Checking date: 06/09/2024


Course: 2024/2025

Calculus II
(18299)
Bachelor in Engineering Physics (Plan: 434 - Estudio: 363)


Coordinating teacher: MOLINA MEYER, MARCELA

Department assigned to the subject: Mathematics Department

Type: Basic Core
ECTS Credits: 6.0 ECTS

Course:
Semester:

Branch of knowledge: Engineering and Architecture



Requirements (Subjects that are assumed to be known)
- Algebra. - Calculus I.
Skills and learning outcomes
CB1. Students have demonstrated possession and understanding of knowledge in an area of study that builds on the foundation of general secondary education, and is usually at a level that, while relying on advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study. CB2. Students are able to apply their knowledge to their work or vocation in a professional manner and possess the competences usually demonstrated through the development and defence of arguments and problem solving within their field of study. CB3. Students have the ability to gather and interpret relevant data (usually within their field of study) in order to make judgements which include reflection on relevant social, scientific or ethical issues. CB4. Students should be able to communicate information, ideas, problems and solutions to both specialist and non-specialist audiences. CB5. Students will have developed the learning skills necessary to undertake further study with a high degree of autonomy. CG2. Learn new methods and technologies from basic scientific and technical knowledge, and being able to adapt to new situations. CG3. Solve problems with initiative, decision making, creativity, and communicate and transmit knowledge, skills and abilities, understanding the ethical, social and professional responsibility of the engineering activity. Capacity for leadership, innovation and entrepreneurial spirit. CG4. Solve mathematical, physical, chemical, biological and technological problems that may arise within the framework of the applications of quantum technologies, nanotechnology, biology, micro- and nano-electronics and photonics in various fields of engineering. CG5. Use the theoretical and practical knowledge acquired in the definition, approach and resolution of problems in the framework of the exercise of their profession. CE1. Solve mathematical problems that may arise in engineering and apply knowledge of linear algebra, differential and integral calculus, numerical methods, numerical algorithms, statistics, differential equations and in partial derivatives, complex and transformed variables. CE22. Design, plan and estimate the costs of an engineering project. CT1. Work in multidisciplinary and international teams as well as organize and plan work making the right decisions based on available information, gathering and interpreting relevant data to make judgments and critical thinking within the area of study. RA1. To have acquired sufficient knowledge and proved a sufficiently deep comprehension of the basic principles, both theoretical and practical, and methodology of the more important fields in science and technology as to be able to work successfully in them. RA2. To be able, using arguments, strategies and procedures developed by themselves, to apply their knowledge and abilities to the successful solution of complex technological problems that require creating and innovative thinking. RA3. To be able to search for, collect and interpret relevant information and data to back up their conclusions including, whenever needed, the consideration of any social, scientific and ethical aspects relevant in their field of study. RA6. To be aware of their own shortcomings and formative needs in their field of specialty, and to be able to plan and organize their own training with a high degree of independence.
Description of contents: programme
1. Differential calculus in several variables 1.1 Basic notions in the Euclidean space Rn. 1.2 Funtions of n variables. 1.3 Limits and continuity. 1.4 Differentiability. 2. Local properties of functions 2.1 Higher-order derivatives and differential operators. 2.2 Optimization with and without constraints. 3. Integral calculus in several variables 3.1 Double integrals. 3.2 Triple integrals. 3.3 Change of variables. 3.4 Applications. 4. Integrals over curves and surfaces 4.1 Line and path integrals. 4.2 Surface integrals. 4.3 Integral theorems of vector analysis.
Learning activities and methodology
AF1. THEORETICAL-PRACTICAL CLASSES. Knowledge and concepts students mustacquire. Receive course notes and will have basic reference texts.Students partake in exercises to resolve practical problems AF2. TUTORING SESSIONS. Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher.Subjects with 6 credits have 4 hours of tutoring/ 100% on- site attendance. AF3. STUDENT INDIVIDUAL WORK OR GROUP WORK.Subjects with 6 credits have 98 hours/0% on-site. AF9. FINAL EXAM. Global assessment of knowledge, skills and capacities acquired throughout the course. It entails 4 hours/100% on-site MD1. THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support in which the subject`s main concepts are developed, while providing material and bibliography to complement student learning MD2. PRACTICAL CLASS. Resolution of practical cases and problem, posed by the teacher, and carried out individually or in a group MD3. TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with teacher as tutor. Subjects with 6 credits have 4 hours of tutoring/100% on-site.
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40

Calendar of Continuous assessment


Extraordinary call: regulations
Basic Bibliography
  • J. E. Marsden and A. J. Tromba. Vector Calculus. Freeman. 2013
  • S. Salas, E. Hille, and G. Etgen. Calculus: One and several variables. Wiley. 2007
Additional Bibliography
  • B. E. Blank and S.G. Krantz. Calculus: Multivariable. Wiley. 2011
  • J. Stewart. Calculus. Cengage Learning. 2012
  • R. C. Wrede and M. Spiegel. Schaum's Outline of Advanced Calculus. McGraw Hill. 2002
  • R. Larson and B. H. Edwards. Calculus. Cengage Learning. 2014
  • S. Lang. Calculus of Several Variables. Springer Verlag. 1987

The course syllabus may change due academic events or other reasons.