Numerical successions and series (monotonous and limited successions; sub-successions; the notion of limit; operations with limits; convergent series; convergence criteria; conditional convergence; commutativity).

Successions and series of functions (simple convergence and uniform convergence; potencies series; series developments; Taylor series; Fourier series).

Scalar functions of several variables (limits and continuity; partial derivative; directional derivative and gradient vector; implicit function theorem; extremes; Lagrange multipliers).

[1] José Miguel Urbano, Análise Matemática II, Notas de Curso, Coimbra, 2007.

[2] James Stewart, Cálculo, vol. I e vol. II, Thomson Learning, 2001.

Bibliografia complementar:

[3] Jerrold E. Marsden e Anthony Tromba, Vector Calculus, W. H. Freeman (5th edition), 2003.

[4] Jaime Campos Ferreira, Introdução à Análise Matemática, Fundação Calouste Gulbenkian, 1993.

[5] Elon Lages Lima, Curso de Análise, vol. 1 (11ª edição), Projecto Euclides, IMPA, 2004.