# 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

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.