I am a first year student of applied mathematics. I currently find myself always trying to explain any phenomenon with mathematical models- the few ones (models) that I encountered till now. I always try to fit phenomenas to models like a data scientist does when he fits data to models. Recently I found this book:
Robert B. Banks Growth and Diffusion Phenomena: Mathematical Frameworks and Applications
This book is different from other applied mathematics books in the sense that it focuses on a particular model unlike others that try to model the whole world in a single book. It particularly focuses on growth and diffusion phenomena. Which is , to me , great because this book studies these two models in great detail rather than just stating many models on the surface level. I also found some book that is specific to some single phenomenon like this book on Hysteresis Mathematical Models of Hysteresis and their Applications
Can someone please recommend to me some books like these that describes a certain phenomena or discusses a certain mathematical framework to study in detail and apply some phenomena? Any book that discusses and models in detail some phenomena: could be growth,could be decline, could be (what happens in the limiting case)- type of thing, could be something else, could be anything...
There is a hidden gem I read during my PhD study, and it is co-authored by Lions (founding father of many methods in my field and still serves as my bread and butter).
It is like an encyclopedia of PDE models used in physics and mechanics. However, it is not for beginners, but rather an extremely good reference book for research.