Reform the semester courses Mathematical Analysis IIi and IV,
offered to 2nd year sudents of all IST Engineering degrees

Modernizing the syllabus with aspects of 20th-century Mathematics (at the time, nothing more recent than the mid-19th century was taught), with a concern not only to provide the general foundations for engineers, but also to illustrate the application of concepts in Engineering and Science, and to induce a study strongly supported by the resolution of exercises, some of high difficulty, and to arise the curiosity and interest of the best students in Mathematics.

The reform was progressive over several years, and led to the introduction of differential manifolds, Lebesgue integral, Complex Analysis and Fourier Analysis with a modern perspective, and Elementary Theory of Ordinary and Partial Differential Equations.

Exercise classes were changed to problem-solving sessions by students in groups of 4, with the Teaching Assistant clarifying doubts and helping the groups, instead of the former presentation of solved exercises by the Teaching Assistant.

The two books Integrais Múltiplos and Integrais em Variedades e Aplicações by Luis T. Magalhães were published in 1993 by Texto Editora, after several versions in the form of lecture notes, and the initial versions of the lecture notes Métodos de Resolução de Equações Diferenciais e Análise de Fourier com Aplicações by Luis T. Magalhães were made available to students.

The new orientation of these courses had consequences for engineering research by the generation that attended them, facilitating the use of the powerful mathematical tools of today, based on Lebesgue integration and the analysis of nonlinear systems.

The best students (>17/20 in written exams) were required to take an oral exam to decide the final grade from 17/20 to 20/20. This exam generally lasted a little over 1 hour and was not aimed at assessing comprehension of the material taught, but rather what students could do with what they had learned when confronted with problems new to them. These oral exams, introduced for the first time ever in IST courses, proved to be a very effective to arise the interest of the best students in Mathematics; many of the future Professors in the IST Department of Mathematics took these oral exams enthusiastically.