Mathematical Analysis I

Recommended Prerequisites

High School Mathematics, 

Teaching Methods

The classes are of theoretical and theoretical-practical type. The teaching methods in the theoretical components will be predominantly expository and should include examples that lead the students to understanding the material being taught. In the practical components problems will be solved under the guidance of the teacher. The independent resolution of problems must be encouraged.

The interaction between concepts and their practical application must be discussed, giving a central role in the visualization and analysis of particular situations before making a progressive abstraction of the

Learning Outcomes

Give the students the basic knowledge of differential and integral calculus for real functions of a real variable. Know how to solve differential equations and apply this knowledge in modeling and solving problems. The relevance of the results presented in the context of applications should be emphasized, especially in the framework of Electrical and Computer Engineering. It is also intended that students acquire knowledge of the concepts in order to assess the scope and limitations of the materials studied and their applications.

 

The course aims at developing the following skills: analysis and synthesis, organization and planning, oral and written communication, problem-solving skills and computational ability. On the personal level it also allows to develop self-learning skills and independent thinking.  

Work Placement(s)

No

Syllabus

Real functions of one real variable

 - Limit, continuity and derivation

 - Integral defined and applications

 - Improper Integral

First order differential equations

 - Separable variables and linear equations

 - Examples and applications

Linear differential equations of higher order than the first

 - Method of the cancelling polynomial

 - Method of lowering of order

 - Method of variation of arbitrary constants

 - Examples and applications 

Head Lecturer(s)

Jaime Maria Monteiro de Carvalho e Silva

Assessment Methods

Assessment 1
Frequency: 100.0%

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

Assessment 3
Exam: 100.0%

Bibliography

 [1] Stewart, J. (2014) – Cálculo, Volumes I e II, traduzido da 7ª ed. norte-americana, Cengage Learning, S. Paulo.

 [2] Zill, D. G. (2016) – Equações Diferenciais com aplicações em modelagem, traduzido da 10ª ed. norte-americana, Cengage Learning, S. Paulo.

 [3] Carvalho e Silva, J. (1994) – Princípos de Análise Matemática Aplicada, McGraw-Hill, Lisboa..

 [4] Breda, A., Costa, J (1996) – Cálculo com funções de várias variáveis, McGraw-Hill, Lisboa.

 [5] Campos Ferreira, J. (1993) – Introdução à Análise Matemática, Fund. Calouste Gulbkenkian.