﻿ Mathematical Analysis II - Engenharia MecânicaInstituto Politécnico de Tomar

# Bachelor's Degree in Engenharia Mecânica

## Mathematical Analysis II

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

Prerequisites
Not applicable.

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 (0-9) with minimum mark of 2; two presentations 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 presentations 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
- Community, C. (0). Single and Multivariable Calculus, early transcendentals. Acedido em 5 de março de 2022 em https://www.whitman.edu/mathematics/multivariable/

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

Software used in class
Productivity tools and Moodle platform.