Engineering Mathematics — DU B. Sc. (Hons) Electronics Previous Year Question Papers

ANDC Library, 7/1224. (c) Use Cauchy's nth root test for convergence of series (d) Find the value of m if u = 2x2 - my? + 3x is harmonic. (e) Reduce the following matrix to unit matrix. (3) (f) Explain the difference between symmetric and skew symmetric matrices using example. Determine whether the following functions y, and У½ are linearly dependent or independent : y, = In(x), y2 = In(x"), where n is a non-negative integer. (3) 2. (a) Determine the solution of the following differential equation Also specify the type of the differential equation (linear or non-linear, homogenous or non-homogenous) (6) (b) Check whether the given differential equation is exact or non-exact and then determine the solution (c) Solve the following differential equation (6) 3. (a) Determine the solution for the given set of simultaneous linear equations using Gauss-Jordan (b) Find the Eigen Values and Eigen vectors of the following matrix A (6) (c) Determine the solution for the given set of simultaneous linear equations using Gauss-Seidel (a) Test for convergence of Series given below : (b) Test the series Zü=1 Untunt for convergence. (C) State the D'Alembert's Ratio test and use it to test the convergence of (2n)! (6) 5. (a) Examine whether the function analytic or not. (6) (b) Determine the analytic function w = u + iv if u = ex (x cos 2y - y sin 2y). (6) (c) Use Cauchy's integral formula to evaluate Jc (2472) dz where C is the cirete lel =t 6. (a) Locale and classify the ordinary points (OP). regular singular point (RSP) and irregular singular point (ISP) of the following differential equation (b) State and prove Taylor's series Theorem and evaluate the Taylor Series for f(x) = cosx for x=0. (6) 1. (a) Prove that every differentiable function is continuous. (6) (b) Reduce the following matrix to upper triangular form. (6) (c) Determine the solution for the given set of simultaneous linear equations using LU Decomposition