### Análise Matemática II - Matemática - Sem Ramos - Especialidades

7.5
ECTS / Credit Units
 Year: 1 / 2º Semestre Plan: 2015/16 Scientific Area: MAT Level: Básico

 Theorical: 48.00 Theorical-Pratical: 32.00 Pratical and Laboratorial: Fieldwork: Seminar: Internship: Tutorial:
 Assigned Internship Hours: Assigned Projects Hours: Assigned Fieldwork Hours: Assigned Study Hours: Assigned Evaluation Hours: Others:

### Degree having this Course

Degree - Branch Degree Plan Year
Matemática - Sem Ramos - Especialidades 2015/16

### Teaching Staff

Maribel Gomes Gonçalves Gordon

Responsibilities:
Regência
Responsável pelas Pautas
Ensino teórico
Ensino teórico-prático

## Course Information

### Course Objectivs

1 Stimulation and development of reasoning, formalization, rigour, computational, argumentation, deduction and abstraction skills.

2 To equip students with the basic theoretical and pratical notions of Mathematical Analysis which will then be used in more advanced courses.

3 The study of the fundamental concepts in the theory of integration of functions in one variable and its main applications.

4 Introduction and formalization of the theory of Mathematical Analysis in R^n with the correponding applications to concrete problems.

5 The generalization to R^n of the notions of limit, continuity and differentiability which were introduced in Mathematical Analysis I.

6 To familiarize students with prooving results and requiring the knowledge of some them.

### Evaluation Criteria

Classification Type: Quantitative (0-20)
Evaluation Methodology: Oral and written exposition of the currricular unit's syllabus. Discussion and solving exercises and concrete problems in small groups or individually. The evaluation is done through the realization of two tests (each worth 50% of the final grade) to be solved individually. In this way the student can assess his progress and change his studying strategies if necessary. During the supplementary Exam period students who have not successfully completed the curricular unit can choose between retaking one of the tests or doing an exam which includes all the contents of the curricular unit. The importance of this exam is to test the student's ability to relate the notions and results introduced throughout the curricular unit.

### Main Bibliography

Agudo, D. (1969). Lições de Análise Infinitesimal, Vol I e II,. Escolar Editora.
Apostol, T. (1983). Cálculo, Vol II, 2ª Edição. Ed. Reverté Lda..
Ávila, G. S. S. (1979). Cálculo III-Diferencial e Integral. Livros Técnicos e Científicos Editora S.A..
Campos Ferreira, J. (2002). Introdução à Análise em IR^n. IST.
Kaplan, W. (1972). Cálculo Avançado, Vol II. Editora da Universidade de S. Paulo.
Lang, S. (1980). Cálculo, Vol II. Livros Técnicos e Científicos Editora.
Piskounov N. (1986). Cálculo Diferencial e Integral, Vol. I e II. Lopes da Silva Editora.
Swokowski, E. W. (1983). Cálculo com Geometria Analítica, Vol II. McGraw-Hill.
Courant, R., John, F. (1989). Introduction to Calculus and Analysis I. Springer.
Dieudonné, J. (1972). Eléments d'Analyse I. Hermann, Paris.
Cartan, H. (1972). Cours de Calcul Différentiel. Hermann, Paris.
Lang, Serge (1993). Real and Functional Analysis. Springer.