Class Mathematical Analysis I

Introduction and exploration of basic concepts of Mathematics.

Not applicable

1. Revisions on set of numbers and geometry in the plane. 2. Successions. Limited successions, monotony, convergent. Arithmetic and geometric progressions. 3. Real Functions of a real Variable. General information about functions. Complete study of the different types of functions. Graphs. Transformations. Trigonometry. Properties. Limits. Properties. 4. Differential calculus. Rules of derivation. Derivatives of the main functions. Derivatives of composite and inverse functions. Derivatives of higher order than the first. Applications: finding maxima, minima and inflection points. Rule of Cauchy/L'Hôpital. 5. Integral calculus. Indefinite integral. Definition and properties. Integration techniques: immediate antiderivative, substitution and by parts. Integration of different types of functions. Definite integral. Geometric meaning. Improper integrals. Applications.

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.