Prerequisites
Not applicable.
Objectives
Master concepts and techniques of differentiable and integral calculus in one variable. Develop analytic thinking, creativity and innovation capacity, through the application of those concepts and techniques in different contexts.
Program
Real numbers: algebraic, order and supremum axioms. Natural numbers and mathematical induction. Sequences: the concept of limit; applications. Real functions of one real variable: limits and continuity; elementary functions. Global properties of continuous functions: intermediate value and Weierstrass theorems. The concept of derivative. Derivatives of elementary functions. Rolle, Lagrange and Cauchy theorems. L'Hôpital's rule. Derivatives of higher order. Inverse functions. Primitives: parts, substitution, rational functions. Riemann's integral. Fundamental Theorem of Calculus. Barrow's rule. Applications: calculation of areas; definition of functions (ex.: logarithm, error and gamma functions); examples of separable differential equations of the form f(y) y’(t) = g(t). Taylor's polynomial. Numerical series. Convergence criteria. Simple and absolute convergence. Power series, convergence radius. Taylor series: definition, examples and convergence.
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/845953938489997
