Course: 2022/2023

Vector Calculus

(18258)

Requirements (Subjects that are assumed to be known)

Linear Algebra (First year, first semester)
Differential Calculus (First year, first semester)

Skills and learning outcomes

Description of contents: programme

1. The Euclidean Space Rn.
2. Functions.
3. Differentiability.
5. Taylor Polynomial and Extrema.
6. Lagrange multipliers and the implicit function theorem.
7. Curves.
8. Surfaces.

Learning activities and methodology

LEARNING ACTIVITIES AND METHDOLOGY
THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.76 ECTS]
Knowledge and concepts students must acquire. Student receive course notes and
will have basic reference texts to facilitate following the classes and carrying
out follow up work. Students partake in exercises to resolve practical problems
and participate in workshops and evaluation tests, all geared towards
acquiring the necessary capabilities.
TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.16 ECTS]
Individualized attendance (individual tutoring) or in-group (group tutoring)
for students with a teacher.
STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.92 ECTS]
FINAL EXAM. [4 hours with 100% on site, 0.16 ECTS]
Global assessment of knowledge, skills and capacities acquired throughout the
course.
METHODOLOGIES
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.
PRACTICAL CLASS. Resolution of practical cases and problems, posed by the
teacher, and carried out individually or in a group.
TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or
in-group (group tutoring sessions) for students with a teacher as tutor.

Assessment System

- % end-of-term-examination 60
- % of continuous assessment (assigments, laboratory, practicals...) 40

Basic Bibliography

- J. E. Marsden and A. J. Tromba. Vector Calculus, 6th. edition. W. H. Freeman. 2012
- Manfredo P. Do Carmo. Differential Geometry of Curves and Surfaces. Dover Publications; Updated, Revised (2nd) edition. 2016
- Seán Dineen. Multivariate Calculus and Geometry, 3rd Edition. Springer. 2014
- Tom M. Apostol. Mathematical Analysis, 2nd ed.. Pearson Education, Inc.. 1974

Additional Bibliography

- J. E. Marsden and M. J. Hoffman. Elementary Classical Analysis, 2nd ed.. W. H. Freeman and Company. 1974
- J. Rogawski and C. Adams.. Calculus: Early Transcendentals. . W. H. Freeman and Company (Third Edition Volume I and II). . 2015
- J. Stewart. Calculus. Cengage. 2008
- M. D. Weir, J. Hass, and G. B. Thomas. Thomas' Calculus 12th ed. Addison-Wesley . 2006
- M. J. Strauss, G. L. Bradley, and K. J. Smith. Multivariable Calculus. Prentice Hall. 2002
- R. Larson and B. H. Edwards. Calculus II, 9th. edition. Cengage. 2009
- S. Salas, E. Hille, and G. Etgen. Calculus. One and several variables. Wiley. 2007
- T. M. Apostol. Calculus. Wiley. 1975

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