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Apart from their intrinsic interest and their relevance to mechanics and physics, differential equations are also studied as an essential tool in differential geometry (see 7.2.3 and 8.6.13, for example). We start by defining the notion of a differential equation and that of a solution, and by reformulating these concepts in terms of vector fields and integral curves. In 1.2.6 we prove the local existence and uniqueness of integral curves. We also discuss the problem of extending an integral curve into a maximal one (section 1.3).
KeywordsVector Field Open Interval Local Flow Integral Curve Local Existence
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