Complements of Mathematics

Recommended Prerequisites

Basic knowledge of Real Analysis, Linear Algebra and Analytic Geometry.

Teaching Methods

In theoretical classes, the most relevant concepts and theoretical results are presented, accompanied by illustrative examples of the theory, with simple and motivating applications. In TP classes, students must solve the proposed exercises, having various degrees of difficulty, and will be confronted with problems in the context of Science and Engineering applications. Active participation of students in class discussions, individual and team work, and correct use of  the available  office hours should be strongly encouraged by the instructor.

Learning Outcomes

Having a basic knowledge of Real Analysis, acquired  in the curricular units of BSc programs, students learn,  in this curricular unit, concepts and methods of differential and integral calculus of functions defined in Rn. Another goal of the unit is to provide fundamental knowledge about ordinary differential equations (ODE), including concepts and theoretical results and methods to solve them, as well as to become familiar with basic techniques of mathematical modeling for solving real problems. The approach used in the presentation of the topics is essentially addressed to applications to Science and Engineering.

The main competences to be developed are: ability to formulate and solve problems; knowledge of mathematical results; design, analyze and correctly use mathematical models; ability to work in teams; critical thinking.

Work Placement(s)

No

Syllabus

1. Cálculo em Rn

1.1 Cálculo Diferencial: limites e continuidade; derivadas parciais; derivadas direccionais e extremos

1.2 Cálculo integral: integrais duplo e triplo; coordenadas cilíndricas e esféricas; integral curvilíneo e integral de superfície

2. Equações Diferenciais Ordinárias

2.1 EDO e modelação matemática: noções básicas, construção e validação de modelos, exemplos clássicos

2.2 EDO de 2ª ordem

2.3 Transformada de Laplace:  aplicação à resolução de equações diferenciais de ordem n

Assessment Methods

Final Assessment
Exam: 100.0%

Continuous Assessment
Project: 15.0%
Mini Tests: 15.0%
Frequency: 70.0%

Bibliography

J. Stewart, Cálculo, Volume II, 7ªEd., Cengage Learning, 2012

J. Glyn, D. Burley, D. Clements, P. Dyke, J. Searl, N. Steele, Advanced Modern Engineering Mathematics, 4ªEd., Prentice Hall, 2010