the calculus block: To evaluate the follow-up of the calculus block, two tests will be carried out throughout the semester. The first test will correspond to the subject taught in Topic 4, and the second to the subject taught in Topics 5 and 6. If the grades obtained in these tests are not less than 3, the average grade between the two is considered, with a weighting of 90%, to which would be added the evaluation of the continuous follow-up of the matter, with a weighting of 10%; If the total result is greater than or equal to 5, then the student may choose not to take the final exam, in which case the grade obtained by continuous assessment and partial exams will represent 100% of the final grade for the Calculus block. Observation of the evaluation of the statistics block: To evaluate the monitoring of the statistics block, two tests will be carried out throughout the semester. The first test will correspond to the matter taught in Theme 1, and the second to the matter taught in Themes 2 and 3. If the grades obtained in these tests are not less than 3, the average grade between the two is considered, with a weighting of 90%, to which would be added the evaluation of the continuous follow-up of the matter, with a weighting of 10%; If the total result is greater than or equal to 5, then the student may choose not to take the final exam, in which case the grade obtained by continuous assessment and partial exams will represent 100% of the final grade for the Statistics block. *Second opportunity* (July): The evaluation of second chance students will be based on the following sections: - Final exam: It will consist of two theoretical-practical tests, corresponding to the subject of each block: Calculus and Statistics. Those students who have passed one of the blocks in the first opportunity, may choose not to take the exam in that block, since the grade obtained in the first opportunity is saved. - Evaluation of the continuous follow-up of the subject, equal to that established for the first opportunity. The final exam has a weight of 90% and the continuous evaluation has a weight of 10% in the course grade. To pass the subject on the second chance, it will be necessary to obtain an average grade, between the two blocks, greater than or equal to 5, and not have a grade lower than 4 in any of them. Students who do not meet any of these requirements will have a fail grade on the second chance (the numerical grade will be the minimum between 4.5 and the average of the grades obtained in each block). Both opportunities:** 1) The students with recognition of part-time dedication and academic dispensation of exemption from attendance (which they must communicate to one of the teachers of the subject), will be evaluated, both in the first and on a second opportunity, only for the grade obtained in the final exam. Like the rest of the students, to pass the subject, they will have to have an average grade between the two blocks of the exam, greater than or equal to 5, and not have a grade lower than 4 in any of them. 2) There are no differentiated evaluation criteria for repeating students. 3) Indication referring to plagiarism and improper use of technologies in carrying out tasks or tests: For cases of fraudulent carrying out of exercises or tests, the provisions of the "Regulations for evaluating the academic performance of students" will apply. students and the review of grades" of the USC and in the "Rules for evaluation, review and claim of the grades of Bachelor's and Master's degree studies" of the UDC. The fraudulent completion of the tests or evaluation activities, once verified, will directly imply the grade of failing "0" in the subject in the corresponding call, invalidating any grade obtained in the tests and/or evaluation activities, as established in the academic regulations at the UDC.

Basic
	CÁLCULO: • Larson, R.; Hostetler, R. P.; Edwards, B. H. (2006). Cálculo, volúmenes 1 y 2. Madrid, McGraw-Hill. • Robert A. Adams (2009). Cálculo. Pearson Educación S. A., Madrid. • Rogawski, J. (2016). Cálculo. Una variable. Barcelona, Editorial Reverté.https://elibro-net.accedys.udc.es/es/ereader/bibliotecaudc/46777 • Rogawski, J. (2012). Cálculo. Varias variables. Barcelona, Editorial Reverté. https://elibro-net.accedys.udc.es/es/ereader/bibliotecaudc/46778 ESTADÍSTICA: • Arriaza Gómez, A.J. y otros (2008). Estadística básica con R y R-commander. Universidad de Cádiz. • Delgado de la Torre, R. (2008). Probabilidad y Estadística para Ciencias e Ingenierías. Delta Publicaciones. • Espejo Miranda, I. (2006). Estadística Descriptiva y Probabilidad (Teoría y Problemas). Universidad de Cádiz. http://sestio.uca.es/repos/l_edyp/pdf/febrero06/lib_edyp.c1.pdf • Espejo Miranda, I. (2015). Inferencia Estadística (Teoría y Problemas). Universidad de Cádiz. http://sestio.uca.es/repos/l_inf_est/pdf/actual/lib_inf.pdf • Cao, R. e outros (2006). Introducción a la Estadística y sus aplicaciones. Ed. Pirámide. • Framiñán Torres, J.M. y otros (2016). Problemas resueltos de probabilidad y estadística. Universidad de Sevilla. • Madsen, B. S. (2016). Statistics for non-statisticians. Springer. • Mendenhall, W.M. (2016). Statistics for engineering and the sciences. CRC Press, Taylor & Francis Group. • Montgomery, D. C. y Runger, G.C. (2010). Probabilidad y Estadística aplicadas a la Ingeniería. Limusa Wiley. • Moore, D. S. (2005). Estadística aplicada básica. Antoni Bosch, D.L.
Complementary
	CÁLCULO • Ayres, F. (1992). Cálculo Diferencial e Integral. Madrid, McGraw-Hill. • Granero, F. (2001). Cálculo integral y aplicaciones. Madrid, Prentice-Hall. • Martínez Sagarzazu, E. (1996). Ecuaciones diferenciales y cálculo integral. Servicio Editorial Univ. del País Vasco. • Simmons, G. F.; Krantz, S. G. (2007). Ecuaciones diferenciales. Teoría, técnica y práctica. México, McGraw-Hill. • Larson, R. y Edwards, B. (2017). Matemáticas I: cálculo diferencial. Cengage Learning. https://elibro-net.accedys.udc.es/es/lc/bibliotecaudc/titulos/108520 • Larson, R. y Edwards, B. (2017). Matemáticas II: cálculo integral. Cengage Learning. https://elibro-net.accedys.udc.es/es/lc/bibliotecaudc/titulos/108522 • Larson, R. y Edwards, B. (2017). Matemáticas III: cálculo de varias variables. Cengage Learning. https://elibro-net.accedys.udc.es/es/lc/bibliotecaudc/titulos/108524 ESTADÍSTICA: • Martínez, M (2009): R for Biologist. NIMBioS.(http://cran.r-project.org/) • Milton, J. S. (2007). Estadística para biología y ciencias de la salud. McGraw-Hill • Navidi, W. (2006). Estadística para Ingenieros y Científicos. McGraw-Hill. • Parra Frutos, I. (2003). Estadística Empresarial con Microsoft Excel. Problemas de Inferencia Estadística. Ed. AC. • Ross, S.M. (2014). Introduction to probability and statistics for engineers and scientists. Elsevier-Academic Press. • Ryan, T.P. (2007). Modern Engineering Statistics. John Wiley & Sons. • Ross, S.M. (2014). Introduction to probability and statistics for engineers and scientists. Elsevier-Academic Press. • Ryan, T.P. (2007). Modern Engineering Statistics. John Wiley & Sons. • Walpole, R. E. y otros (1999). Probabilidad y estadística para ingenieros. Prentice-Hall.