Not sure about the forum, sorry.
Are series expands featured prominently in vector calculus?
Courses vary depending on the school. Infinite series is not covered for most, if not all, "Calc III' courses I have seen (this is usually left for courses in Real Analysis). If you are covering multiple, line, and surface integrals in this class then you should need to know appropriate techniques (integration by parts, trig substitution, etc). Polar coordinates are used frequently to simplify integration.
All of it. Calc III is Calc I and Calc II except in the n-th dimension, integration and differentiation in the n dimensions, calc i and ii are only in the 1st dimension. Vector calculus is basically the same... Calc I and Calc II integration and differentiation. but this time it's in the n-th dimension AND don't just have a magnitude, but also have direction in n-dimensional euclidean vector space. So as you progress in calculus it is the same concept except more variables, and vectors which complicates things alot more than it sounds.
also infinite series are used more for partial differential equations to obtain solutions to complicated equations whose solution isn't compromised entirely of elementary functions and you're introduced to them in calc II
How many "Calc II' courses have you "seen"? Many courses do one variable series in calc 2 and multiple variable series. Some courses do series in only in one term. Some couses are two or four terms instead of three and are adjusted accordingly. Real analysis is for things like banach spaces, spectral theory, and abstract measure and integration, it would be quite sad if time was wasted introducing series; especially since many students would be third year and would have needed series sooner, like freshman physics.
sorry, my question was horribly put.
i want to study electromagnetism, but I only have calc I (i'm taking calc II in my high school, but we're pretty slow) and I heard that calc III is recommended for electricity and magnetism. my question is, how can I most efficiently study just the math I need while deferring other topics not directly dealt with in E&M for coursework?
Study it out of a 'Physics for scientists and engineers' textbook like Serway or something. They will leave out the heavy calculus stuff but keep the things needed to get a very good grasp on E&M. I self studied out of Serway to learn E&M and watched the ocw mit videos on physics by Walter Lewin. If you do this combo you will be in really good shape. Later on you could read a book like Griffiths to get a more 'mathy' understanding once you have the needed Calc 3 experience.
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