The words contained in this file might help you see if this file matches what you are looking for:

...Lecture general theory of first order ordinary dierential equations there are several basic questions one can ask about a equation the existence problem does solution exist howcan tell that uniqueness if howunique is it other solutions way to parameterize all given howdoesoneactuallysolve or constructasolutionof agivendierential in preceding lectures we have addressed only third shown how construct approximate but not discussed whether possible nd when our method for constructing might fail i now wish present more thorough discussion these problems and rst linear answered by following fundamental theorem which shall prove suppose f x y continuous functions on an open rectangle r...