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Universidade Lusófona do Porto

Calculus I


Introduction and exploration of basic concepts of Mathematics.


Science in Aerospace Engineering

Level of Qualification|Semesters|ECTS

| Semestral | 5

Year | Type of course unit | Language

1 |Mandatory |Português



Recommended complementary curricular units

Not applicable.

Professional Internship



Revisions on set of numbers and geometry in the plane.


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.


It is intended that the students revisit and deepen their knowledge of property and of operations of successions and real functions of real variable, as well as differentiation and its applications. Based on this knowledge, the objective is that the student learns to operate and differentiate in IRn.

Teaching methodologies and assessment

TEACHING METHODOLOGY: The theoretical sessions will be of an expository nature, always accompanied by the resolution of illustrative exercises. The practical sessions will be essentially dedicated to solving exercises, individually or in a global group, on the topics addressed in the course unit, sequentially in relation to their presentation in the theoretical sessions.

With remote teaching, adopted in some of the classes: i) transmitting some more theoretical concepts and knowledge; ii) strengthening the students' autonomy, who are challenged to work on a set of practical works.

EVALUATION: Continuous evaluation - two tests, with equal weight. Exam - written test (100%).


B. Demidovitch, (1996) 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.


Office Hours

Nome do docente  

Horário de atendimento


Nuno Correia dos Santos

Sexta-feira, das 10.30 às 11.30

Gabinete do docente