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- Interactive introduction to first-order ordinary differential and its applicationsPublication . Coelho, Celestino; Marreiros, Rui; Conceição, Ana C.Differential equations constitute a large and very important branch of modern mathematics. From the early days of the calculus this subject has been an area of great theoretical research and practical applications in several branches of science. Despite this importance, the largest part of the students reveals strong difficulties to understand the theory of differential equations and its applications. As a consequence of what was mentioned above we decided to create a new educational tool that accomplishes some of those goals, describing how this dynamic device can be used in the classroom when teaching the first approach of the first- order Ordinary Differential Equations (ODEs).
- Symbolic computation applied to the study of the kernel of a singular integral operator with non-carleman shift and conjugationPublication . Conceição, Ana C.; Marreiros, Rui; Pereira, José C.On the Hilbert space the singular integral operator with non-Carleman shift and conjugation is considered, where are the Cauchy projectors, , , , are continuous functions on the unit circle , U is the shift operator and C is the operator of complex conjugation. We show how the symbolic computation capabilities of the computer algebra system Mathematica can be used to explore the dimension of the kernel of the operator K. The analytical algorithm [ADimKer-NonCarleman] is presented; several nontrivial examples are given.