Applied Math Foundational Books I have a BA in mathematics from a pretty good school, where I effectively exhausted the mathematics sequence.  The sequence mostly focused on pure math (including measure theoretic real analysis and some functional analysis).  I am now interested in learning about financial mathematics, at an intermediate to advanced level.
I have studied probability to what I would call an "intermediate" level (using Feller, Ross's "Introduction to Probability Models", Gut's "An Intermediate Course in Probability", and I have begun learning probability in a measure-theoretic context.  I probably have some gaps in my knowledge here, for example, with branching, recurring processes, and queues, and ....
I am, however, concerned that this is not enough of a foundation in applied mathematics.  For example, I have had very little exposure to differential equations (and I couldn't solve one to save my life).  I have seen references to stochastic differential equations, so obviously, I should learn about the deterministic kind first.
Can you suggest a list of applied mathematics books that would serve as a foundation for an advanced course in applied mathematics?  What I mean is, I suspect I will have to fill in the gaps in my knowledge.  What books would you suggest as references/introductions to the field?

I recommend Gilbert Strang's books: 1) Introduction to Applied Math; 2) Computational Science and Engineering.
