By Rajesh Pandey
Quantity i of this sequence serves as a textbook for semester i of thesubject engineering arithmetic. compatible figures and diagrams havebeen used to make sure a simple realizing of the innovations concerned. to stress software of the subjects mentioned, compatible examplesare included in the course of the e-book. Solved examples, within the bookinclude suggestions of questions from past u. P. T. U. Examinations. past years query papers were incorporated as to exposestudents to the trend and sort of questions they could face in anexamination. This publication is particularly necessary for measure, honours andpostgraduate scholars of all indian universities and for ias, pcsand different aggressive examinations. concerning the writer dr. Rajesh pandey he has greater than fourteen years experiencein instructing scholars of undergraduate, postgraduate and engineeringlevel. He bought his b. Sc and m. Sc measure in 1991 and 1993respectively from gorakhpur collage and phd in yr 2003 andparticipated in quite a few seminars & meetings of nationwide andinternational point. For graduate & postgraduate, the authorhas additionally written books on strengthen calculus, vectors, numericalanalysis, summary algebra, mechanics, fluid mechanics and so on. almost immediately, he's operating as an assistant professor/reader inmathematics, sherwood university of engineering, learn andtechnology, lucknow. desk of contents uncomplicated effects and ideas successive differentiation and leibnitz's theorem partial differentiation curve tracing enlargement of functionality jacobian approximation of blunders extrema of services of numerous variables lagranges approach to undetermind multipliers matrices a number of integers beta and gamma services vector differential calculus vector imperative calculus exam papers of uptu from 2001-2009
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Additional resources for A Text Book of Engineering Mathematics. Volume I
1) 2Yl y2 + (2X)Yl2 = m 2. 1)Yn+2 + n (2X)Yn+2+ (2) yn] + [xy n+1 + n(1)YnJ - m 2 yn =0 ~ or (x2-1) yn+2 + (2n+1) Xyn+l + (n2 - m2) yn =0 Hence Proved Example 10: If yl/m +y -l/m = 2x Prove that (X2 -1) yn+2 + (2n +1)XYn+l+(n2 - m2) =0 Solution: Given y l/m + _1_ = 2x yl/nt or y2/m - 2xyl/m + 1 =0 2x±~(4x2 -4) or y 11m = ---"-'------'2 or yl/m = X±~(X2 -1) ory= [x±~(X2-1)r when y =[ X+~(X2 -1) (i) r ,we have Yl=m[x+~(X2-1)r-l[1+21,,(x2x-1) 1 2 or Yl ~(X2 -1) = my or Y1 2 (X2 -1) = m2y2 wheny =[ X_~(X2 -1) r, (ii) we have Yl=m[x-~(X2_1)JIll_I[1-m[ x _~(X2 -1) = r 2x ~(X2 -1) 1 N=1 or yl ~(X2 -1) = - my or Y12(xL1) = m2y2 (iii) which is the same result as (ii).
U. 2001, 2003) 42 Partial Differentiation 1 1 log x - log y af af 23. Iff(x,y)= -2 +-+ 2 2 ,showthat x~+y:\+2f(x,y)=0 x xy x +y ux uy (PTV 2004) 24. 2003) ~+I+~ 25. 2003) 2 1t(2X + y2 + xzt2 ) 26. 1991) 27. If u = x2 - y2 + sin yz where y = ex and z = log x; find du dx 1 Ans. 2(x - e2x )+ex cos (ex log x) (log x + -). x au au au 28. If u = f(r, s) and r = x+y, s = x-y; show that - + - = 2 ax ay ar r r 02U 29. If x = e cosS, y = e sinS, show that ax 2 au (a u 02U) + ay2 = e- ar2 + OS2 2 2 2r 30.
2005) ~X2 + y2 and x3 +y3 +3axy = 5a2, find the value of dz when x = y =a. dx au au 33. 1997) 32. If z = 43 A Textbook of Engineering Mathematics Volume - I 34. Prove that if z = az 2 a 2z (y + ax) + ",(y - ax) then a 2- - - 2 = 0 for any twice ay2 ax differentiable and "', a is a constant. (LAS. 1f u= f(~ ,I ,~)prove that x au + y au + z au = 0 y z x ax ay az Tick the Correct answer from the choices given below 1. If u = f(y Ix), then au . au au au 0 (1) x--y-=O (11") x-+y-= ax ay ax ay .
A Text Book of Engineering Mathematics. Volume I by Rajesh Pandey