Integrals and Ordinary Differential Equations

  • Jürgen Jost
Part of the Universitext book series (UTX)


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).


Ordinary Differential Equation Step Function Bounded Interval Local Existence Unique Fixed Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jürgen Jost
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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