Advanced calculus; . DIFFERENTIAL CALCULUS. reducible to the circuit AC A. It must not be forgotten that although the lines ABand BA coincide, the values of the function are not necessarily the same on ABas on BA but differ by the amount of change introduced in/ on passing around the irreducible circuit BCB. One of thecases which arises most frequently in practice is that inwhich the successive branches of fix, y) differ by a constantamount as in the case z = tan-1 (y/x) where 2 tt is the differ-ence between successive values of z for the same values of the variables. If now a circuit such as
Advanced calculus; . DIFFERENTIAL CALCULUS. reducible to the circuit AC A. It must not be forgotten that although the lines ABand BA coincide, the values of the function are not necessarily the same on ABas on BA but differ by the amount of change introduced in/ on passing around the irreducible circuit BCB. One of thecases which arises most frequently in practice is that inwhich the successive branches of fix, y) differ by a constantamount as in the case z = tan-1 (y/x) where 2 tt is the differ-ence between successive values of z for the same values of the variables. If now a circuit such as A BCB A be considered, where it is imaginedthat the origin lies within BCB, it is clear that the values of z along AB andalong BA differ by 2 ir, and whatever z gains on passing from A toB will be lost on passing from B to A, although the values throughwhich z changes will be different in the two cases by the amount2 7r. Hence the circuit ABCBA gives the same changes for z asthe simpler circuit BCB. In other words the result is obtainedtha
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