Class Mathematical Analysis I

Introduction and exploration of basic concepts of Mathematics.

Not applicable

Revisions on set of numbers and geometry in the plane. Succession. Limited succession monotonous, convergent. Arithmetic and geometric progressions. Real functions of a real variable. Function graphs. Properties of the main functions. Limits. Complete study of functions. Differential calculus in IR. Definition and intuitive notion of derivative. Derivation rules. Derivatives of the main functions. Derivative of composite and inverse functions. Derivatives of higher than first order. Applications: maximum, minimum research and inflection points. Cauchy rules and L'Hôpital. Differential calculus in IRn. Domains. Partial derivatives. Gradient. Derived directional. Total differential. Derivatives of composite functions and implicit functions. Search free and conditioned extremes.

Whenever appropriate, the methodologies to support the teaching-learning process are student – centred as well as in the development of their autonomy. In this context, students will often be encouraged to carry out a set of practical exercises.

Demidovitch, B. (2010) Problemas e Exercícios de Análise Matemática, McGraw-Hill.   Azenha, A. & Jerónimo, M. A. (1995). Elementos de cálculo diferencial e integral em IR e IRn. Brasil: Mc-Graw Hill.   Apostol, T. M (2004). Calculus (volume 2). Editorial Reverté.   N. Piskounov, Cálculo Integral e Diferencial (Vol.I e II), Editora Lopes da Silva, 1974.   Larson, R., e Edwards, B. (2018). Calculus of a single variable (11th edition). Cengage Learning.