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First Order ODEs: Mathematica and Symbolic-Numerical Methods

Ciro D'Apice
Organization: Universita degli Studi di Salerno
Department: DIIMA - Dipartimento diIngegneria dell'Informazione e Matematica Applicata
Giuliano Gargiulo
Manzo Rosanna
Organization: University of Salerno
Department: Department of Information Engineering and Applied Mathematics
Journal / Anthology

Computational Science - ICCS 2004
Year: 2004
Volume: 3039
Page range: 351-357

The use of information technology in addition to traditional lectures affords a means to develop student intuition and curiosity, reaching in the same time a deep knowledge of the subject of study. The aim of this work is to show the didactic use of a Computer Algebra System to illustrate and compare different symbolic-numerical methods for solving first order ordinary differential equations (ODEs). In particular, we apply, relate and compare the built-in functions of Mathematica, the method of integration by series, the Picard process and the linearization method in solving some first order ODEs. This approach allows students not only to master the basic methods for solving ODEs, but also to be naturally led to theoretical deepening of such areas as power series, stability and convergence theory, elements of functional analysis or the local-global relationship via linearization.

*Mathematics > Calculus and Analysis > Differential Equations