This download link is referred from the post: PTU B.Tech Dec 2018 5th Semester Question Papers || Punjab Technical University
Roll No. [ | [ [T TTT] Total No. of Pages : 03
Total No. of Questions : 09
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B.Tech (Automation & Robotics) (2011 & Onwards) (Sem.=5)NUMERICAL METHODS IN ENGINEERING
Subject Code : ME-309
M.Code : 70482
Time : 3 Hrs. Max. Marks : 60
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INSTRUCTIONS TO CANDIDATES :
- SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
- SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt ANY FOUR questions.
- SECTION-C contains THREE questions carrying TEN marks each and students have to attempt ANY TWO questions.
SECTION-A
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- Write briefly :
- Write Newton’s formula for interpolation.
- Find the condition number of the function f'(x) = sin x.
- Define a cubic spline interpolant with clamped boundary.
- Determine the Lagrange interpolating polynomial passing through the points (1, 1), (2,4) and (3, 9).
- Find the L, norm of the vector (1, 5, 9)T.
- Explain least square curve fitting.
- Compute ∫xexdx using Simpson’s rule.
- Use the forward-difference formula to approximate the derivative of f(x) = ln x at x0=1.8 using h =0.1.
- What is the order of convergence when Newton Raphson’s method is applied to the equation x2 — 6x + 9 = 0 to find its multiple root.
- Out of chopping of numbers and rounding off of numbers, which one introduce less error?
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SECTION-B
- Use forward-difference method with steps sizes h = 0.1 and k = 0.01 to approximate the solution to the heat equation :
∂u/∂t (x,t) = ∂2u/∂x2 (x,t) = 0, 0 < x < 1, t > 0,
with boundary conditions--- Content provided by FirstRanker.com ---
u(0,t)=u(1,t)=0, t>0,
and initial condition
u(x,0)=sin(πx), 0 < x < 1. - Apply Taylor’s method of order 2 with N = 10 to initial value problem
y'=y-t2+1, 0- The following data is given
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1.0 1.3 1.6 1.9 2.2 0.76519771 0.6200860 0.4554022 0.2818186 0.1103623 - Use Lagrange’s formula to approximate f'(1.5).
- Use the data points (0, 1), (1, e), (2, e2) and (3, e3) to form a natural spline S(x) that approximates f (x) = ex.
- Find the largest interval in which p* must lie to approximate p with relative error at most 10-4 for p= (√17).
- The following data is given
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SECTION-C
- Derive Secant’s formula for solving the equation f (x) = 0 (specifying the assumptions made). Use the secant method to solve the equation x = cos x starting with an initial guesses 0.5 and 1.
- Use Gauss elimination method with partial pivoting to solve the following linear system of equations.
√3x1+√5x2—x3+x4=0,
x1 — x2 +x3+2x4=1,--- Content provided by FirstRanker.com ---
x1+x2—√5x3+x4=2,
-x1 —x2+x3—√5x4=3. - Determine the values of h that will ensure an approximation error of less than 10-6 when approximating I= ∫e-xsin3xdx and employing :
a) Composite trapezoidal rule.
b) Composite Simpson’s rule.
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NOTE : Disclosure of identity by writing mobile number or making passing request on any page of Answer sheet will lead to UMC case against the Student.
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This download link is referred from the post: PTU B.Tech Dec 2018 5th Semester Question Papers || Punjab Technical University