By V. I. Smirnov and A. J. Lohwater (Auth.)

ISBN-10: 0080102077

ISBN-13: 9780080102078

**Read or Download A Course of Higher Mathematics. Volume II PDF**

**Similar calculus books**

**Download e-book for iPad: A First Course in Integral Equations by Abdul-Majid Wazwaz**

"The moment variation of this publication is a well-explained preliminary direction in necessary equations and it really is supplied with various examples and workouts. This booklet could be important for researchers, undergraduate and graduate scholars in utilized arithmetic, technology and engineering. " Zentralblatt Math This moment version integrates the newly constructed equipment with classical thoughts to provide either smooth and robust ways for fixing fundamental equations.

**Download e-book for iPad: Calculus for The Life Sciences by Sebastian J. Schreiber**

Initial model: Authored via special researchers/teachers and an reviews, profitable textbook writer, Calculus for all times Sciences is a beneficial source for all times technology classes. As life-science departments elevate the mathematics specifications for his or her majors, there's a want for better mathematic wisdom between scholars.

**Additional resources for A Course of Higher Mathematics. Volume II**

**Sample text**

E. the set of two straight lines y = ± a , which we obtained pre viously. 2. The general solution of Clairaut's equation y = xy' + q>(y') is y = xC +

Y**""1*, be excluded from the equation, which has t h e form: &(xyyW,y(k+1\.. ,yW) = 0. ,4n-k>) thus lowering the order = O. ,Cn-k)f which we discussed in [15]. 2. e. ,v(n))==o, we take y as independent variable and introduce the new function V =

_<.. _ , + ja. x 44 [14 ORDINARY DIFFERENTIAL EQUATIONS Let s be the length of arc of the integral curve, and let a be the angle that the positive direction of the tangent forms with the positive direction of OX. We have [I, 70]: dy dx a n a ; ds cos a, dx and we obtain, on differentiating w i t h ]respect to x: 1 d22/ — dx2 cos2 a 1 da __ da? cos 2 a da ds ds dx _ 1 cos 3 a but da/ds is the curvature of the curve, as we know from [I, 71] da 1 ~ds~ = R ' da ~di~ (13) and the previous equation gives us: 1 cos 3 a R ~ &2y dx2 (14) We take R positive here, if a increases with increasing s, and negative if a decreases with increasing s.

### A Course of Higher Mathematics. Volume II by V. I. Smirnov and A. J. Lohwater (Auth.)

by Richard

4.3