The course complets the basic formation in Mathematical Analysis and it is focused on succession and series (numerical and of functions) and in the introduction to Calculus of several variables.
Competence in analysis and synthesis;
Competence to solve problems;
Competence in critical thinking;
Competence in independent learning;
Competence to apply in practice the theoretical knowledge.
Numerical successions and series (monotonous and limited successions; subsuccessions; notion of limit, operations with limits; convergent series; convergence criteria; conditional convergence; commutative).
Successions and series of functions (simple convergence and uniform convergence, power series, developments in series, Taylor series, Fourier series).
Scalar functions of several variables (limits and continuity; partial derivatives, directional derivative and gradient vector, implicit function theorem; extreme; 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
Sseminar or study visit
Laboratory or field work
Synthesis work thesis
2 Frequências | 2 Midterm exams (<100) %
1 Exame | 1 Exam (<100) %
assessment implementation in 20202021 Continuous assessment Frequency: 100.0% Assessment by Final Exam Exam: 100.0%
Bibliography of reference
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.
There are theoretical and theoretical-practical classes.
The theoretical classes are mainly expository, where each concept is introduced, if possible, in different ways (geometrically, numerically or algebraically). To facilitate the understanding of the concepts, many application examples are also described.