The subject Calculus is one of the basic subjects of the 1st year of the Engineering Degrees in the Industrial branch. It is located within the module called basic training and is complemented by the subjects Algebra and Statistical Methods of Engineering.

In this subject, the mathematical instruments used to analyze the functions of one and several real variables and to solve Differential Equations are developed.

Given its basic and applied nature, it should serve as support for both subjects that require simple mathematical knowledge and those that require a more complex mathematical base, such as the Physical Fundamentals of Engineering, Mechanics or Electricity.

The work that will be developed in this subject will allow students to make basic calculations such as the volume of a solid, which have a very relevant importance in the calculation of structures in Engineering.

In order to develop Calculus without excessive difficulty, one must have a basic mastery of elementary functions of a variable (polynomial, trigonometric, exponential, logarithmic), of drawing their graphs and of elementary tools for their study (derivation and integration). In addition, basic knowledge of solving equations and operations with mathematical expressions is necessary.

C1.- Understand and manage the concepts of Mathematical Analysis that allow progress in subsequent studies and that train them to learn new methods and theories.



RA1.-Consistently use the procedural knowledge associated with scientific methodology in the resolution of problematic situations of infinitesimal calculation, both numerical, simulation or pencil and paper.



C2.- Apply theoretical results in the resolution of problems derived from basic sciences and technology, especially related to the profile of the degree, and analyze the solutions obtaining conclusions from the results achieved.



RA2.-Apply basic knowledge about differential and integral calculus, differential geometry, differential equations and in partial derivatives and numerical methods in problematic situations typical of engineering.



RA3.-Critically analyze the results and their implications.



C3.- Communicate to others the results of the knowledge processes through written and oral means, using

adequately understand language, terminology and mathematical formulas.



RA4.-Use oral, written, graphic and mathematical language in contexts corresponding to engineering processes.



C4.- Work in a group integrating skills and knowledge.



RA5.-Show an attitude of respect both in the expression and in the reception of the ideas that are expressed within the equipment.



RA6.- Identify the roles and rules of constitution and operation of a work team aimed at achieving goals.



RA7.-Value teamwork, accepting the potential of diversity as a learning opportunity.

Topic 1: Complex Numbers



Topic 2: Real functions of a real variable: Limits, continuity, differentiability and local study



Topic 3: Real functions of several real variables: Limits, continuity, differentiability and local study



Topic 4: Integral calculus of functions of one variable



Topic 5: Integral calculus of functions of several variables



Topic 6: Ordinary differential equations



Topic 7: Laplace transform



Topic 8: Fourier series

In this subject, various teaching methodologies are used, the most used being problem solving. Autonomous work will be promoted through the use of computer and bibliographic resources that help students understand the different aspects of the subject.

Classes will be given to present the conceptual contents of the subject, with the participation of students in occasional debates about them.

The resolution of issues and problems in the classroom will be carried out in a participatory manner. Problems and exercises will be provided that they will develop individually or in groups, which will allow them to deepen their theoretical knowledge of the subject. The formulation of questions and open discussion will be encouraged, so that students acquire skills related to oral communication, the ability to synthesize and teamwork.

To facilitate and ensure student learning, tasks will be monitored so that students have the opportunity to become aware of their learning, as well as ways to improve it.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 80
  • Realization of Practical Work (exercises, cases or problems) (%): 20

According to the regulations governing student evaluation (BOPV 3/13/2017), the evaluation is continuous and in case of wishing to benefit from the final evaluation system must be submitted in writing to the teaching staff responsible for the subject in the first 18 teaching weeks of the course his/her renunciation of continuous evaluation.



I) CONTINUOUS EVALUATION SYSTEM



The types of evaluation tests that will be carried out to obtain 100% of the final grade in the ordinary call are the following:



1) Three individual written exams with a weight of 80% of the grade. Below is indicated for each test the subject and the weight they have on the final grade:



-First exam: topics 1,2,3 (30%)



-Second exam: topics 4,5 and 6 (30%)



-Third exam (coincides with that of the official ordinary call): topics 7.8 (20%) if the student has passed the first and second exam, topics 4,5,6,7,8 (50%) if the student has passed the first exam and has failed the second, topics 1,2,3 and 7,8 (30%+20%=50%)if the student has passed the second exam and has failed the first, topics 1,2,3,4,5,6,7,8 (80%) otherwise. In any case, in this third exam, a minimum grade of 3 points out of 10 is needed. If this condition is not met, the student will appear with a failure in the final calification with a maximum grade of 4.5.



2) Evaluation of classroom work, team work and individual non-face-to-face work: 20% of the grade.



II) FINAL EVALUATION SYSTEM



In the final evaluation system, 100% of the grade will correspond to a final test that can be divided into different parts, so that the capabilities acquired through the different tasks carried out can be evaluated along the course.



RESIGNATION FROM THE CALL



In either of the two evaluation modalities, students who do not take the final written exam

will obtain the final grade "Not Presented" regardless of whether or not they have completed the rest of the tasks.

which will mean automatic resignation from this call.



ALLOWED MATERIALS, MEDIA AND RESOURCES



For the development of each of the evaluation tests, the material provided by the teaching team may be used.The use of books, notes, as well as telephone devices or other electronic devices, including calculators, is prohibited.

The written exam will count for 100% of the final grade.



RESIGNATION FROM THE CALL



Students who do not take the final written exam will obtain the final grade "Not Presented", which

which will mean automatic resignation from this call.



MATERIALS, MEDIA AND RESOURCES ALLOWED



For the development of each of the evaluation tests, the material provided by the teaching team may be used.The use of books, notes, as well as telephone devices or other electronic devices, including calculators, is prohibited.

Irakasle bakoitzak Moodle plataforman jarritako teoria-apunteak eta ariketak.

Basic bibliography

- DE BURGOS, J. "Cálculo Infinitesimal de una variable" y "Cálculo Infinitesimal de varias variables" Ed. Mc Graw-Hill

- LARSON-HOSTETLER "Cálculo y Geometría Analítica" Ed. Mc Graw-Hill.

- PISKUNOV. "Cálculo diferencial e integral" Ed. Reverté.

- PISKUNOV. Kalkulu diferentziala eta integrala I eta II. Arg. UPV eta UEU

- MANTEROLA. Ingeniaritzarako oinarri matematikoak. Ariketa ebatziak. Arg. ElHuyar

- MIJANGOS,E. Oinarri Matematikaok . Arg UPV-EHU

- SAGARZAZU. "Ecuaciones diferenciales y cálculo integral. Aplicaciones y ejercicios". Servicio Editorial Universidad del País Vasco.

- SAGARZAZU. Ekuazio diferentzialak. Aplikazioak eta ariketak. Arg. UPV eta UEU

- GRANERO, F. "Cálculo" Ed. Mc Graw-Hill

- SAN MARTÍN, J Y OTROS."Métodos Matemáticos. Ampliación de Matemáticas para Ciencias e Ingeniería" Thomson Editores.

- AYRES "Cálculo diferencial e integral" y " Ecuaciones diferenciales" Serie Schaum. Ed. Mc Graw-Hill

- DEMIDOVICH "5000 problemas de Análisis Matemático" y "Problemas y ejercicios de Análisis Matemático" Ed. Paraninfo.

- BERMAN "Problemas y ejercicios de Análisis Matemático" Ed. Mir.

- TEBAR FLORES. "Problemas de Cálculo Infinitesimal" Tomos I y II. y "909 problemas de Cálculo Integral" Ed Tebar Flores

- KISELIOV, KRASNOV, MAKARENKO. "Problemas de ecuaciones diferenciales" Ed. Mir

- SPIEGEL. "Transformada de Laplace" Serie Schaum Ed. Mc Graw-Hill.

In-depth bibliography

- SIMMONS, F. "Ecuaciones Diferenciales" Ed. Mc Graw-Hill.
- SPIVAK "Calculus" Ed. Reverté
- LINÉS, E. "Principios de Análisis Matemático" Ed Reverté
- FERNANDEZ VIÑA J. "Ejercicios y Complementos de Análisis Matemático" Ed Tecnos

Journals

- SUMA (Publicación de la Federación Española de Sociedades de Profesores de Matemáticas FESMP)
- SIGMA (Publicada por el Departamento de Educación del Gobierno Vasco en colaboración con los Berritzegunes)
- MAT2 Materials Matemâtics (Revista electrónica de Divulgación editada por el Departamento de Matemáticas de la Universidad Autónoma de Barcelona) mat.uab.es/~matmat/Cast/index.html

Web addresses

http://mathworld.wolfram.com/
http://www.rinconmatematico.com/
http://www.terra.es/personal/casanchi/matematica.htm
http://www.divulgamat.net/
http://www.campus-oei.org/oeivirt/matematica.htm
http://recursostic.educacion.es/descartes/web/
http://www-history.mcs.st-andrews.ac.uk/history/
http://www.vc.ehu.es/matematicaaplicada/
http://www.vc.ehu.es/matematikaaplikatua/
http://www.zientzia.net/