ae-ac-at 51_engg maths 1
DESCRIPTION
Some Solved Engineering Mathematics ProblemTRANSCRIPT
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AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013
IETE 1
Q.2 a. If Z is a homogeneous function of degree n in x and y, show that
( )z 1nny
zyyxzxy2
xzx 2
22
2
2
22 =
+
+
Answer: Page Number 221 of Text Book 1 b. Use method of differentiation under integral sign to show that
( ) 0a,a1log2
dx)x1(x
axtan
02
1+
=
+
Answer:
Q.3 a. Change the order of integration and then evaluate dy dxay2
a4y
a4
0 2
Answer: Page Number 298-299 of Text Book 1 b. Find the volume bounded by the xy-plane, the cylinder 1yx 22 =+ and
the plane x+y+z = 3. Answer:
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AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013
IETE 2
Q.4 a. Find the eigen values and eigen vectors of the matrix
312132
226
Answer:
b. Determine the rank of the following matrices:
(i)
562241321
(ii)
0211201311011310
Answer: Page Number 40 of Text Book 1
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AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013
IETE 3
Q.5 a. Use Regula-Falsi method to compute real root of 2xex = correct to three decimal places.
Answer:
b. Find by Runge-Kutta method of order four, an approximate value of y at
x = 0.2 for the equation ( ) 10y,xyxy
dxdy
=+
= . Take h = 0.2.
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AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013
IETE 4
Answer:
Q.6a. Solve the differential equation ( ) ye21dxdy1x =++
Answer:
b. Find the orthogonal trajectories of family of curves 32 xay = Answer:
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AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013
IETE 5
Q.7 a. Solve the differential equation Sinxxey25dxdy6
dxyd x22
2++=+
b. Solve the equation 222
xxlog12
dxdy
x1
dxyd
=+
Answer:
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AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013
IETE 6
Q.8 a. Obtain the series solution of ( ) 0y2dxdyx2
dxydx1 2
22 =+
Answer:
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AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013
IETE 7
b. Show that ( )nm
n mn,m
+=
Answer: Page Number 854 of Text Book 1 Q.9 a. State and prove Rodrigues formula. Answer:
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AE51/AC51/AT51 ENGINEERING MATHEMATICS-I DEC 2013
IETE 8
b. Prove that ( ) ( ) ( )nJxn2nJnJ n1n1n =+ +
Answer:
TEXT BOOKS
1. Higher Engineering Mathematics, Dr. B.S.Grewal, 40th edition 2007, Khanna publishers, Delhi. 2. Text book of Engineering Mathematics, N.P. Bali and Manish Goyal, 7th Edition 2007, Laxmi Publication (P) Ltd.