Calculus II

Code	11847
Year	1
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	non applicable
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) Integrate functions of several variables. g) 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 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 I e II, Tradução da 6a edição Norte-Americana, Cengage Learning, 2010.
Language	Portuguese. Tutorial support is available in English.