Here are 3 applied math gems:

1) Nonlinear Dynamics and Chaos by Strogatz completely changed my relationship with applied math. I'd studied diffyqs and PDEs earlier but that was under duress and hasn't been particularly useful. Traditional books don't tell you that analysis solves only a tiny subset of important real-world problems, and for me, were just another boring dose of plug-and-chug calculus.

Strogatz immediately motivates the subject and uses analysis as a jumping-off point (with some pretty hard analytical HW problems!), but he quickly pivots to numerical methods with a very strong intuitive and visual/geometric approach. Years later, I'm using this knowledge surprisingly often.

https://www.amazon.com/Nonlinear-Dynamics-Student-Solutions-...

2) Linear Programming by Chvatal was the book that made LP duality really click for me. Prior to reading Chvatal I mechanically understood duality but with no intuition. Chvatal explains duality from a bounding perspective, and even better, motivates duality through simple dimensional analysis, just like in physics! (The Strogatz book above also motivates dimensional analysis and dimensionless groups, which has been very useful to me over the long term.)

https://www.amazon.com/Linear-Programming-University-Vasek-C...

3) Statistical Methods: The Geometric Approach, Saville and Wood was my bridge from meaningless opaque algebraic and calculus stats to a solid understanding. The book builds everything on vector space projections at the level of undergrad linear algebra. Even a simple mean of 3 numbers now sparkles with intuition and insight.

https://www.amazon.com/Statistical-Methods-Geometric-Approac...

They also published a short paper that conveys the key ideas https://www.jstor.org/stable/2684537

I believe he's referring to Strogatz's introductory textbook "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering".

Amazon link: http://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-...