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Speaking as someone who is in the engineering field i can tell you that calculus serves no purpose at all for me. Everything is just done with a calculator or a computer so it's all just a bunch of hogwash they put you through for Engineering school that you will never use in the real world unless you are to become a program writer or work in physics.

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Q: Why is calculus so useful in science and engineering?
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What percentage of college freshman take calculus?

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.


Why vector calculus are used in mechanical engineering?

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.


Do you suck at physics and engineering if you are good at math but bad at computer science?

I don't think so! Long before there were computers (and computer science), there were brilliant physics and engineering students and they obviously were good at math.


How are equations used in real life?

If you work in engineering and science, you'll need equations all the time in your "real life" (i.e., at work), to solve all sorts of problems. Apart from that, most people don't use equations much - not so much because they can't be useful, but because "regular" people usually don't like to bother themselves with remembering algebra.


Which is harder calculus 1 or differential and integral calculus?

Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.