{"id":166,"date":"2026-01-28T13:53:50","date_gmt":"2026-01-28T13:53:50","guid":{"rendered":"https:\/\/staymind.shop\/?p=166"},"modified":"2026-01-28T13:53:51","modified_gmt":"2026-01-28T13:53:51","slug":"paper-of-numerical-computing-department-of-computer-science-and-software-engineering","status":"publish","type":"post","link":"https:\/\/staymind.shop\/?p=166","title":{"rendered":"Paper Of Numerical Computing Department Of Computer Science and Software Engineering"},"content":{"rendered":"\n<p>Let&#8217;s get this straight:&nbsp;<strong>Numerical Computing<\/strong>&nbsp;is where the perfect, pristine world of mathematics collides with the gritty, finite reality of computers. It&#8217;s not about getting&nbsp;<em>the<\/em>&nbsp;answer; it&#8217;s about getting a&nbsp;<em>good enough<\/em>&nbsp;answer, knowing&nbsp;<em>how good<\/em>&nbsp;it is, and not setting your computer on fire in the process. This past paper is your stress test for doing real, useful math with machines that can&#8217;t even represent the number 0.1 perfectly.<\/p>\n\n\n\n<p>Forget symbolic algebra and neat closed-form solutions. This is the toolbox for simulating galaxies, predicting weather, training AI, and valuing financial derivatives\u2014all problems where &#8220;just solve the equation&#8221; is a fantasy.<\/p>\n\n\n\n<p><strong>What This Paper Actually Calculates: Your Pragmatic Math Intelligence<\/strong><\/p>\n\n\n\n<p><strong>1. The Foundation: Sources of Error (The Real Enemy)<\/strong><br>The first questions attack the core truth:&nbsp;<strong>All numerical answers are wrong. Some are useful.<\/strong>&nbsp;You must diagnose and quantify the error:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rounding Error:<\/strong>\u00a0Inevitable from finite-precision arithmetic (floating-point). You&#8217;ll explain why\u00a0<code>(0.1 + 0.2) != 0.3<\/code>\u00a0and analyze catastrophic cancellation.<\/li>\n\n\n\n<li><strong>Truncation\/Discretization Error:<\/strong>\u00a0From approximating infinite processes (infinite series, infinitesimal steps) with finite ones. The error of cutting off a Taylor series or approximating a derivative.<\/li>\n\n\n\n<li><strong>Stability &amp; Condition Number:<\/strong>\u00a0Does the algorithm magnify small errors? Is the\u00a0<em>problem itself<\/em>\u00a0sensitive to input perturbations? You&#8217;ll calculate condition numbers and identify ill-conditioned systems.<\/li>\n<\/ul>\n\n\n\n<p><strong>2. The Core Toolkit: Solving Problems Computers Can&#8217;t &#8220;Solve&#8221;<\/strong><br>The paper tests your mastery of replacing unsolvable problems with solvable approximations.<\/p>\n\n\n\n<p><strong>A. Equations &amp; Optimization:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Root-Finding:<\/strong>\u00a0<strong>Bisection<\/strong>\u00a0(slow, bulletproof),\u00a0<strong>Newton-Raphson<\/strong>\u00a0(fast, needs a good guess and the derivative). You&#8217;ll perform iterations by hand and analyze convergence.<\/li>\n\n\n\n<li><strong>Systems of Linear Equations:<\/strong>\u00a0<strong>Gaussian Elimination with Partial Pivoting<\/strong>\u00a0(to avoid instability), understanding\u00a0<strong>LU Decomposition<\/strong>. You&#8217;ll solve a small system and discuss computational complexity (<code>O(n\u00b3)<\/code>).<\/li>\n\n\n\n<li><strong>Eigenvalues &amp; Eigenvectors:<\/strong>\u00a0Power method for dominant eigenvectors. Understanding their use in stability analysis, PageRank algorithms, and principal component analysis.<\/li>\n<\/ul>\n\n\n\n<p><strong>B. Approximation &amp; Data:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Interpolation:<\/strong>\u00a0Constructing polynomials (<strong>Lagrange, Newton&#8217;s Divided Difference<\/strong>) that pass exactly through data points. Knowing the perils of high-degree polynomials (Runge&#8217;s phenomenon).<\/li>\n\n\n\n<li><strong>Curve Fitting \/ Regression:<\/strong>\u00a0<strong>Least Squares<\/strong>\u00a0approximation. You&#8217;ll set up and solve the normal equations to fit a line or polynomial to noisy data.<\/li>\n\n\n\n<li><strong>Numerical Differentiation &amp; Integration:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Differentiation:<\/strong>\u00a0Finite-difference formulas (forward, backward, central) and their error terms (<code>O(h)<\/code>\u00a0vs.\u00a0<code>O(h\u00b2)<\/code>).<\/li>\n\n\n\n<li><strong>Integration:<\/strong>\u00a0<strong>Trapezoidal Rule, Simpson&#8217;s Rule<\/strong>\u00a0(higher accuracy). You&#8217;ll apply them and calculate error bounds.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>C. Differential Equations (The Workhorse of Science):<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Ordinary Differential Equations (ODEs):<\/strong>\u00a0<strong>Euler&#8217;s method<\/strong>\u00a0(simple, low accuracy),\u00a0<strong>Runge-Kutta methods<\/strong>\u00a0(especially 4th order \u2013 the workhorse). You&#8217;ll perform step-by-step iterations to approximate a solution.<\/li>\n\n\n\n<li><strong>Partial Differential Equations (PDEs):<\/strong>\u00a0Introduction to discretizing Laplace&#8217;s or the Heat Equation using\u00a0<strong>Finite Difference Methods<\/strong>, leading to a large system of linear equations.<\/li>\n<\/ul>\n\n\n\n<p><strong>3. The Implementation Mindset: Algorithms Over Formulas<\/strong><br>You are tested on turning mathematical ideas into concrete, step-by-step&nbsp;<strong>algorithms<\/strong>. You&#8217;ll write pseudocode for methods like Newton-Raphson or Gaussian elimination, paying attention to loops, stopping criteria (<code>|x\u2099\u208a\u2081 - x\u2099| &lt; tolerance<\/code>), and avoiding division by zero.<\/p>\n\n\n\n<p><strong>4. Analysis: The &#8220;Why&#8221; Behind the Method<\/strong><br>For every technique, you must know:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Cost:<\/strong>\u00a0How many floating-point operations (flops)? Is it\u00a0<code>O(n\u00b2)<\/code>\u00a0or\u00a0<code>O(n\u00b3)<\/code>?<\/li>\n\n\n\n<li><strong>Accuracy:<\/strong>\u00a0What is the order of convergence\/error? (<code>O(h\u00b2)<\/code>\u00a0means halving the step\u00a0<code>h<\/code>\u00a0quarters the error).<\/li>\n\n\n\n<li><strong>Trade-offs:<\/strong>\u00a0Speed vs. stability, memory vs. accuracy.<\/li>\n<\/ul>\n\n\n\n<p><strong>The Paper&#8217;s Real Challenge: Multi-Step Problem Solving<\/strong><br>The hardest questions are&nbsp;<strong>synthesis problems<\/strong>. For example:<br>*&#8221;Given this differential equation modeling a pendulum, derive the finite difference approximation. Using a step size of h=0.1 and the 4th-order Runge-Kutta method, perform two iterations. Then, discuss how you would verify the stability of your numerical solution.&#8221;*<br>This combines modeling, algorithm application, and critical analysis.<\/p>\n\n\n\n<p><strong>How to Conquer This Past Paper:<\/strong><\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Embrace Approximations.<\/strong>\u00a0Let go of the desire for exactness. Your goal is a controllable error bound.<\/li>\n\n\n\n<li><strong>Perform Hand Iterations Fluently.<\/strong>\u00a0Practice carrying out 3-4 steps of a method (Newton, Euler, Gaussian Elimination) neatly and accurately. Exam success depends on this manual execution.<\/li>\n\n\n\n<li><strong>Master Error Terminology.<\/strong>\u00a0Be precise: &#8220;The truncation error is\u00a0<code>O(h\u00b2)<\/code>, but due to rounding error, there is an optimal\u00a0<code>h<\/code>\u00a0below which the total error increases.&#8221;<\/li>\n\n\n\n<li><strong>Connect Methods to Motives.<\/strong>\u00a0Don&#8217;t just memorize steps. Know\u00a0<em>when to use what<\/em>: Need a robust root? Use Bisection. Need a fast root with a good guess? Use Newton. Fitting experimental data? Use Least Squares.<\/li>\n\n\n\n<li><strong>Write Clean, Indexed Pseudocode.<\/strong>\u00a0Use\u00a0<code>k<\/code>\u00a0for iteration counters,\u00a0<code>x_k<\/code>\u00a0for iterates. Clearly state inputs, outputs, and stopping conditions.<\/li>\n<\/ol>\n\n\n\n<p>This past paper is your&nbsp;<strong>certification in practical computation<\/strong>. It proves you have the humility to accept error, the skill to minimize it, and the wisdom to measure it. Passing it means you are equipped to turn the unsolvable problems of science and engineering into actionable, computational results.<\/p>\n\n\n\n<p><strong>Numerical Computing Fall 21 past paper<br><\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"762\" height=\"650\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/ncp.jpg\" alt=\"\" class=\"wp-image-168\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/ncp.jpg 762w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/ncp-300x256.jpg 300w\" sizes=\"auto, (max-width: 762px) 100vw, 762px\" \/><\/figure>\n<\/div>\n\n\n<p><strong>Numerical computing final paper<br><\/strong><\/p>\n\n\n\n<p>1. Solve the following system using Jacobi method (with 4 digu roues arithmetic, at least). Assume the error tolerance as 0.0001.<\/p>\n\n\n\n<p>15x\u2081-2X2-6Xj+0x\u2081 -2x)+12\u00d72-4X3-X4=300<\/p>\n\n\n\n<p>0 -6\u00d71-4\u00d72+19\u00d73-9\u00d74 =0<\/p>\n\n\n\n<p>0x1-X2-9X3+21x\u2081=0<\/p>\n\n\n\n<p>(Marks 10)<\/p>\n\n\n\n<p>2. Obtain the first and second derivative at x-7 using Stirling formula. Where<\/p>\n\n\n\n<p>Xp= 12<\/p>\n\n\n\n<p>X<\/p>\n\n\n\n<p>5<\/p>\n\n\n\n<p>6<\/p>\n\n\n\n<p>7<\/p>\n\n\n\n<p>8<\/p>\n\n\n\n<p>9<\/p>\n\n\n\n<p>10<\/p>\n\n\n\n<p>f(x)<\/p>\n\n\n\n<p>196<\/p>\n\n\n\n<p>394<\/p>\n\n\n\n<p>686<\/p>\n\n\n\n<p>1090<\/p>\n\n\n\n<p>1624<\/p>\n\n\n\n<p>2306<\/p>\n\n\n\n<p>(Marks-10)<\/p>\n\n\n\n<p>x<\/p>\n\n\n\n<p>3. Use the table in Question no. 2 of values by Newton forward differentiation formula. To compute f (0.25), (0.50), (0.75).<\/p>\n\n\n\n<p>2125 (Marks= 15)<\/p>\n\n\n\n<p>4. Use Question no. lequations, to find X1, X2, X3, and x, values using Gauss<\/p>\n\n\n\n<p>Jordan Elimination Method.<\/p>\n\n\n\n<p>(Marks 10)<\/p>\n\n\n\n<p>5. Compute ff(x) dx based on Trapezoidal rule. 0.6<\/p>\n\n\n\n<p>X<\/p>\n\n\n\n<p>0<\/p>\n\n\n\n<p>0.1<\/p>\n\n\n\n<p>0.2<\/p>\n\n\n\n<p>0.3<\/p>\n\n\n\n<p>0.4<\/p>\n\n\n\n<p>0.5<\/p>\n\n\n\n<p>0.6<\/p>\n\n\n\n<p>f(x)<\/p>\n\n\n\n<p>0<\/p>\n\n\n\n<p>0.0998<\/p>\n\n\n\n<p>0.1987 0.2955 0.38994<\/p>\n\n\n\n<p>0.4794<\/p>\n\n\n\n<p>0.5646<\/p>\n\n\n\n<p>(Marks-05)<\/p>\n\n\n\n<p><strong>Numerical Computing\u00a0 Mid term paper<br><\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"394\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-54-1024x394.png\" alt=\"\" class=\"wp-image-169\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-54-1024x394.png 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-54-300x115.png 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-54-768x295.png 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-54.png 1363w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"517\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-55-1024x517.png\" alt=\"\" class=\"wp-image-170\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-55-1024x517.png 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-55-300x151.png 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-55-768x388.png 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-55.png 1254w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"715\" height=\"339\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-57.png\" alt=\"\" class=\"wp-image-172\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-57.png 715w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-57-300x142.png 300w\" sizes=\"auto, (max-width: 715px) 100vw, 715px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"292\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-59-1024x292.png\" alt=\"\" class=\"wp-image-174\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-59-1024x292.png 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-59-300x85.png 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-59-768x219.png 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-59.png 1137w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><strong>Numerical Computing Sessional 1 question paper<br><\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"737\" height=\"697\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-61.png\" alt=\"\" class=\"wp-image-176\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-61.png 737w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-61-300x284.png 300w\" sizes=\"auto, (max-width: 737px) 100vw, 737px\" \/><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">Numerical Computing Sessional 2 question paper<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Filling the blanks (Score: 2 5=10)<\/li>\n<\/ol>\n\n\n\n<p>(1) &nbsp;&nbsp;&nbsp; Let \u03be=g(\u03be)\u2208[a, b] be a fixed point of the real-valued and continuous function g(x). If g(x) has a continuous derivative in some neighborhood of \u03be with ________.<\/p>\n\n\n\n<p>Then the sequence (x<sub>k<\/sub>) defined by x<sub>k+1<\/sub>=g(x<sub>k<\/sub>) converges to \u03be as k\u2192\u221e, provided that x<sub>0<\/sub>&nbsp;is sufficiently close to \u03be.<\/p>\n\n\n\n<p>(2)&nbsp;&nbsp;&nbsp;&nbsp; Assume that .Let be distinct real numbers and suppose that are real numbers. Then, there exists a unique Lagrange polynomial such that ____________.<\/p>\n\n\n\n<p>(3) &nbsp;&nbsp;&nbsp; Suppose that a real-valued function g(x) has a fixed point \u03be in [a, b]. Then, the corresponding expression can be written as________.<\/p>\n\n\n\n<p>(4) &nbsp;&nbsp;&nbsp; Given that 4x<sup>2<\/sup>-a=0, where a is positive real number. Then, the iteration for solving this equation by the secant method can be expressed as ____________with x<sub>0<\/sub>&nbsp;and x<sub>1<\/sub>&nbsp;being the starting values.<\/p>\n\n\n\n<p>(5)&nbsp;&nbsp;&nbsp;&nbsp; During the process of finding the single solution to the equation f(x) =0 in [a<sub>0<\/sub>, b<sub>0<\/sub>] with f(a<sub>0<\/sub>)f(b<sub>0<\/sub>)&lt;0, the first step is to consider the midpoint . If (the given tolerance), then we need to choose the new interval:[a<sub>1<\/sub>, b<sub>1<\/sub>]=[a<sub>0<\/sub>, c<sub>0<\/sub>] in the case of _____;or [a<sub>1<\/sub>, b<sub>1<\/sub>]=[c<sub>0<\/sub>, b<sub>0<\/sub>] in the case of _____.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Find solution using Bessel\u2019s formula Score= 10<\/strong><\/li>\n\n\n\n<li><strong>Find Solution using Newton\u2019s Backward Difference formula\u00a0\u00a0\u00a0 Score=10<\/strong><\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"315\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-62-1024x315.png\" alt=\"\" class=\"wp-image-177\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-62-1024x315.png 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-62-300x92.png 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-62-768x237.png 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-62.png 1227w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><strong>x = 4.75<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Numerical Computing Final question paper<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>MCQ\u2019s (Marks=10)\n<ol start=\"204\" class=\"wp-block-list\">\n<li>How much significant digits in this number 204.020050?\n<ol class=\"wp-block-list\">\n<li>5<\/li>\n\n\n\n<li>7<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>9<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>11<\/li>\n\n\n\n<li>In which of the following method, we approximate the curve of solution by the tangent in each interval.\n<ol class=\"wp-block-list\">\n<li>Hermite\u2019s method<\/li>\n\n\n\n<li>Euler\u2019s method<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Newton\u2019s method<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Lagrange\u2019s method<\/li>\n<\/ol>\n\n\n\n<ol class=\"wp-block-list\">\n<li>When\u00a0\u00a0\u00a0do\u00a0\u00a0\u00a0we\u00a0\u00a0\u00a0apply\u00a0\u00a0\u00a0Lagrange\u2019s\u00a0\u00a0\u00a0interpolation?\n<ol class=\"wp-block-list\">\n<li>Evenly spaced<\/li>\n\n\n\n<li>Unevenly spaced<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Both<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>None of above<\/li>\n\n\n\n<li>When\u00a0\u00a0\u00a0Newton\u2019s\u00a0\u00a0\u00a0backward formula is used?\n<ol class=\"wp-block-list\">\n<li>To interpolate values<\/li>\n\n\n\n<li>To calculate difference<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To find approximate error<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>None of above<\/li>\n<\/ol>\n\n\n\n<ol class=\"wp-block-list\">\n<li>What are the errors in Trapezoidal rule of numerical integration?\n<ol class=\"wp-block-list\">\n<li>E&lt;Y<\/li>\n\n\n\n<li>E>Y<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>E=Y<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li>None of above<\/li>\n<\/ol>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>Consider the initial value problem; give the condition of the absolute stability for the Euler method. (Marks= 10)<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/cuitutorial.com\/wp-content\/uploads\/2021\/12\/nc1.png\" alt=\"\" class=\"wp-image-12455\"\/><\/figure>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>Suppose that the function values of f(x) are given in the following table.<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"97\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-63-1024x97.png\" alt=\"\" class=\"wp-image-178\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-63-1024x97.png 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-63-300x28.png 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-63-768x72.png 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-63.png 1229w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>(Marks= 10)<br>Find the approximate function value at the point &nbsp;by the Lagrange\u2019s interpolation polynomial of degree 2.<\/p>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li>Use the predictor-corrector method to get the approximate solution of the following initial value problem (Marks= 10)<\/li>\n<\/ol>\n\n\n\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/cuitutorial.com\/wp-content\/uploads\/2021\/12\/nc2.png\" alt=\"\" width=\"146\" height=\"74\" srcset=\"https:\/\/cuitutorial.com\/wp-content\/uploads\/2021\/12\/nc2.png 146w, https:\/\/cuitutorial.com\/wp-content\/uploads\/2021\/12\/nc2-20x10.png 20w\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; with&nbsp;<em>h&nbsp;<\/em>= 0.1, 0 &lt;&nbsp;<em>x&nbsp;<\/em>&lt; 0.5.<\/p>\n\n\n\n<ol start=\"5\" class=\"wp-block-list\">\n<li>Consider the function f(x) = cos x\u2212x=0. Approximate a root of f(x) via Newton\u2019s Method. (Marks= 10)<\/li>\n<\/ol>\n\n\n\n<p><strong>Numerical Computing Final Paper 2022<br><\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"666\" height=\"1024\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/1-2.jpeg-666x1024.webp\" alt=\"\" class=\"wp-image-179\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/1-2.jpeg-666x1024.webp 666w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/1-2.jpeg-195x300.webp 195w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/1-2.jpeg-768x1182.webp 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/1-2.jpeg.webp 832w\" sizes=\"auto, (max-width: 666px) 100vw, 666px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"345\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/mth-1024x345.jpg\" alt=\"\" class=\"wp-image-180\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/mth-1024x345.jpg 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/mth-300x101.jpg 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/mth-768x259.jpg 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/mth.jpg 1179w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let&#8217;s get this straight:&nbsp;Numerical Computing&nbsp;is where the perfect, pristine world of mathematics collides with the gritty, finite reality of computers. It&#8217;s not about getting&nbsp;the&nbsp;answer; it&#8217;s about getting a&nbsp;good enough&nbsp;answer, knowing&nbsp;how good&nbsp;it is, and not setting your computer on fire in the process. This past paper is your stress test for doing real, useful math with [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":167,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[40],"tags":[4,5,41,6,8,10,31],"class_list":["post-166","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-numerical-computing","tag-comsats","tag-new","tag-numerical-computing","tag-paper","tag-past_paper","tag-start","tag-visual-programming"],"_links":{"self":[{"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/posts\/166","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=166"}],"version-history":[{"count":1,"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions"}],"predecessor-version":[{"id":181,"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/posts\/166\/revisions\/181"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/media\/167"}],"wp:attachment":[{"href":"https:\/\/staymind.shop\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}