Numerical Analysis

Daffodil International University Faculty of Science & Information Technology Department of Software Engineering Final Examination, Summer 2026 Course Code: SE341; Course Title: Numerical Analysis Sections & Teachers: A, B, C, D (RT), E(TR) Time: 2:00 Hrs Marks: 40 Answer ALL Questions [The figures in the right margin indicate the full marks and corresponding course outcomes. All portions of each question must be answered sequentially.] 1. a) Demonstrate the concept of nonlinear equations and examine the methods used to find the root of nonlinear equation [Marks-3] CLO-3 Level-3 b) Calculate the root of the equation f(x) = x^3+x^2+2x-5 = 0 using the Secant Method correct to four decimal places, starting with initial guesses x0 = 1 and x1 = 2. Perform the necessary iterations of the method until the root is approximated and show your step-by-step calculations. [Marks-5] c) Compute the root of the equation f(x) = x^4-5x^2-3x-5=0 using the Newton Raphson Method with 4 decimal points allowed. [Marks-5] d) Express the concept of numerical differentiation and approaches to solve it. [Marks-5] e) Derive the first derivative of the function f(x)=2e^(2x) + x^3 at x=2, at decreasing values of h from 0.4 to 0.2, with a step size of 0.05 using backward differentiation. Round the value to 4 decimal places. [Marks-5] f) Illustrate the idea of gauss elimination, merits and demerits of gauss elimination. Express the difference between gauss elimination and gauss elimination with partial pivoting. [Marks-7] 2. a) Determine the value of x, y and z of the following equations using LU Decomposition. [Marks-10] CLO-4 Level-5 x+y+z=6 2x+3y+z=9 x+4y+2z=17