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ISMAT 505

Mathematics II

Data Science
  • ApresentaçãoPresentation
    Mathematics II belongs to the scientific area of Mathematics and deepens the knowledge of differential and integral calculus by extending it to multivariable functions and ordinary differential equations. These topics provide an essential foundation for mathematical modelling, optimization and methods used in Data Science.  
  • ProgramaProgramme
    S1. Functions of several independent variables: Algebraic and topological structure of Rn; Limit and continuity; Differentiability; Partial derivatives; Derived from the composite function; Taylor's theorem in Rn and application to the study of extremes; Theorems of inverse function and implicit function; Conditioned extremes. S2. Integral calculus in several real variables: Double integral and triple integral (geometric interpretation, fundamental properties, Fubini's theorem; Variable change theorem, applications). S3. Ordinary differential equations: separable variable equations; 1st order linear equations; Numerical methods: Euler and Runge-Kutta; applications.  
  • ObjectivosObjectives
    At the end of this unit students should know: LO1: Extend the study of functions to problems with more than one real variable; LO2: Master the differential and integral calculus of functions of more than one real variable, including the fundamental theorems of calculus; LO3: Use real problems involving functions with more than one independent variable; LO4: Solve differential equations and understand their applications.  
  • BibliografiaBibliography
    Apostol, T.M. (1987). Cálculo. (1º Vol.). Reverté. Ayres, F. & Mendelson, E. (1994). Cálculo diferencial e integral. S.Paulo: Makron.  
  • MetodologiaMethodology
    The teaching methodology includes the expository method (TM1) to present the contents, the demonstrative method (TM2) to illustrate its application to practical cases and the active method (TM3) to solve classroom exercises, with and without the use of a computer. Whenever appropriate, mathematical software is used to support concept visualization and problem solving.    
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    6
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não