The subject of CALCULUS is a subject of the first term of the first course and has 6 ECTS credits. The Presential classes are divided into three types: master classes (30 hours), classroom practices (23 hours) and seminars (7 hours).

In addition to the classes, students will have to work 45 hours of lectures, 34.5 hours of classroom practice and 10.5 hours of seminars.

Knowledge or Content:

RCO1: The graduate will be capable of identifying concepts and techniques from basic and specific subjects that allow the learning of new methods, theories, and modern engineering tools, providing sufficient versatility to adapt to new situations in their professional practice.

RCO5: The graduate will be able to identify concepts and methods related to mathematics that are applicable in the field of engineering.



Competencies:

RC4: The graduate will be capable of applying the strategies inherent to the scientific methodology: analyzing problematic situations both qualitatively and quantitatively, formulating hypotheses and solutions using models specific to renewable energy engineering.



Skills or Abilities:

HE1: The graduate will be capable of solving problems with initiative, decision-making, creativity, and critical reasoning.

HE5: The graduate will be capable of working effectively in a team constructively, integrating skills and knowledge to make decisions.

HE6: The graduate will be capable of acquiring new knowledge and skills for continuous learning, as well as pursuing further studies, with a high degree of autonomy.



Learning outcomes of the subject:

- Analyze and express ideas correctly using mathematical terminology.

- Knows how to operate with complex numbers in their different forms.

- Carries out the complete study of a real function of a real variable.

- Calculates the primitive of a function and knows how to apply it in technological subjects.

- Knows the concept of partial derivative and calculates the directional derivative in a point.

- Knows the concept of double and triple integral and knows how to apply it to different areas

Item 1. The complex number.

Definition and graphic representation. Trigonometric, exponential and polar form. Operations with complex numbers and decomposition of polynomials into factors



Item 2. Real functions of real variable.

Limit and continuity. Applications.



Item 3. Derivability of real functions from real variables.

Derivability and continuity. Successive derivatives. Rule of the chain. Implicit functions. L'hopital rule. Polynomial from Taylor. Applications.



Item 4. Functions of several variables.



Item 5. Derivability of functions of several real variables.

Partial derivatives. Geometric interpretation. Directional derivation. Gradient. Higher order partial derivatives. Derivability of composite functions.



Topic 6. Integral calculation of functions of a variable.

Indefinite integral. Change of variable, integrals by parts, rationals, trigonometrics and irrationals.



Item 7. Defined integral.

Riemann's integral. Barrow's rule. Applications.



Item 8. Multiple integrals.

Iterated integrals. Double and triple integrals. Applications.

The course will follow a methodology characterized by the following aspects:



Preliminary work: the students will carry out the tasks indicated by the teacher, in a non-presential way.

In class: the teacher will propose various training activities. Among others, they will solve the doubts that have arising from previous work done.

Deliverables and tests: students will deliver the deliverables and perform the tests that the teacher indicates and will be will provide the corresponding feedback.



As for the evaluation, the tools and percentages of qualification are the following:

Deliverables and tests: 30%

Final exam: 70%



Note: it is necessary to obtain at least a 4/10 in each of the two parts indicated in order to pass the course.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 70
  • Realization of Practical Work (exercises, cases or problems) (%): 30

Article 8.

In any case, the students will have the right to be evaluated by means of the final evaluation system, independently whether or not it has participated in the continuous or mixed evaluation system. To do so, students must submit the teachers in charge of the course will be asked to waive the continuous or mixed assessment, and will have of a period of 9 weeks, starting from the beginning of the term, in accordance with the academic calendar of the center. In this case, the student will be evaluated with only one final exam, which will include a theoretical and practical part, and which will comprise 100% of the grade.



Article 12. Waiver of the call

12.2.- In the case of continuous evaluation, if the weight of the final test is greater than 40% of the grade of the If you do not take the final exam, the final grade for the course will be no

submitted or not submitted. Otherwise, if the weight of the final test is equal to or less than 40% of the grade of the subject, students may waive the call within a period of at least one month before the date of the end of the teaching period of the corresponding subject. This resignation must be submitted by written to the teachers responsible for the subject.

Article 9

The evaluation of the subjects in the extraordinary calls will be carried out exclusively through the system of final evaluation.



The final evaluation test of the extraordinary call will consist of as many tests and assessment are necessary to be able to evaluate and measure the defined learning outcomes, in a way that is comparable to as they were evaluated in the ordinary call. Positive results obtained by the students during the course.

Workbook

Neither a calculator nor any electronic device may be used in the examinations and/or face-to-face tests.

Basic bibliography

-Piskunov, N. (1970). Cálculo diferencial e integral. Ediciones Montaner y Simón.

-Granero, F. (1993). Cálculo. Ediciones Mc. Graw Hill.

-Prieto, M. (1970). Cálculo diferencial: funciones de una variable. Index, Madrid.

-Losada M. R. (1972). Cálculo diferencial de varias variables.

-Ayres, F. (1982). Teoria y problemas de cálculo diferencial e integral. McGraw-Hill, Mexico [etc.].

-Ayres, F. (1991). Cálculo diferencial e integral. McGraw-Hill, Madrid.

-Soler, M. (1997). Cálculo diferencial e integral: una y varias variables. Síntesis, Madrid.

-García, F. & Gutiérrez, A. (1994). Cálculo infinitesimal II. Ediciones Pirámide.

In-depth bibliography

PROBLEMAS:
-Demidovich, B. (1993). Problemas y ejercicios de análisis matemático. Ediciones Paraninfo.
-Marín J. A. (1972). Problemas de cálculo diferencial. S.A.E.T.A., Madrid.
-Olmo. V. (1987). Problemas de cálculo diferencial, funciones de varias variables. Universidad Politécnica de Valencia, Valencia.

Journals

LA GACETA DE LA REAL SOCIEDAD MATEMÁTICA ESPAÑOLA

Web addresses

http://www.divulgamat.net
http://www.hiru.com
http://es.wikipedia.org/wiki/Cálculo_infinitesimal
http://www.vitutor.com/
https://www.geogebra.org/
https://es.mathworks.com/
https://www.khanacademy.org/