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Cálculo II

Código 13403
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 IR.I nt he end on this curricular unit the student must be able to:
a) Solving some 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) Compute implicit derivatives.
g) Integrate functions of several variables.
h) Apply the integral calculus to compute areas and volumes.
Syllabus 1. Introduction to differential equations. Separable and linear first order equations and constant coefficients second order linear equations.
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 constrains: Lagrange multipliers; Chain rule and implicit derivatives.
4.Integral Calculus in R^n: Riemann integral: definition and examples; Properties of integrable functions; Change of coordinates; Applications.
Main Bibliography - Apostol,T.M., "Calculus",Volume II, John Wiley & Sons, 1968.
- Lang, S., "Calculus of Several Variables", Undergraduate Texts in Mathematics, Third Edition, Springer-Verlag,
1987.
-Stewart, J., Cálculo, Volumes 1 and 2, North American 7th edition translation, Cengage Learning, 2013.
Language Portuguese. Tutorial support is available in English.

Regente

Não tem Fotografia.
 Sandra Margarida Pinho da Cruz Bento

Curso

Ciências Biomédicas
Data da última atualização: 2025-06-06
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