Mathematical Analysis III

 

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

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

Lecturer
- Maria Helena Morgado Monteiro

Prerequisites
Not applicable.

Objectives
Extend students' knowledge about the differential and integral calculus so they can formulate, analyze and solve problems which are related to:
a) The effect of vector fields in the movement of particles.
b) The behavior of physical phenomena when their variation rates and restrictions are known.

Program
1. Vectorial calculus - vectorial functions, line integrals, surface integrals;
2.Differential equations - first-order differential equations and linear differential equations of order n, Laplace?s transform, linear differential equations systems.

Evaluation Methodology
Ongoing assessment: two written tests (0-9) with minimum mark of 2; presentation in class of two exercises 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
- Monteiro, H. (2020). Apontamentos de Análise Matemática III. Abrantes: ESTA
- Stewart, J. (2012). Calculus. Belmont, USA: Cengage Learning
- Zill, D. (2001). Equações Diferenciais. (Vol. I). São Paulo: Makron Books
- Larson, R. e Hostetler, R. e Edwards, B. (2006). Cálculo. (Vol. II). São Paulo: McGraw-Hill
- Ramos, M. (2011). Curso Elementar de Equações Diferenciais - Textos de Matemática. (Vol. 14). Lisboa: Departamento de Matemática da Faculdade de Ciências da Universidade de Lisboa
- Mora, W. (2019). Cálculo en Varias Variables, Visualización interactiva. Costa Rica: Escuela de Matemática, Instituto Tecnológico de Costa Rica

Method of interaction
Lectures.
Worksheets solved in class under the teacher's supervision.

Software used in class
Not applicable.