Test Paper - Applied Maths - Mumbai University - Chemical Engineering -3rd Semester, Study notes of Mathematics

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VUE any 1OUr QUESTIONS OUT OF remaining Six questions. Non-programmable calculator is allowed. =< Find L [ t cost (wt ~ a) ] where w and a are constant. 5 z-1 Under the transformation W = ead ST. the map of the straight line x = y is a circle and 5 find it's centre and radius. _ PT. ly (x) = [= coshx 5 Using Adam’s predictor corrector methad find y(0-4) given 2% = xy + y?-with y(0) = 1 5 y(0-1) = 1-1169, y(0-2) = 1.2774, y(0-3) = 1-5041. Express J,(x) in terms of J, (x) and J) (x). « HL[tsinat}] = 288 then Evaluate ‘ 6 (s? +a?) (i) Liat cosat + Sin at} (ji) _L(2 cosat - at sin at] d 2 Solve : a + y+ xy? =0 with y(0) = 1 over [ 0, 0-2] ( take h = 0-1) by Runge Kutta B Method of 4th order [correct to 4-decimal places } Using Laplace transform solve : 6 dy 4% 4— = i = Ve = a + a 7 8Y 1 giveny =0, y'=Oatt=0. Find the orthogonal trajectories of the family of curve represented by equation x8 y—xy3=a, 6 Prove that— 8 . 30 1 , @ 4 0)-(2 1) 4, 69-2 4,00 x x d we 1 at {ii) a sh (Vk) =5 x Jn (Vx). > : d Using modified Euler's method find y(0-2) and y(0-4) given = 5 n+Jfy with y(0)=1. 6 : 2+3 Evaluate | -———dz wherecisiz+i-i! = 2. ] J z? 42745 8 = “ 3s Find gut 8 j (2s+1/? (iy [ cot! 2/s? ] [ TURN OVER