Conteúdo / Main content
Menu Rodapé
  1. Início
  2. Cursos
  3. Biotecnologia
  4. Cálculo II

Cálculo II

Código 15851
Ano 1
Semestre S2
Créditos ECTS 6
Carga Horária TP(60H)
Área Científica Matemática
Mode of delivery Lectures and practical classes with face-to-face teaching.
Work placements Not applicable.
Learning outcomes This course constitutes an introduction to differential and integral calculus in R^n. At the end of this curricular unit, the student must be able to:
a) Solve some first and second-order ordinary differential equations
b) Compute limits of functions of several variables.
c) Investigate the continuity of functions of several variables.
d) Compute the derivatives of functions of several variables.
e) Apply the derivatives to compute maximums and minimums.
f) Integrate functions of several variables.
g) Apply integral calculus to compute areas and volumes.
h) Solve line integrals.
Syllabus 1. Ordinary differential equations: separable equations; first-order linear differential equations; second-order linear differential equations with constant coefficients
2. Functions from R^n into R ^m: Brief notions of topology in R^n; Functions from R^n into R^m; Limits; Continuity
3. Differential Calculus in R^n: Partial derivatives and directional derivatives; Differentiability of functions from R^n into R^m; Derivatives of higher order; Schwarz’s theorem; Local and absolute extreme values; Extremes with constraints: Lagrange multipliers
4. Integral Calculus in R^n: Riemann integral: definition and examples; Properties of integrable functions; Change of coordinates; Applications
5. Line integrals: parameterization of curves; line integrals of scalar functions (length); line integrals of vector fields; Green's Theorem
Main Bibliography - Apostol, T.M., "Cálculo", Volume 1 e 2, Reverté, 1993.
- Azenha, A., Jerónimo, M.A., Elementos de Cálculo Diferencial e Integral em R e Rn, McGraw-Hill, 1995
- Stewart, J., Cálculo, Volumes I e II, Tradução da 6a edição Norte-Americana, Cengage Learning, 2010.
- Course Slides (Moodle)
Language Portuguese. Tutorial support is available in English.

Regente

Imagem d@ José Carlos Alves Martins Aleixo [Ficheiro Local]
 José Carlos Alves Martins Aleixo

Curso

Biotecnologia
Data da última atualização: 2025-03-05
As cookies utilizadas neste sítio web não recolhem informação pessoal que permitam a sua identificação. Ao continuar está a aceitar a política de cookies.