Do you use a lot of Calculus III Multivariable Calc (Lagrange multipliers, level curves, 3D spaces, partial derivatives, polar coordinates) in a mathematic field?

Answer 1

That is a tricky answer because it all depends on where you go into mathematics as it is such a broad field. Calculus 3 subjects are mostly used as an intro to differential equations so if you are going into an engineering firm then yes you do use a lot. The only other area I know of calculus 3 being used a LOT is in mathematical research and theoretical physics where you use the concepts of the course but translate them to higher dimensional analysis. To top off the question, calculus is the beginning foundation of mathematical courses and is crucial in some way, shape, or form in every mathematical problem that one attempts to solve.