ISMAT 1

Mathematics I

• ApresentaçãoPresentation

  Mathematics I belongs to the scientific area of Mathematics and provides the fundamental concepts of mathematical analysis required for the remaining curricular units of the programme. It covers differential and integral calculus, sequences and series, promoting logical reasoning, mathematical modelling and problem solving. The acquired knowledge provides an essential foundation for Data Science, Statistics, Machine Learning and optimisation.
• ProgramaProgramme

  S1. Real functions of real variable: real numbers; topological notions; generalities about functions; polynomial, rational, exponential, logarithmic and trigonometric functions; limits and continuity; derivatives and applications. S2. Integral calculation in R: Riemann integral; integration rules; decomposition, parts and substitution integration; indefinite integral and definite integral; Fundamental Theorem of Integral Calculus; Integral Calculation applications. S3. Numerical series: successions; geometric and Mengoli series; comparison criteria; absolutely convergent series; power series; Taylor series.  
• ObjectivosObjectives

  At the end of this unit students should know: LO1. Use logical thinking to organize and relate information; LO2. Understand the fundamental notions about sets and real numbers; LO3. Determine function limits; LO4. Study functions and make graphs; LO5. Calculate and interpret derivatives of functions; LO6. Calculate integrals and use the integral calculation to determine areas, lengths, masses, probabilities, etc; LO7. Investigate the convergence of sequences and series; LO8. Know and apply the fundamental theorems; LO9. Demonstrate mathematical propositions and properties; LO10. Solve real-life problems using mathematical methods.  
• BibliografiaBibliography

  Adams, R.A. & Essex, C. (2022). Calculus - A Complete Course. (10ª ed.). Pearson. Apostol, T.M. (1994). Cálculo. (1º vol.). Reverté. Ferreira, J.C. (2018). Introdução à Análise Matemática. (12ª ed.). Lisboa: Fundação Calouste Gulbenkian.  
• 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. The active learning is promoted through problem solving, real-world applications and the use of digital learning tools. Whenever appropriate, mathematical software is used to support concept visualisation and foster students' autonomy.
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  6
• NaturezaNature

  Mandatory
• EstágioInternship

  Não