Define significant figure, precision and error propagation.
[3 marks]Discuss about the pitfalls of Gauss elimination method and techniques for improvement.
[4 marks]Fit a second-degree polynomial y = a +bx+cx2 using least squares method to the following data: x 1 2 3 y 1.7 1.8 2.3 3.2
[4 marks]Describe intermediate value properties.
[3 marks]Suggest a method to plot the variables y and x given in the following equation, so that on curve fitting the data will fall on equation of a straight line. 𝛼x y = 1+x(𝛼−1)
[4 marks]Find root of the equation x3 − 2x −5 = 0 using secant method correct up to three decimal places.
[7 marks]Find a real root of the equation x3 − 9x +1 = 0 correct up to three decimal places in the interval [2, 3] by the regula falsi method.
[7 marks]Derive formula for Trapezoidal rule for numerical integration.
[3 marks]Evaluate the sum S = 3 + 5 + 7 04 to 4 significant digits and calculate its absolute and relative error.
[ marks]Derive the equation for Newton’s forward difference polynomial.
[7 marks]Explain about the system of ill-conditioned equations using appropriate example.
[3 marks]Derive formula for Simpson’s 1/3 rule of numerical integration.
[4 marks]Fit an exponential curve y = aebx to the following data using the principle of least squares: x 0 2 4 6 y 150 63 28 12 5.6
[8 marks]Discuss about convergence criteria for the Gauss-Siedel method.
[3 marks]Explain the algorithm for Gauss-Jordan method.
[4 marks]Derive the formula of Newton - Raphson method & also prove that Newton - Raphson method is quadratically convergent.
[7 marks]Discuss bracketing methods and open methods.
[3 marks]Using Newton’s backward difference formula, construct an interpolating polynomial of degree 3 for the data: f(−0.75) = −0.0718125, f(−0.5) = −0.02475, f(−0.25) = 0.3349375, f(0) = 1.10100.
[4 marks]Evaluate ∫ 0.6 e−x2 dx using the trapezoidal rule and Simpson’s 1/3 rule, taking h07 = 0.1.
[ marks]Establish Newton’s backward interpolation formula.
[3 marks]Explain Milne’s predictor-corrector method.
[4 marks]Use the Taylor series method to calculate y (0.2), given that dy/dx = 2y + 3ex , y(0) = 1. Taking h = 0.2.
[7 marks]Explain the principle of least squares.
[3 marks]Explain in brief about ordinary differential equation - boundary value problems.
[4 marks]Applying Euler’s method to solve the initial value problem, dy y = x − where y(0) = 1 over [0, 3] using step size 0.5. dx
[2 marks]