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ISMAT 1

Mathematics I

IT Engineering
  • ApresentaçãoPresentation
    This curricular unit deals with the fundamental concepts of calculus. The following topics are addressed; elements of mathematical logic, elements of set theory, real numbers, real sequences and series, real functions of a single real variable, continuity and limit and differentiation of functions. The contents and teaching/learning strategies addressed promote the development of skills to better understand and develop Computer Engineering projects. Namely, the development of skills to deal with abstract concepts and the calculation, analysis and synthesis, formulating and the resolution of algorithms and real-life problems, organization and planning of critical thinking and autonomous learning.
  • ProgramaProgramme
    CP1. Elements of mathematical logic; CP2. Elements of set theory; CP3. Real numbers, CP4. Mathematical sequences and series; CP5. Mathematical functions; CP6. Continuity and limit of functions CP7. Differentiation of functions; CP8. Extreme Values of Functions.
  • ObjectivosObjectives
    At the end of this unit students should be able to: OA1. Apply the Logical concepts to organize and to relate the various types of information; OA2. describe the fundamental concepts about real numbers and Sets; OA3. calculate limits of mathematical functions and mathematical sequences; OA4. investigate about mathematical functions; OA5. investigate about convergence of mathematical sequences and series; OA6. calculate derivatives of functions OA7. apply the fundamental theorems; OA8. demonstrate propositions and mathematical properties; OA9. Solve real-life problems using mathematical methods including: the precision and rigor required in the language used to describe a problem; the systematic study and the designs od algorithms: OA10: Relate the mathematical concepts presented with computer theory.
  • BibliografiaBibliography
    Ferreira, J. C. - Introdução À Análise Matemática. 12ª ed.: F. C. Gulbenkian, 2018. Apostol, T.M. - Cálculo. 1º vol.,2ª ed. :Reverté, 1988. Adams, R.A., Essex C. - Calculus - A Complete Course, 7ª ed.: Pearson, 2010. Ferreira, J. C. - Elementos de Lógica Matemática e Teoria dos Conjuntos, IST, 2001. Exercícios de Análise Matemática I e II, 3ª ed.: Departamento de Matemática, IST Press, 2010  
  • MetodologiaMethodology
    The theoretical-practical component is presented using predominantly expositive and formal methods of concepts, based on case discussion, with detailed manual elaboration on the board and explanation of the objectives and contents corresponding to each theme, accompanied by discussion, placement and clarification of doubts. The practical component is based on the discussion and solving of exercises, in groups and individually, on paper and / or using mathematical software tools to support calculations and representations and to identify and correct errors. The assessment is governed by the ISMAT assessment regulation and consists of continuous assessment and a final exam (100% final grade). Continuous assessment consists of two written tests (90% final grade) and active participation in class (10% final grade
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    6
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não