Sumários

Lecture 6

18 Setembro 2026, 19:00 • Jorge Miguel Cruz Pereira Varelas da Rocha

Metric spaces: contractions; fixed points; Banach fixed point theorem.

Numerical solutions of algebraic equations in one variable: introduction; review of single variable calculus; differentiability; Taylor expansions.

Lecture 5

18 Setembro 2026, 17:30 • Jorge Miguel Cruz Pereira Varelas da Rocha

Metric spaces: the notion of continuity for functions defined between metric spaces; complete (and non-complete) metric spaces; spaces of functions; convergence in function spaces.

Lecture 4

14 Setembro 2026, 19:00 • Jorge Miguel Cruz Pereira Varelas da Rocha

Metric spaces: introduction; definition of distance function and metric space; examples with balls in different metric spaces; equivalent metrics.

Introduction to MATLAB.

Lecture 3

14 Setembro 2026, 17:30 • Jorge Miguel Cruz Pereira Varelas da Rocha

Sequences of real numbers: Cauchy sequences, their definition, and equivalence with convergent real sequences.

Exercises solved in class.

Lecture 2

7 Setembro 2026, 19:00 • Jorge Miguel Cruz Pereira Varelas da Rocha

Sequences of real numbers: real sequences; basic results about convergence.

Some examples and exercises solved.