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Presentazione disciplinare per l'organizzazione di eventi a basso impatto EBI2012
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# Bwm21403 mathematics iv assignments

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### Bwm21403 mathematics iv assignments

1. 1. BWM21403 Mathematics IV Sem I 2013/2014 Instruction : Do the calculations in 3 decimal places. First Individual assignment: (submit 3rd meeting) 10% Q1. Given graph of f ( x ) = x 3 −10 x +10 beside. (a) Find the least positive root by using bisection method with | b −a |=1 . (b) Find the most positive root of f (x ) by using Newton-Raphson method. Iterate until | f ( xi ) |< ε = 0.005 . y 30 20 10 1 2 3 -3 -2 -1 Second Individual assignment: (submit 4th meeting) 10% Q1. Solve the system of linear equation by using 2 x1 Doolittle method − 5 x2 + + + 2 x2 x2 − 7 x3 + x3 -4 3x1 − 3x1 Q2 Find the approximate value for (a) trapezoidal rule, ∫ x3 4 x = 2 = = 1 1 1 dx and n = 10 subintervals by using x (b) 1/3 Simpson’s rule. 4 0.25 Group assignment : (submit 5th meeting) ( max 4 person in a group) 20% Q1. Solve the system of linear equation by using 2 x1 − 5 x 2 + Gauss Seidel iteration 3x1 − 3x1 Q2 Given f ( x ) = e −x . (a) Complete the following table. x 0 0.25 + + 0.75 2 x2 x2 x3 − 7 x3 + x3 = 2 = = 1 1 1.0 f ( x ) = e −x (b) Hence, find (i) P3 (0.4) by using Lagrange interpolation (ii) Newton divided-difference method. (c) If (0.5, 0.607) is added into the data above, find f (0.4) by using Newton divideddifference method. Q3 Given the first-order initial value problem (IVP) y ′ + 2 y = xe 3 x , with initial condition y (0) = 0 ; 1 3x 1 3x 1 −2 x xe − e + e . Solve by 5 25 25 Euler’s method with step size h = 0.2 for interval 0 ≤ x ≤ 1 . Find its errors. Runge-Kutta method with step size h = 0.2 for interval 0 ≤ x ≤ 0.4 . Find its errors. And given that the exact solution is y ( x) = (a) (b)

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