Mathematical Analysis II

Recommended Prerequisites

Mathematical Analysis I.

Teaching Methods

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.

Learning Outcomes

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.

Generic skills:
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.

Work Placement(s)

No

Syllabus

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).

Head Lecturer(s)

Joana Margarida Mavigné de Andrade Alves de Sousa Nunes da Costa

Assessment Methods

Assessment
Exam: 100.0%

Bibliography

Base:

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

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


Bibliografia complementar:

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

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

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