a the mobius strip and stokes theorem 1 stokes theorem let us recall stokes theorem theorem 1 1 let m be an oriented surface in r3 with boundary given by ...
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...A the mobius strip and stokes theorem let us recall m be an oriented surface in r with boundary given by closed curve orientation induced from that of right hand rule f x y z vector eld then zz nds i dr words ux curl through direction n is equal to circulation around associated now describe maobius try use on it obtained taking rectangular paper gluing two sides together after performing twist s more precise first imagine constructing revolution plane rotating about axis our will straight line segment l for some positive constants this case we just get cylinder as figure however suppose rotates also counterclockwise its centre at half rate so returns starting point upside down refer note assume ensure resulting has no self intersections can write parametrization using rcos v rsin obtain t tsin cos sin tcos shown dierent viewpoints front back views identify since turned time comes if follow top come bottom angle hence parametrized lsin lcos you should check equivalent trig identities bo...