Download A Textbook of Engineering Mathematics-I, 2nd Edition by H.S. Gangwar, Dr. Prabhakar Gupta PDF
By H.S. Gangwar, Dr. Prabhakar Gupta
Written for the scholars of BTech I 12 months of UP Technical collage, Lucknow and different states, this ebook discusses intimately the ideas and strategies in Engineering arithmetic.
Read or Download A Textbook of Engineering Mathematics-I, 2nd Edition PDF
Similar textbook books
Humans have to comprehend advertising from the viewpoint of customers and electorate. somebody is often attempting to promote us anything, so we have to realize the equipment they use. after they are looking for jobs, humans need to marketplace themselves. Many will begin their careers inside a revenues strength, in retailing, in ads, in learn or in a single of the numerous different advertising parts.
Written at an intermediate point in a manner that's effortless to appreciate, basics and purposes of Ultrasonic Waves, moment version offers an up to date exposition of ultrasonics and a few of its major purposes. Designed in particular for rookies to the sphere, this totally up to date moment variation emphasizes underlying actual thoughts over arithmetic.
Realizing irregular habit, eleventh version bargains balanced and transparent insurance of psychopathology theories, examine, and medical implications. absolutely up to date to mirror DSM-5 and the latest clinical, mental, multicultural and psychiatric examine, the publication introduces and integrates the Multipath version of psychological issues to provide an explanation for how 4 crucial factors-biological, mental, social, and sociocultural-interact to reason psychological issues.
Completely revised and up to date to include Microsoft® visible Studio® 2010, Computing with C# and the . internet Framework, moment version rigorously introduces object-oriented and event-driven programming with various examples, so scholars can take hold of those tough innovations after which observe them.
Additional info for A Textbook of Engineering Mathematics-I, 2nd Edition
N = 5 By Euler’s theorem, we get x ∂u ∂u + y ∂y = 5u. Proved. ∂x Next, we know that (from Corollary 1, on page 36) or x2 ∂ 2u ∂ 2u ∂ 2u 2 + 2xy +y ∂y2 = n (n – 1) u = 5 (5 – 1) u ∂x∂y ∂x2 x2 ∂ 2u ∂ 2u ∂ 2u 2 + 2xy + y = 20 u. Hence proved. ∂x∂y ∂y2 ∂x2 45 DIFFERENTIAL CALCULUS-I FG y IJ H xK Example 12. If u = x f1 x2 + f2 FG y IJ , prove that H xK 2 ∂ 2u ∂ 2u 2 ∂ u = 0. + 2 xy + y ∂x∂y ∂x 2 ∂y 2 u1 = Sol. Let FG y IJ H xK x f1 and u2 = x0f2 FG y IJ , then u = u H xK 1 + u2 Since u1 is a homogeneous function of degree one.
I), (ii) and (iii), we get ∂u ∂u ∂u + ∂y + ∂x ∂z = e 3 x 2 + y 2 + z 2 – xy − yz − zx x + y + z − 3xyz 3 3 3 j e 3 x 2 + y 2 + z 2 – xy − yz − zx = bx + y + zgex j + y + z − xy − yz − zx 2 2 2 a j f As a 3 + b 3 + c 3 – 3abc = a + b + c ( a 2 + b 2 + c 2 − ab − bc − ca) ∂u ∂u ∂u + + ∂x ∂y ∂z or = 3 . (iv) F ∂ + ∂ + ∂ I u = FG ∂ + ∂ + ∂ IJ FG ∂ + ∂ + ∂ IJ u GH ∂x ∂y ∂z JK H ∂x ∂y ∂z K H ∂x ∂y ∂z K F ∂ ∂ ∂ I F ∂u ∂u ∂u I F ∂ ∂ ∂ I F 3 I = G ∂x + ∂y + ∂z J G ∂x + ∂y + ∂z J = G ∂x + ∂y + ∂z J G x + y + z J , H KH K H KH K L ∂ F 1 I ∂ F 1 I ∂ F 1 IO = 3 M ∂x G x + y + z J + ∂y G x + y + z J + ∂z G x + y + z J P K H K H K PQ MN H L 1 OP 1 1 −9 − − = 3 M− MN bx + y + zg bx + y + zg bx + y + zg PQ = bx + y + zg .
E1 + y j e1 + x + y j e1 + x + y j ∂ ∂x 2 2 2 = Example 10. If 2 2 2 2 2 −1/2 2 2 2 2 2 2 3/2 2 2 3/2 y2 x2 z2 + + = 1, show that a2 + u c2 + u b2 + u FG ∂u IJ + FG ∂u IJ + FG ∂u IJ H ∂x K H ∂y K H ∂z K 2 2 2 2 2 = 2 2 2 =2 F x ∂u + y ∂u + z ∂u I . , 2002) Sol. (ii) 2 2 LM 2x O 2y 2z P + + ∑ LMNx / e a + uj OPQ MN e a + uj eb + uj e c + uj PQ 2 2 2 2 ∑ LMNx 2 / e a 2 + uj 2 2 OP Q 2 2 1 2 2 2 , from (i) F x ∂u + y ∂u + z ∂u I GH ∂x ∂y ∂z JK . (iii) Hence proved. Example 11. If xx yy zz = c, show that at x = y = z, ∂ 2z = – (x log ex)–1.