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ODE/PDE book

Hello guys,
I currently am finishing up my ODE course and will be taking a PDE course in spring. However, both of those courses are only methods to solve problems without thinking too much. Can anyone suggest a good self-contained book for me to learn PDE's rigorously and/or an ODE book to build a solid foundation before jumping into a rigorous PDE book. (Currently I only have a solid background in Real analysis and linear algebra)

Thank you.

Daniel Duffy

C++ author, trainer
rigorous PDE book

That's a big area. There are many ways to learn PDE depending on your goals and the PDE types etc. . A list of topic is here.

There is no single best PDE book in this sense. To reduce the scope one needs to know what kinds of PDE are relevant (to finance?), how to find them and what to do with them 'going forward'. PDE is a yuge area.
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