Checking date: 12/07/2022

Course: 2022/2023

Calculus II
Study: Bachelor in Engineering Physics (363)


Department assigned to the subject: Department of Mathematics

Type: Basic Core
ECTS Credits: 6.0 ECTS


Branch of knowledge: Engineering and Architecture

Requirements (Subjects that are assumed to be known)
- Algebra. - Calculus I.
Skills and learning outcomes
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
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.