It is a tool for an engineer. I am a mechanical engineer, and you MUST know your calculus to be able to get through it, or through physics with calc. Good luck!
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Because calculus is lots of fun! Also because it is useful in science and engineering.
Vector calculus is applied in electrical engineering especially with the use of electromagnetics. It is also applied in fluid dynamics, as well as statics.
Mechanical engineering usually deals with forces and their effects on materials. Forces are vectors and so, to study their effects you need to use vector calculus.
These are the general math courses in an undergraduate program of Mechanical Engineering. Actually, these are also the math courses required in ANY undergraduate Engineering curriculum: Algebra Trigonometry Analytic Geometry Differential Calculus Integral Calculus Mutivariable Calculus Differential Equations