Guías Docentes Electrónicas
1. General information
Course:
CALCULUS II
Code:
56306
Type:
BASIC
ECTS credits:
6
Degree:
351 - UNDERGRADUATE DEGREE PROG. IN MECHANICAL ENGINEERING (ALM)
Academic year:
2020-21
Center:
106 - SCHOOL OF MINING AND INDUSTRIAL ENGINEERING
Group(s):
55  56 
Year:
1
Duration:
C2
Main language:
Spanish
Second language:
Use of additional languages:
English Friendly:
Y
Web site:
Bilingual:
N
Lecturer: CARLOS FUNEZ GUERRA - Group(s): 55 
Building/Office
Department
Phone number
Email
Office hours
Despacho 2.09 - Edificio E¿lhuyar
MATEMÁTICAS
6049
carlos.funez@uclm.es

Lecturer: PEDRO JOSE MORENO GARCIA - Group(s): 56 
Building/Office
Department
Phone number
Email
Office hours
Elhuyar / Matemáticas
MATEMÁTICAS
6049
PedroJose.Moreno@uclm.es

Lecturer: DOROTEO VERASTEGUI RAYO - Group(s): 55  56 
Building/Office
Department
Phone number
Email
Office hours
Elhuyar / Matemáticas
MATEMÁTICAS
6049
doroteo.verastegui@uclm.es

2. Pre-Requisites
The programming of this subject that includes the theoretical, practical and technical knowledge of the differential and integral calculus of a variable and linear algebra is the subject of the Calculus I and Algebra subjects of the first semester. Students who have access to this prior knowledge, monitoring the subject is much more expensive and difficult in time and effort.
3. Justification in the curriculum, relation to other subjects and to the profession
The Calculus II is part of the subjects that make up the Mathematics module for the degree of Engineering. These subjects are basic for the scientific and technical education of the student when promoting the development of their capacities of abstraction and scientific rigor, as well as those of analysis and synthesis.

The differential calculation of several variables allows the analysis of the optimization of functions and acquire quantitative techniques essential for the allocation of resources, decision-making and management in various problems that the future engineer may pose throughout his professional life. With the contribution of the integral calculation, it will help not only the resolution of multiple problems in the world of science and engineering, but also a better understanding of the knowledge and instrumental and analytical techniques that can be used in them.

The subject, as a whole, will allow to understand more deeply other subjects studied previously (Calculus I, Algebra, Physics, ...) and will facilitate the study of new ones, both basic and specific.

4. Degree competences achieved in this course
Course competences
Code Description
A01 To understand and have knowledge in an area of study that moves on from the general education attained at secondary level and usually found at a level that, while supported in advanced text books, also includes some aspects that include knowledge found at the cutting edge of the field of study.
A02 To know how to apply knowledge to work or vocation in a professional manner and possess the competences that are usually demonstrated by the formulation and defence of arguments and the resolution of problems in the field of study.
A03 To have the capability to gather and interpret relevant data (normally within the area of study) to make judgements that include a reflection on themes of a social, scientific or ethical nature.
A07 Knowledge of Information Technology and Communication (ITC).
A08 Appropriate level of oral and written communication.
A12 Knowledge of basic materials and technologies that assist the learning of new methods and theories and enable versatility to adapt to new situations.
A13 Ability to take the initiative to solve problems, take decisions, creativity, critical reasoning and ability to communicate and transmit knowledge, skills and abilities in Mechanical Engineering.
A17 Ability to apply principles and methods of quality control.
B01 Ability to solve mathematical problems that occur in engineering. Aptitude to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential and partial differential equations; numerical methods; numerical algorithms; statistics and optimization.
CB01 Prove that they have acquired and understood knowledge in a subject area that derives from general secondary education and is appropriate to a level based on advanced course books, and includes updated and cutting-edge aspects of their field of knowledge.
CB02 Apply their knowledge to their job or vocation in a professional manner and show that they have the competences to construct and justify arguments and solve problems within their subject area.
CB03 Be able to gather and process relevant information (usually within their subject area) to give opinions, including reflections on relevant social, scientific or ethical issues.
CB04 Transmit information, ideas, problems and solutions for both specialist and non-specialist audiences.
CB05 Have developed the necessary learning abilities to carry on studying autonomously
5. Objectives or Learning Outcomes
Course learning outcomes
Description
To know the tundamentals and applications of Optimization
Know the main approaches for resolution through using numerical methods, to use some statistical software packages at user level, data processing, mathematical calculus and vizualization, set out algorithms and program through programming language of a high level, vizualize functions, geometric figures and data, design experiments, analyze data and interpret results
Know the use of the functions of one and various variables including its derivation, integration and graphic representation
Be familiar with the concepts of differential geometry and use them appropriately.
Additional outcomes
Description
6. Units / Contents
  • Unit 1: Differential Geometry
  • Unit 2: Multivariate functions: Limits and Continuity
  • Unit 3: Multivariate functions: Differential Calculus
  • Unit 4: Optimization of scalar functions
  • Unit 5: Multivariate functions: Multiple Integrals
  • Unit 6: Vector Analysis
  • Unit 7: Introduction to partial differential equations
7. Activities, Units/Modules and Methodology

All training activities will be recoverable, in other words, there must be an alternative evaluation test that allows to reassess the acquisition of the same skills in the ordinary, extraordinary and special call for completion. If exceptionally, the evaluation of any of the training activities cannot be recovered, it must be specified in the description and be expressly authorized by the department.

Training Activity Methodology Related Competences ECTS Hours As Com Description
Class Attendance (theory) [ON-SITE] Combination of methods A01 A02 A03 A07 A12 B01 CB01 CB02 CB03 CB04 CB05 1 25 N N
Individual tutoring sessions [ON-SITE] Problem solving and exercises A01 A02 A03 A08 A13 A17 B01 CB01 CB02 CB03 CB04 CB05 0.2 5 N N
Problem solving and/or case studies [ON-SITE] Problem solving and exercises A02 A07 A13 B01 CB01 CB02 CB03 CB04 CB05 0.6 15 Y N
Workshops or seminars [ON-SITE] Workshops and Seminars A02 A08 A12 A13 A17 B01 CB01 CB02 CB03 CB04 CB05 0.1 2.5 N N
Computer room practice [ON-SITE] Practical or hands-on activities A02 A07 B01 CB01 CB02 CB03 CB04 CB05 0.3 7.5 Y N
Final test [ON-SITE] Assessment tests A01 A02 A03 A07 A08 A12 A13 A17 B01 CB01 CB02 CB03 CB04 CB05 0.2 5 Y Y
Other off-site activity [OFF-SITE] Self-study A02 A03 A08 B01 CB01 CB02 CB03 CB04 CB05 3.6 90 N N
Total: 6 150
Total credits of in-class work: 2.4 Total class time hours: 60
Total credits of out of class work: 3.6 Total hours of out of class work: 90

As: Assessable training activity
Com: Training activity of compulsory overcoming (It will be essential to overcome both continuous and non-continuous assessment).

8. Evaluation criteria and Grading System
Evaluation System Continuous assessment Non-continuous evaluation * Description
Assessment of activities done in the computer labs 5.00% 5.00% For the evaluation of the practices in the computer room, with application of specific software, the delivery of the work carried out in the same ones and a documentation with the resolution of the same will be valued.
Final test 70.00% 70.00% Finally, there will be a written test that will consist of questions, theoretical questions and problems whose evaluation criteria will be similar to those of the academic works described above.
Assessment of problem solving and/or case studies 5.00% 5.00% For the evaluation of the academic works carried out by the students in class, a memory should be given where the approach of the problem will be assessed, the use of appropriate terminology and notation to express the mathematical ideas and relationships used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleaning and presentation of the document.
Progress Tests 20.00% 20.00% Partial exams to prove the way the students are learning the subject.
Total: 100.00% 100.00%  
According to art. 6 of the UCLM Student Evaluation Regulations, it must be provided to students who cannot regularly attend face-to-face training activities the passing of the subject, having the right (art. 13.2) to be globally graded, in 2 annual calls per subject , an ordinary and an extraordinary one (evaluating 100% of the competences).

Evaluation criteria for the final exam:
  • Continuous assessment:
    In order to obtain the final grade, the 4 evaluation systems described are computed, with the specified weights, and a grade equal to or greater than 4 points out of 10 must be obtained in the final written test. If the grade obtained in said test was less than 5 points, it will be considered as the final grade of the subject.
  • Non-continuous evaluation:
    Evaluation criteria not defined

Specifications for the resit/retake exam:
There will be a final written test, whose weight will be 100% of the global grade of the subject and which will consist of questions, theoretical issues and problems where the approach of the subject or problem will be assessed, the use of terminology and appropriate notation to express the ideas and mathematical relationships used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleanliness and presentation of the document.
Specifications for the second resit / retake exam:
There will be a final written test, whose weight will be 100% of the global grade of the subject and which will consist of questions, theoretical issues and problems where the approach of the subject or problem will be assessed, the use of terminology and appropriate notation to express the ideas and mathematical relationships used, the choice of the most appropriate procedure for each situation, the justification of the different steps of the procedure used, the results obtained and the cleanliness and presentation of the document.
9. Assignments, course calendar and important dates
Not related to the syllabus/contents
Hours hours
Individual tutoring sessions [PRESENCIAL][Problem solving and exercises] 5
Workshops or seminars [PRESENCIAL][Workshops and Seminars] 2.5
Computer room practice [PRESENCIAL][Practical or hands-on activities] 7.5
Final test [PRESENCIAL][Assessment tests] 5

Unit 1 (de 7): Differential Geometry
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 1.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 1
Other off-site activity [AUTÓNOMA][Self-study] 4

Unit 2 (de 7): Multivariate functions: Limits and Continuity
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 3.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 2
Other off-site activity [AUTÓNOMA][Self-study] 12

Unit 3 (de 7): Multivariate functions: Differential Calculus
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 6.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 4
Other off-site activity [AUTÓNOMA][Self-study] 24

Unit 4 (de 7): Optimization of scalar functions
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 3
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 1.5
Other off-site activity [AUTÓNOMA][Self-study] 12

Unit 5 (de 7): Multivariate functions: Multiple Integrals
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 6
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 3.5
Other off-site activity [AUTÓNOMA][Self-study] 24

Unit 6 (de 7): Vector Analysis
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 3
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 2
Other off-site activity [AUTÓNOMA][Self-study] 10

Unit 7 (de 7): Introduction to partial differential equations
Activities Hours
Class Attendance (theory) [PRESENCIAL][Combination of methods] 1.5
Problem solving and/or case studies [PRESENCIAL][Problem solving and exercises] 1
Other off-site activity [AUTÓNOMA][Self-study] 4

Global activity
Activities hours
10. Bibliography and Sources
Author(s) Title Book/Journal Citv Publishing house ISBN Year Description Link Catálogo biblioteca
A. Garcia, A. López, G. Rodríguez, S. Romero, A. de la Villa Calculo II. Teoría y problemas de funciones de varias variables Madrid CLAGSA 84-921847-0-1 1996  
APOSTOL, T. Calculus Ed. Reverté 1995  
ARANDA, E; PEDREGAL, P. Problemas de cálculo vectorial Lulu.com 2004  
BURGOS, J. Cálculo infinitesimal de varias variables. McGraw-Hill  
DEMIDOVICH, B. 5000 problemas de análisis matemático. Ed. Paraninfo.  
GARCIA, A.; LOPEZ, A.; RODRIGUEZ, G; ROMERO, S; DE LA VILLA, A. Cálculo II. Ed. Clagsa 2002  
GRANERO Cálculo infinitesimal McGraw-Hill.  
LARSON , R; HOSTETLER, R; EDWARDS, B; Cálculo y geometría analítica Ed. McGraw Hill  
LOPEZ DE LA RICA, A ; DE LA VILLA, A. Geometría diferencial. CLAGSA.  
PERAL ALONSO, I. Primer curso de ecuaciones en derivadas parciales Ed. Addison-Wesley/Universidad autónoma de Madrid  
SALAS, S; HILLE, E. Calculus Ed. Reverté.  
STEWART, J. Cálculo multivariable THOMSON  
ZILL, D. Ecuaciones diferenciales. THOMSON  



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