PTU Punjab Technical University B-Tech May 2019 Question Papers 4th Semester Robotics ECE Engineering
Total No. of Pages : 02
Total No. of Questions : 09
B.Tech.(Electronics & Computer Engg.) (2011 Onwards) (Sem.?4)
NUMERICAL METHODS
Subject Code : BTEL-401
M.Code : 62021
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of T EN questions carrying T WO marks
each.
2.
SECTION-B contains FIVE questions carrying FIVE marks each and students have
to attempt any FOUR questions.
3.
SECTION-C contains T HREE questions carrying TEN marks each and students
have to attempt any T WO questions.
SECTION?A
1.
Answer briefly :
a. Is the sequence xn+1 = 0.5xn, n 0, x0 = 1 a convergent sequence?
dy
b. Write the forward finite difference formula for
.
dx
c. Define the row rank of a matrix.
d. Define a singular matrix and also give one example.
e. Write the formula for Simpson's 1/3 rule.
f. Can we use composite Simpson's rule with even number of node points?
2
g. Compute xedx using Trapezoidal rule.
0
h. Use the forward-difference formula to approximate the derivative of f(x) = In x at
x0 = 1.8 using h = 0.1.
i. What is the order of convergence when Newton Raphson's method is applied to the
equation x2 ? 4x + 4 = 0 to find its multiple root.
j. Explain complete pivoting.
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SECTION-B
2.
Use Newton's method to find a sequence converging to the root 0 of the equation
ln(x +1) ? x = 0 starting with an initial guess x0 = 1.
3.
Apply Taylor's method of order 2 with N = 10 to initial value problem :
y = y ? t2 + 1, 0 t 2, y(0) = 0.5.
4.
Find the order of convergence of Newton's method.
5.
Solve the following system of equations
x1 + 2x2 ? x3 = 3
2x1 + x2 + x3 = 3
?3x1 + x2 + 2x3 = 4
/ 4
6.
Approximate the integral
sin
x
xdx using composite Simpsons rule with 5 nodes.
0
SECTION-C
7.
Use R-K method of order 2 to find out y(0.2) with h = 0.1 for the following initial value
problem
y = te3t ?2y, 0 t 1, y(0) = 0.
8.
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 starting with an initial guesses 0.5 and
.
4
2
9.
Approximate
2x
e
sin 3xdx
employing:
0
a. Gaussian 2 point formula.
b. Gaussian 3 point formula.
Also compute the errors in both the cases.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 04 November 2019