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Applied Mathematical Methods by Bhaskar Dasgupta

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31

Existence and Uniqueness Theory

In the previous two chapters, we studied numerical methods to solve ordinary differential equations and their systems. In the following chapters, we go into a thorough analytical treatment of the same. In between, the present chapter forms a bridge, by exploring fundamental questions of existence and uniqueness of solutions, that are relevant in both the segments of analysis.

Well-Posedness of Initial Value Problems

The unprecedented success of Newtonian mechanics and other contemporary developments in the explanation of nature (in science) and its conquest (in technology) in the 18th and 19th centuries led to the optimism and euphoria that complete knowledge of the universe may be around the corner. If you ...

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