## CALCULUS

### Course

Code: 1225

Degree: Bachelor's in Mechanical Engineering

School of Engineering of Elche

Year: Year 1 of Bachelor's in Mechanical Engineering

Semester: Fall

Type: Core

Language: Spanish

ECTS credits: 6 Lecture: 3 Laboratory: 3 | Hours: 150 Directed: 60 Shared: 30 Autonomous: 60 |

Subject matter: Mathematics

Module: Core Instruction

Department: Statistics, Mathematics and Informatics

Area: APPLIED MATHEMATICS

Course instructors are responsible for the course content descriptions in English.

### Description

### Faculty

Name | Coordinator | Lecture | Laboratory |
---|---|---|---|

PARRA LOPEZ, JUAN | ■ | ||

CARRILLO ZAPATA, BLAS FRANCISCO | ■ | ■ | |

CREVILLEN GARCIA, DAVID | ■ | ■ | |

GARCIA BARBERA, ANTONIO MANUEL | ■ |

### Professional interest

- Mathematical formalization of sentences and properties

- Problem modeling

- Direct application to the resolution of real engineering problems

- Basic tool for other subjects

### Competencies and learning outcomes

#### General competencies

- Knowledge about basic and technological material that enables learning new methods and theories, providing versatility for adapting to new situations.

#### Specific competencies

- Capacity for resolving mathematical problems that arise in engineering. Aptitude for applying knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, differential equations and in partial derivatives, numerical methods, numerical algorithms, statistics, and optimization.

#### Objectives (Learning outcomes)

- 01To know the mathematical language and symbology.
- 02To know the different types of numbers, especially the real numbers.
- 03To acquire skills in the management of inequalities, absolute value and dimensions.
- 04To know how to combine the different techniques of calculation of limits in one and several variables.
- 05To know the relationship between the continuity of functions and open, closed, connected and compact sets.
- 06Know and interpret the concepts of directional derivative, partial derivative and differential, as well as the relationships between them.
- 07To handle the chain rule and its impact in relation to changes of variables and implicit differentiation.
- 08To solve local optimization problems without constraints.
- 09To solve global optimization problems over compact sets.
- 010To understand the underlying ideas in the construction of the Riemann integral and its applications.
- 011To know the existence of improper and parametric integrals.
- 012To visualize and represent subsets in two and three dimensions and their transformed by changes to polar, cylindrical and spherical coordinates.
- 013To know how to calculate double and triple integrals on simple sets.
- 014To understand the underlying ideas in the definition of integrals on curves and surfaces.
- 015To know the classic theorems of line and surface integrals as well as their relationship with classical differential operators.
- 016To understand the concept of numerical series and its convergence.
- 017To know the development of some elementary functions in power series.
- 018To have an elementary knowledge of the complex exponential and the Fourier series.

### Contents

#### Teaching units

#### Association between objectives and units

Objective/Unit | U1 | U2 | U3 | U4 |
---|---|---|---|---|

01 | ||||

02 | ||||

03 | ||||

04 | ||||

05 | ||||

06 | ||||

07 | ||||

08 | ||||

09 | ||||

010 | ||||

011 | ||||

012 | ||||

013 | ||||

014 | ||||

015 | ||||

016 | ||||

017 | ||||

018 |

#### Schedule

Week | Teaching units | Directed hours | Shared hours | Autonomous hours | Total hours |
---|---|---|---|---|---|

1 | 4 | 2 | 4 | 10 | |

2 | 4 | 2 | 4 | 10 | |

3 | 4 | 2 | 4 | 10 | |

4 | 4 | 2 | 4 | 10 | |

5 | 4 | 2 | 4 | 10 | |

6 | 4 | 2 | 4 | 10 | |

7 | 4 | 2 | 4 | 10 | |

8 | 4 | 2 | 4 | 10 | |

9 | 4 | 2 | 4 | 10 | |

10 | 4 | 2 | 4 | 10 | |

11 | 4 | 2 | 4 | 10 | |

12 | 4 | 2 | 4 | 10 | |

13 | 4 | 2 | 4 | 10 | |

14 | 4 | 2 | 4 | 10 | |

15 | 4 | 2 | 4 | 10 |

#### Basic bibliography

- Amigó, José María. "Fundamentos de Matemáticas".
- García López, Alfonsa. "Cálculo I Teoría y problemas de análisis matemático en una variable". Madrid CLAGSA D.L. 1994.
- García López, Alfonsa. "Cálculo II Teoría y problemas de funciones de varias variables". [Madrid] Clagsa [1996].
- Larson, Roland E. Hostetler, Robert P. "Cálculo y geometría analítica". Madrid, [etc.] McGraw-Hill D.L. 1994.
- Marsden, Jerrold Eldon. Tromba, Anthony J. "Cálculo vectorial". México Addison Wesley Longman 1998.
- Alejandre Chavero, Manuel J. Soler i Escriváa, Xaro / Toledo Melero, Fco. Javier. "Problemas de matemáticas asistidos con DERIVE 5 Análisis matemático". Elx Universidad Miguel Hernández 2002.

#### Complementary bibliography

- Apostol, Tom M. "Análisis matemático". Barcelona [etc.] Reverté D.L. 1986, 1991, 1996.
- Spivak, Michael. "Cálculo infinitesimal". Barcelona [etc.] Reverté D.L. 1977, 1978, 1981.
- Burgos, Juan de (Burgos Román). "Cálculo infinitesimal (Teoría y problemas)". Madrid Alhambra 1984.
- Burgos, Juan de (Burgos Román). "Cálculo infinitesimal de varias variables". Madrid[etc.] McGraw-Hill D.L. 1995.
- Protter, M.H. Monrrey, C.B. "Análisis real". Madrid editorial A C D. L. 1986.
- Ortega Aramburu, Joaquín M. "Introducción al análisis matemático". Barcelona Labor 1993.
- Alejandre Chavero, Manuel J. Cañavate Bernal, Roberto J. / Herraz Cuadrado, María Victoria. "999 Problemas de análisis matemático". Elche Universidad Miguel Hernández 1999.
- Alejandre Chavero, Manuel J. "Curso elemental de análisis matemático". Elche Universidad Miguel Hernández 1999.
- Thomas, George B. Finney, Ross L. "Cálculo una variable". México [etc.] Addison Wesley Longman cop. 1998.
- Salas, S.L. Hille, Einar. "Calculus". Barcelona [etc.] Reverté , D.L1994-1995.
- Stewart, James. Wisniewski, Piotr Marian rev / López Saura, Irma rev. "Cálculo multivariable". México [etc.] Thomson Learning imp. 2004.
- Steiner, Erich. "Matemáticas para las ciencias aplicadas ". Barcelona [etc.] Reverté D.L. 2005.
- Jarauta Bragulat, Eusebi. "Análisis matemático de una variable fundamentos y aplicaciones". Barcelona Edicions UPC 2000.
- Mazón Ruiz, José M. "Cálculo diferencial Teoría y problemas". Madrid McGraw-Hill D.L. 1997.
- George B. Thomas, JR. ; Ross L. Finney. "Cálculo varias variables". Addison Wesley Longman.

#### Links

#### Software

- DERIVE 6

### Methodology and grading

#### Grading

For the FEBRUARY ORDINARY EVALUATION the student may opt between a continuous evaluation system or a final evaluation one. The continuous evaluation system consists of: - Continuous evaluation test -PEC- (10%): It consists of a test type exam of 1 hour duration normally in the second half of November (date to be specified). It consists of 5 questions, each with 3 options and only one is correct. Each correct answer supposes 0.2 points of the final mark, each erroneous answer takes away 0.1 points and the blank questions neither add nor subtract. - Practice exam (15%): It is done during the second hour of the 4th session of practices of the corresponding group. It consists of the resolution of 3 exercises (0.5 points of the final grade each) to be solved with the help of the Derive program (the use of class notes and printed material is allowed). - Tutorials (5%): Attendance at problem workshops (0.1 points per workshop, 0.5 points for the four workshops) and/or the student's overall participation in class, workshops, tutorials, etc. will be assessed. - Final theory and problems exam (70%): It consists of 4 exercises. The first of the same format as the PEC, with a score of 2 points; the second will be a 2 point problem; the remaining two (1.5 points each) will be two problems to choose from three. To pass the subject it is necessary to obtain at least 3 points (out of 7) in the final exam. The final evaluation system consists of: - Theory, problems and practices exam (100% of the final grade): It consists of 5 exercises. The first of the same format as the PEC, with a score of 2 points; the second will be a 2.5 point problem; the remaining two (of 2 points each) will be two problems to choose from three. The fifth exercise (1.5 points) is intended to evaluate practices without using the computer. For this, the printed computer outputs will be provided through the Derive program necessary to answer the questions in the exercise. The use of calculators of any kind is not allowed in the final exam. For the EXTRAORDINARY EVALUATIONS OF SEPTEMBER AND DECEMBER the evaluation consists of: - Examination of theory and problems (85%): It consists of 4 exercises. The first of the same format as the PEC, with a score of 2 points; the second will be a 2.5 point problem; the remaining two (of 2 points each) will be two problems to choose from three. - Practice exam (15%): It is done immediately after the theory and problems exam. It lasts one hour. It consists of the resolution of 3 exercises (0.5 points of the final grade each) to be solved with the help of the Derive program (the use of class notes and printed material is allowed). If a student does not show up for the September practice exam, he/she will keep the mark they had obtained in the February exam. If the student shows up for the September practice exam, they will automatically lose the mark they had from the February exam and will have the mark they get in September. NOTE: THE EVALUATION OF DECEMBER has a specific regulation that can be seen in the following link http://cgcori.umh.es/normativas/pdf/Normativa%20de%20la%20Convocatoria%20Extraordinaria%20de%20diciembre.PDF

#### Assessment test characteristics

See the section "System and evaluation criteria of the subject". See also the exams from previous years that can be found in the material of the subject.

#### Correction criteria

They are provided in each exam. To get an idea see the exams of previous years in the material of the subject.

#### Additional requirements

Students may not use any type of electronic devices such as calculators and clocks during the theory and problem exam.