Mathematical Analysis III

Year
2
Academic year
2020-2021
Code
01016318
Subject Area
Mathematics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Compulsory
Level
1st Cycle Studies

Recommended Prerequisites

Mathematical Analysis I, Mathematical Analysis II.

Teaching Methods

The teaching method in theorical classes is the expository method.

Practical classes are designed to solve problems under the guidance of the teacher, and to  encourage the autonomous  work by students. As much as possible, examples and exercises of the field of Electrical and Computer Engineering will be used.

In the theoretical exposition it prevails a strong interaction between concepts and

its practical application. As much as possible, visualization and concrete examples are studied.

The transformation of concepts into working tools will be achieved by student’s individual work.

Learning Outcomes

To endow the students with fundamental concepts in order to understand sequences and numerical series, in the scope of  real and complex numbers. To endow the students with basic knowledge in differential and integral calculus for complex functions. It is intended that students acquire skills to use symbolic, formal and  technical  language  in the framework of complex numbers. It is intended that the students acquire a knowledge of concepts which allows to assess the importance and the limitations of the studied material and its applications.

Work Placement(s)

No

Syllabus

1. Sequences and infinite series of  real numbers · Convergence criteria · Power series, · Taylor’s theorem and Taylor series,· Fourier series.

2. Complex Analysis:

· Functions of a complex variable; limits e derivatives; analytic functions.

· Integration in the complex plane; Cauchy´s  integral theorem; the residue theorem.

· Infinite series of complex variables; Taylor series and Laurent series.  

Head Lecturer(s)

Ricardo Nuno Fonseca de Campos Pereira Mamede

Assessment Methods

Assessment 2
Resolution Problems: 50.0%
Mini Tests: 50.0%

Assessment 1
Frequency: 100.0%

Assessment 3
Exam: 100.0%

Bibliography

  • Stewart, J.  (2001) – Cálculo, Vol. 2, Pioneira.

• Breda, A., Costa, J. (1996)  –  Cálculo com funções de várias variáveis, McGraw-Hill.

• Zill, D. G., Shanahan,  Patrick, D. (2003) - A first course in complex analysis with applications, Jones and Bartlett Publishers.

• Spiegel, M. (1977) –  Análise de Fourier, Colecção Schaum.