﻿ Mathematical Analysis II - Engenharia MecânicaInstituto Politécnico de Tomar

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 , Cód. 912307.

Lecturer
- Maria Helena Morgado Monteiro (1)(2)

(1) Docente Responsável
(2) Docente que lecciona

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 (0-8) with minimum mark of 2; six homeworks with presentation in class of two homeworks (0-0.7).
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
- Community, C. (0). Single and Multivariable Calculus, early transcendentals. Acedido em 5 de março de 2022 em https://www.whitman.edu/mathematics/multivariable/
- Costa, J. e Breda, A. (1996). Cálculo com funções de várias variáveis. Lisboa: McGraw-Hill
- Larson, R. e Hostetler, R. e Edwards, B. (2006). Cálculo. (Vol. 2). São Paulo: McGraw-Hill
- Monteiro, H. (2024). Apontamentos de Análise Matemática II. Abrantes: ESTA
- Stewart, J. (2002). Cálculo. (Vol. 2). São Paulo: Pioneira Thomson Learning

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

Software used in class
Productivity tools, WolframAlpha and Moodle platform.