I am about to attempt a qualification exam in applied math in August and in need of a good reference or two. Before you vote to close down my question, I am aware of this answer, where a giant list of PhD qual exam materials are compiled. But I am not concerned about finding actual exam problems, I need to review and master the basics in related topics, spending more time in reading than solving. I did went through a large number of exercises in PDE's and while I can solve them without a context, I still feel like I am not getting it completely.
I took the $2$ semester sequence of Applied Math classes our department offers and we used Peter Olver's Introduction to Partial Differential Equations. We covered most of the stuff up to Chapter $8$ and while I liked the exercises, I need a text that deals with the theory little bit more with more challenging exercises.
Also, I want to learn more advanced Linear Algebra, from which a question or two seems to pop up randomly in the exams. But the classes I took barely even mentioned Linear Algebra and some of optimization problems.
