Syllabus Information

3.2. Competences

BC01. Students have demonstrated knowledge and understanding in a field of study that is part of the general secondary education curricular, and is typically at a level which, although it is supported by advanced textbooks, includes some aspects that involve knowledge of the forefront of their field of study.

BC02. Students can apply their knowledge to their work or vocation in a professional manner and have competences typically demonstrated through devising and defending arguments and solving problems within their field of study.

BC03. Students have the ability to gather and interpret relevant data (usually within their field of study) to inform judgments that include an important reflection on social, scientific or ethical issues.

BC04. Students can communicate information, ideas, problems and solutions to both specialist and non-specialist audiences.

BC05. Students have developed those skills needed to undertake further studies with a high degree of autonomy.

GC04. Ability to organize time effectively and coordinate activities to acquire new knowledge quickly and perform under pressure.

GC05. Capacity to collect, manage, analyze and synthesize information from various sources for the development of design projects and product development. Capacity to use this documentation to obtain conclusions aimed at solving problems and making decisions with initiative, creativity and critical thinking, in order to generate new product concepts, new ideas and solutions.

GC06. Ability to generate the necessary documentation for the proper transmission of ideas through graphics, reports and technical documents, models and prototypes, oral presentations in Spanish and other languages.

GC07. Ability to use and master techniques, skills, tools and techniques and communication and others specific of design engineering needed for design practice.

GC08. Ability to learn continuously, to develop autonomous learning strategies and to work in multidisciplinary groups with motivation and determination to achieve goals.

SC01. Ability to solve mathematical problems that may arise in Engineering in Industrial Design and Product Development. Ability to apply knowledge of linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial differential equations; numerical methods; numerical algorithmic; statistical and optimization.

BC:BASIC COMPETENCES. GC: GENERAL COMPETENCES. SC: SPECIFIC COMPETENCES.

5.1. Methodological overview

This course is divided into:

• Lectures (theory and problem solving) (42 hours).
• Computer lab sessions (12 hours).
• Group work (20 hours).
• Study time (73 hours).
• Exams (3 hours).

Lectures, problem solving and computer lab activities will be used to achieve students learn the topics of the subject. Computer lab sessions will take place in a laboratory. We will make use of Maxima, a computer algebra system. Group work will be guided by regular meetings with the teachers and seminars about the covered topics.

5.2. Learning tasks

1. Lectures.

Lectures will take place three hours a week, until complete 42 hours. Topics will be presented using the blackboard and computer presentations. Theoretical content, illustrative examples and problem solving will be combined during the lectures.

2. Computer lab sessions.

There will be 6 computer lab sessions. Each session is scheduled for 2 hours. The mathematical software Maxima will be used in this course. The emphasis is on the graphic, symbolic and numerical aspects of the subject. The problems are designed to force the student to engage in critical, analytic, and interpretive thinking beyond rote manipulation of calculus formulas.

3. Group work.

Group work will be guided by regular meetings and seminars, where the teacher will provide help and feedback.  Group sizes are between 3-4 students.  Different types of work may be proposed with some or all of the subjects of the first semester.

5.3. Syllabus

1. Single variable differential and integral calculus.

1. Real numbers.
2. Real-valued functions. Limits and continuity.
3. Derivatives. Applications of the derivatives.
4. Numerical methods for solving nonlinear equations.
5. Polynomial approximation: Taylor polynomial. Interpolation.
6. Integration. Techniques of integration. Numerical integration. Applications of the definite integral.
7. Plane curves. Parametric equations and polar coordinates.

 2. Multivariable differential and integral calculus.

1. The geometry of plane and space.
2. Functions of several variables. Domains. Graphs. Limits and continuity.
3. Partial derivatives and the gradient vector. Differentiability and the tangent plane.
4. Higher derivatives. Maximum and minimum values.
5. Multiple integral.

5.4. Course planning and calendar

5.5. Bibliography and recommended resources

[BB: Bibliografía básica / BC: Bibliografía complementaria]

• [BB] Burgos Román, Juan de. Cálculo infinitesimal de una variable / Juan de Burgos Román . - 2ª ed. en español Madrid [etc.] : McGraw-Hill, D.L. 2006
• [BB] Burgos Román, Juan de. Cálculo infinitesimal de varias variables / Juan de Burgos Román . - 2ª ed. Madrid [etc.] : McGraw-Hill/Interamericana, cop. 2008
• [BC] Adams, Robert A.. Cálculo / Robert A. Adams ; traducción, Isabel Portillo García ; revisión técnica, Javier Portillo García . 6ª ed. Madrid : Addison Wesley, D.L. 2011
• [BC] Anton, Howard. Calculus : early transcendentals. Single variable / Anton, H., Bivens, I., Davis, S.. - 8ª ed Jhon Wiley and sons, 2005
• [BC] Carmo, Manfredo P. do. Geometría diferencial de curvas y superficies / Manfredo P. do Carmo ; versión española de José Claudio Sabina de Lis Madrid : Alianza Editorial, cop. 1990
• [BC] Faires, J. Douglas. Métodos numéricos / J. Douglas Faires, Richard Burden; traducción y revisión técnica Pedro J. Paul Escolano . 3a ed. Madrid [etc] : Thomson, D.L. 2004
• [BC] Franco Brañas, José Ramón. Introducción al cálculo : problemas y ejercicios resueltos / José Ramón Franco Brañas . Madrid [etc.] : Prentice Hall, D.L. 2003
• [BC] García Celayeta, Berta. Análisis matemático y métodos numéricos / Berta García Celayeta, Inmaculada Higueras Sanz, Teo Roldán Marrodán . Pamplona : Universidad Pública de Navarra=Nafarroako Universitate Publikoa, 2005
• [BC] Kreyszig, Erwin. Matemáticas avanzadas para ingeniería / Erwin Kreyszig . [1a.ed., 2a. reimp.] México [etc.] : Limusa Noriega, 1990|g(1992 imp.)
• [BC] Larson, Ron. Cálculo 2 de varias variables / Ron Larson, Bruce H. Edwards ; revisión técnica, Marlene Aguilar Abalo ... [et al.] ; [traducción: Joel Ibarra Escutia ... (et al.)] . 9ª ed. México [etc.] : McGraw Hill, cop. 2010
• [BC] Larson, Ron. Cálculo I / Ron Larson, Robert P. Hostetler, Bruce H. Edwards ; traductores, Sergio Antonio Durán Reyes ... [et al.] ; revisores técnicos, María del Carmen Hano Roa, José Job Flores Godoy, Lorenzo Abellanas Rapún. 8ª ed. México [etc.] : McGraw-Hill, cop. 2006
• [BC] Larson, Ron. Cálculo y geometría analítica / Roland E. Larson, Robert P. Hostetler, Bruce H. Edwards ; con la colaboración de David E. Heyd ; traducción, Lorenzo Abellanas Rapún . - 6ª ed. en español Madrid [etc.] : McGraw-Hill, D.L. 1999
• [BC] Marsden, Jerrold E.. Cálculo vectorial / Jerrold E. Marsden, Anthony J. Tromba ; traducción Patricio Cifuentes Muñiz ... [et al.] ; revisión técnica Eugenio Hernández Rodríguez . - 5ª ed., reimp. Madrid [etc.] : Addison-Wesley, 2005
• [BC] Salas, Saturnino L.. Calculus / Saturnino L. Salas, Einar Hille . 3a. ed. Barcelona [etc.] : Reverté, D.L. 1994
• [BC] Thomas, George B.. Cálculo : varias variables / George B. Thomas, Jr. ; revisada por Maurice D. Weir, Joel Hass ; traducción Antonio P. Enríquez Brito ; revisión técnica Carlos Bosch Giral ... [et al.]. - 12ª ed. Naucalpan de Juárez (México) : Pearson Educación, 2010
• [BC] Tomeo Perucha, Venancio. Problemas resueltos de cálculo en una variable / Venancio Tomeo Perucha, Isaías Uña Juárez, Jesús San Martín Moreno . Madrid : Thomson-Paraninfo, D. L. 2007