The curricular unit complements the basic training in Mathematical Analysis and focuses on the study of (numerical and function) successions and series and on the introduction to calculation for different variables functions.
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).
Mathematical Analysis I.
Generic skills to reach
. Competence in analysis and synthesis; . Competence to solve problems; . Critical thinking; . Competence in autonomous learning; . Competence in organization and planning; . Competence in oral and written communication; . Competence in applying theoretical knowledge in practice; . Self-criticism and self-evaluation; (by decreasing order of importance)
Teaching hours per semester
total of teaching hours
assessment implementation in 20112012 Final exam: 100.0% Two midterm tests : 100.0%
Bibliography of reference
Bibliografia principal:  José Miguel Urbano, Análise Matemática II, Notas de Curso, Coimbra, 2007.
 James Stewart, Cálculo, vol. I e vol. II, Thomson Learning, 2001.
 Jerrold E. Marsden e Anthony Tromba, Vector Calculus, W. H. Freeman (5th edition), 2003.
- In the theoretical classes an oral presentation of the subjects will be done using a board and chalk sticks.
Examples will be given and problems will be solved. The teacher will be the centre of the development of these tasks.
- In the theoretical-practical classes, exercises, which were previously proposed to the students, will be solved. Students should take the initiative to choose and solve the problems to be analysed in each class.