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Course: 2022/2023

Vector Calculus

(18258)

Bachelor in Applied Mathematics and Computing (Plan: 433 - Estudio: 362)

Coordinating teacher: MOLERA MOLERA, JUAN MANUEL

Department assigned to the subject: Mathematics Department

Type: Compulsory

ECTS Credits: 6.0 ECTS

Course: 1º

Semester: 2º

Requirements (Subjects that are assumed to be known)

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

Skills and learning outcomes

Link to document

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

SE1 - FINAL EXAM. [60 %]
Global assessment of knowledge, skills and capacities acquired throughout the
course.

SE2 - CONTINUOUS EVALUATION. [40 %]
Assesses papers, projects, class presentations, debates, exercises, internships
and workshops throughout the course.

% 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, 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.