Abstract
A continuous function g is called a primitive of another function f if the derivative of g exists and coincides with f. A primitive thus is an indefinite integral. We derive the basic rules for the computation of integrals. We use the Banach fixed point theorem to derive the Picard-Lindelöf theorem on the local existence of solutions or integrals of ordinary differential equations (ODEs).
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© 2003 Springer-Verlag Berlin Heidelberg
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Jost, J. (2003). Integrals and Ordinary Differential Equations. In: Postmodern Analysis. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05306-5_7
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DOI: https://doi.org/10.1007/978-3-662-05306-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43873-1
Online ISBN: 978-3-662-05306-5
eBook Packages: Springer Book Archive