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EulersMethodHandout

# EulersMethodHandout - Euler's Method Section 2.7 1 Recall...

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1 Euler's Method Section 2.7 ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ 2 Recall As long as the coefficients of our 1 st order differential equation are continuous with continuous partial derivatives with respect to y, it has a unique solution surrounding the initial point. It is usually not possible to find the solution by symbolic manipulations such as elementary integration. So far we have just studied the exceptions to the rule. Namely, those equations that are linear, separable, exact, or those that can be transformed into one of these types. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ 3 What do we do with the problem children? Since the vast majority of 1 st order differential equations cannot be solved using the methods we have learned so far, we have to have some way of dealing with them. On the next two slides you will see our choices. ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________

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4 Choice 1: Direction Fields We could have a computer algebra system draw a direction field for us, which we could use to visualize the behavior of solutions.
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EulersMethodHandout - Euler's Method Section 2.7 1 Recall...

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