BCS054-SOLVED ASSIGNMENT 2016-17 IGNOU BCA 5th SEM

1.

(a)

For the following questions use an eight-decimal digit floating point representation as given in your Block 1, Unit 1, Section 1.3.1 page 29. Perform the following operations:

(i) Represent 3456789 and 3455155 as floating point numbers using chopping in normalised form.

(ii) What are the advantages of representing these numbers in normalised form?

(iii)Compare the error in representation when chopping is used to error in representation when rounding is used for these numbers.

(iv) Subtract the two numbers and find the error in result.

(v) Divide the first number by second. The result should be in normalised form.

(vi) Explain the concept of overflow and underflow using any two numbers.

(b)

Explain the concept of Ill-conditioned problem with the help of an example other than given in the unit.

(c)

Find the Maclaurin series for calculating sin x using the first four terms of this series. Also find the bounds of truncation error for such cases.

(d)

Obtain approximate value of (2.8)-1 using first four terms of Taylor‟s series expansion.

2.

(a)

Solve the system of equations 4x + 2y + z = 14 2x + 4y + 3z = 18 2x + 3y – 2z = 06 using Gauss elimination method with partial pivoting. Show all the steps.

(b)

Perform four iterations (rounded to four decimal places) using

(i) Gauss - Jacobi Method and

(ii) Gauss-Seidel method ,

for the following system of equations.

With initial estimates as (0,0,0)T. The exact solution is (2,1, 1)T. Which method gives better approximation to the exact solution?

3.

Determine the smallest positive root of the following equation: f(x) ≡ x2 - cos (x) = 0 to three significant digits using (a) Regula-falsi method (b) Newton Raphson method (c) Bisection method (d) Secant method

4.

(a)

Find Lagrange‟s interpolating polynomial for the following data. Hence obtain the value of f(3). x 0 2 5 6 f(x) 7 21 51 61

(b)

Using the inverse Lagrange‟s interpolation, find the value of x when y=3 for the following data: x 42 65 95 106 y=f(x) -1 1 4 6

5.

(a)

By decennial census, the population of a town was given below. Year (x) : 1976 1986 1996 2006 2016 Population (y): 37 43 53 58 72 (in lakhs)

(i) Using Stirling's central difference formula, estimate the population for the year 2001

(ii) Using Newton‟s forward formula, estimate the population for the year 1984.

(iii) Using Newton‟s backward formula, estimate the population for the year 2010.

(b)

Derive the relationship between the operators E and δ.

6.

(a)

Find the values of the first and second derivatives of y = x3/2 at x = 23 from the following table. Use forward difference method. Also, find Truncation Error (TE) and actual errors.

(b)

Find the values of the first and second derivatives of y = x3/2 at x = 23 from the following table using Lagrange‟s interpolation formula. Compare the results with part (a) above.

7.

Compute the value of the integral 10 ∫ 2 (3 x3+ 2x2 + 3x +5) dx By taking 8 equal subintervals using (a) Trapezoidal Rule and then (b) Simpson's 1/3 Rule. Compare the result with the actual value.

8.

(a)

Solve the Initial Value Problem, using Euler‟s Method y = 1+xy, y(0) = 1. Find y(1.0) taking (i) h = 0.2 and then (ii) h = 0.1

(b)

Solve the following Initial Value Problem using (i) R-K method of O(h2) and (ii) R-K method of O(h4) y' = x2+ y2 and y(0) = 0. Find y(0.4) taking h = 0.2, where y' = dy/dx

-----------------------------------------------------------------------------------------
Assignment Solution on process | IGNOU BCA MCA Solved Assignment 2016 2017  Join IGNOU BCA MCA Coaching Class |  Synopsis & Project Support 
Powered by IGNOUFriend | www.ignoufriend.co.in |

ignou bca mca synopsis, ignou class, ignou bca mca project, solved ignou assignment,BCA Coaching Institute in Delhi, MCA Coaching Institute in Delhi, BCA MCA Coaching Institute in Delhi, BCA MCA, Tuation Class in delhi, IGNOU BCA MCA Class, IGNOU BCA MCA Tution,IGNOU Solved Assignment, IGNOU BCA Synopsis , IGNOU MCA Synopsis, ignou bca project, ignou mca project, ignou best coaching in delhi, ignou best coaching in new delhi, ignou best coaching in south delhi, ignou best coaching in north delhi, ignou best coaching in east delhi, ignou best coaching in west delhi

ignou, bca, mca, coaching institute, tution class, bcsp064, mcsp060, cs76, mcs044,bcs011, bcs012, mcs011, mcs012, mcs013, mcs015, bcsl021, bcsl022, mcs014, bcs040, mcs021, mcs023, bcs031, bcsl032, bcsl033, bcsl 034, bcs041, bcs042, mcsl016, bcsl043, bcsl044, bcsl045, bcs051, bcs052, bcs053, bcs054, bcs055, bcsl056, bcsl057, bcsl058, bcs062, mcs022, bcsl063, project

mcsp060, mcse011, mcse004, mcse003, mcsl054, mcs053, mcs052, mcs051, mcsl045, mcs044, mcs043, mcs042, mcs041, mcsl036, mcs035, mcs034, mcs033, mcs032, mcs031, mcsl025, mcs024, mcs023, mcs022, mcs021, mcsl017, mcsl016, mcs015, mcs014, mcs013, mcs012, mcs011

nips institute, nipsar, ignoufriend.in, ignoufriend.co.in, ignouhelp, best coaching institute