Mathematical Analysis II

Recommended Prerequisites

Calculus I

Teaching Methods

During theory classes, the main methods will be the exposition of the material. Theory-practical classes are intended for the solving of problems under pedagogic guidance. Students will be motivated to autonomously solve problems.

As for the theory exposition, there will be a strong interaction between the concepts and their application, giving a central role to the visualization and analysis of particular cases, before moving on to a progressive abstraction of other concepts. The integration of concepts into working tools will achieved by motivating students to solve problems on their own.

Learning Outcomes

The main objectives are to acquire basic knowledge about functions of  several  variables as well as fundamental concepts about  sequences, infinite series and sequences of functions. The main competences to be developed are: analysis and synthesis abilities; organization and planning abilities; problem solving abilities; ability to apply theoretical knowledge in practical terms; critical thinking.

Work Placement(s)

No

Syllabus

I-Sequences and and infinite series. Tests of convergence.

II-Sequences and series of functions.  Uniform convergence. Power series. Taylor's Formula. Taylor series.

Fourier series.

III-Functions of several variables. The limit concept and continuity. Partial derivatives. Total differencials and  tangent planes. Differentials of composite functions and the chain rule. The directional derivative. The  gradiente vector. The implicit function theorem. Extremum problems. Extremum problems with side conditions.

Head Lecturer(s)

Amílcar José Pinto Lopes Branquinho

Assessment Methods

Assessment
Exam or Midterm exam: 100.0%

Bibliography

Stewart, J. Cálculo, 4ª ed. Vol. I e Vol. II, Pioneira, São Paulo, 2001

Carvalho e Silva, J., Princípios de Análise Matemática Aplicada, McGraw-Hill, Lisboa, 1994

Breda, A., Costa, J, Cálculo com funções de várias variáveis, McGraw-Hill, Lisboa, 1996

Spiegel, M., Análise de Fourier, Colecção Schaum, São Paulo, 1997