Skip to main content

IPLUSO 24335

Integral Differential Calculus

Computer Engineering and Applications
  • ApresentaçãoPresentation
    In an Engineering study cycle, the curricular units in the scientific area of Mathematics play a relevant role. They are essential for students to acquire solid basic knowledge needed in other curricular units of the cycle of studies that require mathematical knowledge or new skills and competences acquired with the gradual and persistent work in the curricular units in this area. The curricular unit of Differential and Integral Calculus assumes a fundamental and relevant role in the mathematical training of students, in particular in the study of concepts that allow studying the modeling of real-life situations. understanding and consolidation of the different concepts, either in the specific knowledge of their applicability and in the development of new skills and competences acquired with the work in the curricular unit.
  • ProgramaProgramme
    1.- Real numbers. Properties of operations with real numbers. Topology elements. Number e. 2.- Functions. Algebra and composition of functions. Inverse function. Monotony. Trigonometric and inverse trigonometric functions. Hyperbolic functions. Implicit function. 3.- Limits and continuity of functions. Asymptotes. Bolzano's theorem. Weierstrass theorem. 4.- Derivatives and differentials. Geometric interpretation. Derivation rules. Derivative of the composite function and the inverse function. Derivative of implicitly and parametrically defined functions. Cauchy's Rule. Complete study of functions. 5.- Integral calculation in IR. Primitive. Primitive Techniques. Riemann integral. Properties. Fundamental theorem of integral calculus. Mean Value Theorem. Geometric applications of the integral: calculation of areas of flat surfaces; Calculation of lengths, areas and volumes.
  • ObjectivosObjectives
    At a general objective level, it is intended to familiarize students with the fundamental concepts of Functions and differential and integral calculus and with abstract reasoning in general. In specific terms, after addressing the indicated syllabus, tasks and exercises are proposed to apply the concepts explored with the consequent diversity of contexts in which they can be applied in the field of engineering in general. In particular, mastery of knowledge of derivation rules and applications and knowledge of immediate primitives and others that enable their application to the calculation of areas, line lengths and volumes and others likely to be mobilized in the resolution of various problems on the horizon of technologies and engineering and, in particular, computer engineering.
  • BibliografiaBibliography
    Almeida, Ricardo - Cálculo, Teoria e Exercícios. 1ª Edição. Lisboa: Plátano Editora. 2017. ISBN:978 989 760 125 5. Simões, Vasco - Análise Matemática 1. 1ª Edição. Lisboa: Edições Orion. 2009. ISBN: 978 972862 014 1 Monteiro, António, Matos, Isabel e Miranda, Virginia - Derivadas. 1ª Edição. Lisboa: EdiçõesOrion. 2015. ISBN 978 972 862 028 8 Stewart, James - Cálculo - volume I. 5ª edição. São Paulo: Thomson Pioneira. 2005. ISBN:978852 210 479 6  
  • MetodologiaMethodology
    Resource and use other sources of information.
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    6
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não