Prerequisites
Linear Algebra and Differential and Integral Calculus I.
Objectives
Master the differential and integral calculus of scalar and vector valued functions of several real variables and multiple and line integrals, including the fundamental theorems of calculus for line and double integrals, and geometric and physical applications.
Program
Basic topological notions in R^n, sequences. Scalar and vector fields. Limits and continuity. Differentiability and gradient. Applications. Intermediate value theorem. C^k functions, Schwarz lemma. Extremal and sadle points of scalar fields. Weierstrass theorem, Taylor's formula, Hessian matrix, Lagrange multipliers. Inverse and inplicit function theorems. Applications. Multiple integrals and applications. Curves, paths and line integrals. Applications. Fundamental theorem of calculus for line integrals and applications. Greens's theorem and applications. Gradient vector fields of scalar fields.
Evaluation Methodology
Exam/tests, possibly with minimum grade, complemented with continuous evaluation components and oral evaluation for grades above 17 (out of 20).
Cross-Competence Component
The UC allows the development of transversal competences on Critical Thinking, Creativity and Problem Solving Strategies, in class, in autonomous work and in the several evaluation components. The percentage of the final grade associated with these competences should be around 15%.
Laboratorial Component
Not applicable.
Programming and Computing Component
Not applicable.
More information at: https://fenix.tecnico.ulisboa.pt/cursos/lerc/disciplina-curricular/845953938489998
