Introduction to Numerical Methods — DU B.Sc. (Prog.) Physical Science courses pertaining to Electronics Previous Year Question Papers

Course : B. Sc (Prog.) Physical Sciences (NEP: UGCF-2022) Instructions to candidates Answer any three of the remaining four questions. Q.1. (a) Find the absolute error and relative error in the quotient u/v, given that u = 34.56 ± 0.002 and v = 8.3 (b) Find the real root of the equation f (x) = x3 (c) Prove any three of the following: (6) Q.2. (a)Find f (1.15) and f (1.85) from the following table: (10) (b) Using Gauss's forward formula, find the value of y at x = 3.75 from the following table: (5) Q. 3. (a) Evaluate the integral 𝐼𝐼 = ∫ 1𝑑𝑑𝑑𝑑 0 by both the trapezoidal and Simpson’s (1/3) rule using 6 sub intervals. (7) (b) Determine the unique cubic polynomial that fits the following data: Hence calculate the first and second derivatives f’ (1.5) and f ‘’(1.5). (8) Q.4. Using Euler’s modified method, solve the following problems: (a) Find y(0.1) and y(0.2) given the differential equation dy/dx = x + y with initial condition y(0) = 1 and step size h = 0.1. (7) (b) Given that 𝑑𝑑𝑑𝑑 , y(0) = 1, Find y(0.2),where h = 0.1 using Runge-kutta fourth Q.5.(a) Find the missing terms in the following: (b) Find the Lagrange interpolating polynomial of degree 2 approximating the function y = ln x defined by the following tables of values. Hence determine the value of ln 2.7.