I studied a very similar curriculum over ten years ago during my Physics undergrad. While it’s not strictly “useful” in a day to day sense, nor do I remember much of the details of these courses or methods, I can tell you that studying applied math has served me very well during my career as an actuary.
Studying applied math gives you the skills of being able to approach problems in a logical, analytical, and above all PERSISTENT way (because let me tell you will you ever have some late nights banging your head on the desk trying to wrap your brain around these problems). These skills are crucial in any field where you need to create mathematical representations of a system - or break apart and understand someone else’a models.
Also - partial differential equations are just cool! They are like a mathematical rubick’s cube. Solving them will legitimately make you smarter.