Introduction to di erential forms
C y x2 + y2 dx+ x x2 + y2 dy= Z 2ˇ 0 d = 2ˇ From the chain rule, we get LEMMA 1.4.3 Z C Fdx+ Gdy= Z C Fdx+ Gdy If Cand C0are equivalent, then Z C Fdx+ Gdy= Z C0 Fdx+ Gdy While we’re at it, we can also de ne a line integral in R3. Suppose that Fdx+ Gdy+ Hdzis a di erential form with C1 coe ents. Let C: [a;b] !R3 be a piecewise C1 parametric ...
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