<p>The main reason why schools require engineers and other applied scientists/mathematicians to take the more rigorous foundational math is to prepare them for as many POSSIBLE career options and interests. Some engineers/scientists MAY go into research so it is better to be prepared for that option, whether or not one selects that path. It is better to go from courses that include theory TO applied courses than the other way.</p>
<p>Besides, in the traditional Calc & Analytic Geometry sequences, you will still do applied problems like volume, flow of fluids, speed/velocity/acceleration, vector problems that will be the same of what you see in physics, and area coverage problems.</p>