-
Presentation
Presentation
In this 1st year course unit, the fundamental concepts about differential and integral calculus in IRn will be introduced, which are important for learning knowledge in subsequent courses of the Civil Engineering degree.
-
Class from course
Class from course
-
Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 6
-
Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
-
Code
Code
ULP730-551
-
Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
-
Professional Internship
Professional Internship
Não
-
Syllabus
Syllabus
REVIEW OF INTEGRALS IN IR DIFFERENTIAL CALCULUS IN Rn . Study of multivariate scalar and vector functions. Graphic representations. Topological notions in Rn. Calculation of iterated, directional and definition limits. Continuity. - Derivatives of scalar fields. Partial derivatives. Vector gradient. Directional derivatives. Differentials. Continuity. Derived from the compound function. Implicit derivation. - Derivatives of vector fields. - Extremes of functions with 2 and 3 variables, free and conditioned. - Applications. INTEGRAL CALCULUS IN Rn - Integrals with 2 and 3 variables. - Vector field line integrals. Theorem of Green. - Surface integrals. Flow. Gauss's theorem (flow-divergence). - Applications.
-
Objectives
Objectives
At the end of this curricular unit, the student should have acquired skills to master the technical knowledge in fundamental mathematics, in particular: - understand multivariable functions in terms of its domain, codomain, range, derivative, limits and apply them to real cases engineering; - know how to calculate iterated limits, directional and using the definition, and evaluate the continuity of multivariable functions; - know how to calculate the free and conditional extremes in multivariable functions; - solve multiple integrals and line and understand its meaning; - know some theorems of integral calculus in Rn; - modeling engineering problems by applying the knowledge acquired; - be able to apply the knowledge and ability to understand and solve problems in new and unfamiliar situations, in broad multidisciplinary contexts.
-
Teaching methodologies and assessment
Teaching methodologies and assessment
In this UC, some active methodologies will be used that promote greater student involvement in activities, such as learning through PBL, flipped classes and peer feedback. In terms of digital technologies, Moodle will be used.
-
References
References
- Anton, Bivens and Davis (2014). Cálculo 10ªed.- vol. 2: Bookman. - Apostol, T. M (2004). Calculus (volume 2). Editorial Reverté. - Azenha, A. Jerónimo, M. A. (1995). Elementos de cálculo diferencial e integral em IR e IRn. Editora McGraw Hill. - Kreyszig, E., (1998). Advanced Engineering Mathematics (6th Edition). John Wiley & Sons. - Textos de apoio e coleções de exercícios fornecidos ao longo das aulas pela docente.
-
Office Hours
Office Hours
-
Mobility
Mobility
No
