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Topics of Analysis

Topics of Analysis

Code	10835
Year	1
Semester	S1
ECTS Credits	12
Workload	TP(45H)
Scientific area	Mathematics
Entry requirements	-
Mode of delivery	Face to face.
Learning outcomes	This course unit aims to consolidate knowledge of Mathematical Analysis, its history, applications and links with the curricula of Mathematics in the 3rd Cycle of Basic Education and Secondary Education. - To deepen the study of real functions of real variable in a historical perspective, from the Greeks to the present, highlighting results and methods of the mathematicians who contributed most to its development. - To establish links between contents of this course and the curricula of Mathematics in the 3rd cycle of Basic Education and Secondary Educations.
Syllabus	I- The Greek method of exhaustion: Eudoxus, Euclid and Archimedes, Eudoxus principle, application to the study of areas and volumes. II- Creators of Calculus: precursors of Calculus; Newton and Leibniz. III-Promoters of Calculus: the Bernoulli and Euler. IV - Introduction of logical rigor in Calculus: controversies around the new Calculus; Bolzano, Cauchy and Weierstrass. V - Rigorous construction of the Integral: Riemann and Lebesgue. VI - Rigorous construction of the real line: Dedekind and Cantor.
Main Bibliography	1) Boyer, C. B., História da Matemática, Editora Edgar Blücher, 1996. 2) Dunham, W., The Calculus Gallery – Masterpieces from Newton to Lebesgue, Princeton University Press, 2005. 3) Dunham, W., Journey Through Genious – The Greats Theorems of Mathematics, Penguin Books, 1990. 4) Edwards, C. H., The Historical Development of the Calculus, Springer, 1979. 5) Ferreira, J. C., Introdução à Análise Matemática, Fundação Calouste Gulbenkian, segunda edição, 1996. 6) Jahnke, H. N. (editor), A History of Analysis, AMS, 2003.
Language	Portuguese. Tutorial support is available in English.