# RTU Previous Question Papers BE CE 3rd Sem

# Computer Application in Civil Engineering January 2013

**UNIT – I**

1. (a) What is error ? Explain absolute and relative error in detail also explain the meaning of approximations and round of errors in detail.

(b) Write short note on truncation errors.

**OR**

1. (a) If we want to approximate e^{10 5} with an error less than 10^{-12} using the Taylor series for / (*) = e^{x} at 10, at least how many terms are needed.

(b) Explain how truncation errors can be estimated by geometry series.

**UNIT – II**

(a) Iterate two times using the Gauss-Seidel method, stating with the initial approximations as Xj=0.3, x_{2}=-0.8 and *_{3}=0.3.

**OR**

(a) Explain successive substitution method with its derivation and algorithm.

(b) Derive formula for decomposition methods also write down its algorithm.

** **

**UNIT – III**

(a) Fit a second degree parabola to the following data :

x : | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 | 7.0 |

y : | 1.1 | 1.6 | 2.7 | 4.1 | 5.8 | 6.9 | 8.2 |

(b) Explain various applications of difference relations in the solution of differential equations with an example.

**OR**

(a) Given data is

A | 1.0 | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 |

B | 7.989 | 8.403 | 8.781 | 9.129 | 9.451 | 9.750 | 10.031 |

(b) Write short note on non-liner Regression analysis.** **

**UNIT – IV**

4 (a) Write an algorithm for Simpson’s — rule for a known function.

(b) State the assumptions made and derive the expression for numerical integration using Simpson — rule.

**OR**

4. (a) Evaluate, by using Newton’s method for integration.

(b) Trapezoidal method, Simpson method and Simpson method.

**UNIT – V**

5. (a) Give Algorithm and explain Range-Kutta fourth order method for solution of differential equation of first order and first degree.

(b) Derive equations for Numerical solution of ordinary differential equations by Euler method.

**OR**

5. (a) Derive an equation of ordinary differential equation by predictor – corrector method with its Algorithm.

(b) Apply Predictor corrector method to find >’(0.6) for differential equation Dy= > given >^{;}(°) = °_{3} >(0.2) = 0.02, >(0.4) = 0.0795.