# Mathematical Analysis II

**Mechanical Engineering**, Publication in the Diário da República - Despacho nº 14312/2015 - 02/12/2015

6 ECTS; 1º Ano, 2º Semestre, 30,0 T + 30,0 TP + 4,50 OT

**Lecturer**

- Maria Helena Morgado Monteiro

**Prerequisites**

Knowledge of differential calculus and integral calculus in R.

**Objectives**

Develop the skills of students to interpret data, formulate and solve problems that occur in engineering and relate to:

a) Representation of functions by series and calculate approximate values;

b) The differentiation of functions;

c) The integral of functions with two or three variables.

**Program**

1.Series: series of numbers and functions.

2.Differential calculus in Rn: partial derivatives; differentiability; maxima, minima and saddle points, Lagrange´s multipliers.

3.Multiple integrals:definition, properties, evaluation and applications of the double integral and the triple integral.

**Evaluation Methodology**

Ongoing assessment: two written tests (0-8) with minimum mark of 2; three homeworks (0-1); presentation in class of one exercise solved(0-1).

Exam assessment: a written test (0-20).

Minimum mark to pass the exam is 10. Pass mark for ongoing assessment is the sum of the tests with the homeworks and the presentation and must total 10.

**Bibliography**

- Larson, R. e Hostetler, R. e Edwards, B. (2006). *Cálculo*. (Vol. 2). São Paulo: McGraw-Hill

- Stewart, J. (2002). *Cálculo*. (Vol. 2). São Paulo: Pioneira Thomson Learning

- Costa, J. e Breda, A. (1996). *Cálculo com funções de várias variáveis*. Lisboa: McGraw-Hill

- Monteiro, H. (2020). *Apontamentos de Análise Matemática II*. Abrantes: ESTA

**Method of interaction**

Presentation of the theoretical contents. Worksheets solved in class under the teacher's supervision.

**Software used in class**

Productivity tools and Moodle platform.