# Mathematical Analysis I

**Chemical and Biochemical Engineering**, Publication in the Diário da República - Despacho nº 10764/2011 - 30/08/2011

6 ECTS; 1º Ano, 1º Semestre, 30,0 T + 30,0 TP

**Lecturer**

**Prerequisites**

Not applicable.

**Objectives**

a)- Provide the mathematical foundations required in other modules of the programme.

b)- Provide skills to work with differential and integral calculus of functions of one real variable.

**Program**

1- Preliminaries.

2- Real functions of a real variable.

3- Limits and continuity.

4- Differential calculus.

5- Integral calculus.

**Evaluation Methodology**

Continuous assessment:

Continuous assessment consists of two written tests. Each of these tests is graded from 0 to 10 points. The student is exempted from exam, i.e. if he/she has at least 3 marks in each test and obtains a classification higher than or equal to 10 marks, resulting from the sum of the 2 tests.

Exam-based assessment:

If the student has been admitted to an examination, or has been exempted but wishes to improve his classification, he can take the first attempt examination - a written test (graded from 0 to 20 points) on all the subject matter taught. A minimum mark of 10/20 is required to pass.

If the student fails the examination he can apply for resit - a test similar to that of firt attempt.

NOTE:

For any of the assessments, if the student obtains a mark equal to or higher than 17/20 he/she will have to take an extraordinary assessment.

**Bibliography**

- Silva, J. (1999). *Princípios de Análise Matemática Aplicada*. (Vol. 1). Lisboa: McGraw-Hill

- Stewart, J. (2005). *Cálculo*. (Vol. 1). São Paulo: Thomson Pioneira

- Swokowsi, E. (1995). *Cálculo com Geometria Analítica*. (Vol. 1). São Paulo: Makron Books

- Howard, A. (2007). *Cálculo um novo horizonte*. (Vol. 1). São Paulo: Bookman

**Method of interaction**

Theoretical lectures, with presentation and illustration of the proposed subjects. Theoretical-practical lectures in which exercises are proposed and solved.

**Software used in class**