Course: 2020/2021

Vector Calculus

(18258)

Students are expected to have completed

Linear Algebra, Differential Calculus.

ObjectivesFurther information on this link

- Students have shown that they know and understand the mathematical language and abstract-rigorous reasoning as well as to apply them to state and prove precise results in several areas in mathematics.
- Students have shown that they understand the fundamental results from real, complex and functional mathematical analysis.

Description of contents: programme

1. The Eucliean Space Rn.
2. Functions.
3. Differentiability.
5. Extrema.
6. The implicit function theorem.
7. Curves.
8. Surfaces.

Learning activities and methodology

THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support in which the main concepts of the subject are developed, while providing material and bibliography to complement student learning.
PRACTICAL CLASS. Resolution of practical cases and problem, 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 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. 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