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Q: How are calculus and electrical engineering related?

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Vector calculus is applied in electrical engineering especially with the use of electromagnetics. It is also applied in fluid dynamics, as well as statics.

"Electrical Engineering"

Simply, To study related with electricity and its equipments, system etc.. called Electrical Engineering.

Electrical Engineers study and use Electrical Engineering, which is the theory and practice of all things related to the practical use of electrical energy. A closely related topic is Electronics Engineering.

All areas of engineering are heavy in math. For a typical BSEE (Electrical Enginerring) degree, you are required to take three semesters of Calculus and one semester of Differential Equations.

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The majors that require calculus are all mathematics, science, and engineering majors. These include (but are not limited to) mathematics, mathematics education, science education, biology, chemistry, physics, civil engineering, chemical engineering, biological engineering, electrical engineering, biochemistry, pharmeceuticals, and computer science. So about 99% of students in those majors and related majors will take calculus their freshman year (typically the second semester). I say 99% because calculus is a prerequisite for all other courses in those majors (so it must be taken very early), but there is a very small possibility (I'd say 1% chance) that students can take calculus their sophomore year instead.

in which field vector calculus is applied deeply

CALCULUS

For Literally Everything.

Most complex engineering problems cannot be solved without calculus. Force related problems are a great example - how else would you calculate the force exerted on a particle a specific distance from an electrically charged wire?

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