Nonlinear dynamics and chaos by Strogatz.

He really takes the time to explain concepts clearly and unlike any other math book I've read, he proves certain ideas graphically and considers it good enough, without having to write out formal and stuffy sounding proofs

I'm also currently going through Applied Partial Differential Equations by Haberman. He explains the heat and wave equation from scratch and really makes a great effort to build up the complexity instead of just dumping it all in your lap.