Mathematics I

Course: Mathematics I
Year:

1

Semester:

1º Semestre

Curricular Unit:

Matemática Aplicada e Estatística

ECTS:

3.5

Regent:

Ana Maria Fité Alves Diniz

Objectives:

1 – Provide the basic mathematical tools which are necessary for further studies, at the level of Linear Algebra and Mathematical Analysis;
2 – Develop abstract thinking, fundamental for scientific studies;
3 – Pass on to students the relevance of Mathematics in the possible areas of interest both for their studies and professionally.

Contents:

1 – Vectors and matrices
1.1 – Vectors in R^n
1.2 – Matrices and linear systems
2 – Series
2.1 – Sequences (revision)
2.2 – The concept of a series
2.3 – Series convergence and convergence criteria
3 – Differential calculus
3.1 – Limits (Cauchy's rule), derivatives and the drawing of graphs
3.2 – Inverse trigonometric functions and hyperbolic functions
4 – Integral calculus
4.1 – Primitivation
4.2 – Riemann integral
4.3 – Indefinite integral and the fundamental theorem of calculus
4.4 – Applications to mechanics and probability

Evaluation:

Teaching is done starting from examples to make it very clear at all points the relevance of the concepts. Whenever possible, these examples are taken from practical situations known to the majority of students or, in some cases, from research work where the usage of these concepts or techniques is clear – here we are not talking about an analysis of a scientific article, which would be beyond the intended scope, but to use it to illustrate practical relevance. In all lectures students are given series of exercises and problems to be solved by the next lecture, at which point they may put forward questions and doubts they had while solving them. The mini-tests are based on these exercises.
Assessment: 1. Four or five minitests during term, plus a final test encompassing all the topics or 2. Final exam.
The final grade in the course is computed via a process which may be found in http://www.fmh.ulisboa.pt/pt/doc/1o-ciclo/desciplinas/2766-metodos-de-avaliacao-matematica/file

Bibliography:

Loura, Luís, Tópicos de Matemática, FMH, 2002 Freitas, Pedro, Folhas de Problemas de Matemática, FMH 2009

Program in pdf:

Português

English

2019/2020

2019/2020

2018/2019

2018/2019

2017/2018

2017/2018

2016/2017

2016/2017

2015/2016

2015/2016

2014/2015

2014/2015

2013/2014

2013/2014



Erasmus Incoming