Higher Mathematics. a Text-Book for Classical And Engineering Colleges

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Prob. 76. The polar equation of a parabola being r — a sec 2 £0, referred to its focus as pole, express s in terms of 6.
Prob. 77. Find the intrinsic equation of the curved/a = cosh x/a r and of the curve y/a = log sec x/a.
Prob. 78. Investigate a formula of reduction for^y cosh"^^r; also integrate by parts cosh" 1 x dx, tanh" 1 .* dx, (sinh" 1 *) 2 ^; and show that the ordinary methods of reduction for / cos m xsin B *^ic can be applied to / cosh" 1 x sinh" x dx.
Art. 27. Functions of Complex
...Numbers.
As vector quantities are of frequent occurence in Mathe- matical Physics ; and as the numerical measure of a vector in terms of a standard vector is a complex number of the form x-\-iy, in which x, y are real, and i stands for V— 1; it becomes necessary in treating of any class of functional oper- ations to consider the meaning of these operations when per- formed on such generalized numbers.* The geometrical defini- tions of cosh 7^, sinh u, given in Art. 7, being then no longer applicable, it is necessary to assign to each of the symbols *The use of vectors in electrical theory is shown in Bedell and Crehore's Alternating Currents, Chaps, xiv-xx (first published in 1892).


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