UNIT - 2 Unit-02/Lecture-01
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1 UNIT - 2 Unit-02/Lecture-01 Solution of algebraic & transcendental equations by regula falsi method
2 Unit-02/Lecture-01 [RGPV DEC(2013)] [7]
3 Unit-02/Lecture-01 [RGPV JUNE(2014)] [7]
4 Unit-02/Lecture-01 S.NO Q.1 RGPV QUESTIONS Define algebraic and transcendental equations. Q The equation x x x 1 0,has one real root RGPV,DEC between 1.4 and 1.5. find the root to four decimal places 2014 by the method of false position. Year RGPV,DEC 2014 Marks 2 3
5 Unit-02/Lecture-02 [RGPV JUNE(2014)] [2] Newton Raphson Method
6 Unit-02/Lecture-02
7 Unit-02/Lecture-02
8 Unit-02/Lecture-02 [RGPV JUNE(2002)] [7] S.NO Q.1 Q. 2 RGPV QUESTIONS Year Find the smallest positive root of the equation RGPV,DEC, 2014 x3 2 x by Newton raphson method. Find the negative root of the equation RGPV,DEC 2013 x3 21x correct to 2 decimal places by Marks 2 7 newton raphson method.
9 Unit-02/Lecture-03 Iterative Method
10 Unit-02/Lecture-03 [RGPV MARCH(2010),JUNE(2003,2008,2010),FEB(2005,2010)] [7] S.NO Q.1 RGPV QUESTIONS Year Find the root of the equation 3x cos x 1 by RGPV,JUNE 2014 iterative method correct to 2 decimal places. Q. 2 Find the cube root of 15 correct to four significant RGPV, DEC 2010 figures by iterative method. Marks 3 7
11 Unit-02/Lecture-04 [RGPV JUNE(2007)] [7] Secant Method
12 Unit-02/Lecture-04
13 Unit-02/Lecture-04
14 Unit-02/Lecture-05 [RGPV DEC(1999)] [7] Solution of simultaneous linear equations by gauss elimination method
15 Unit-02/Lecture-05 S.NO Q.1 RGPV QUESTIONS Year Marks Solve by gauss elimination method the following RGPV JUNE 7 system of equations: x+y+2z=13,3x+10y+z=14, 2x+3y+10z=15.
16 Unit-02/Lecture-06 [RGPV DEC(2001)] [7] Gauss Jordan Method
17 Unit-02/Lecture-06 S.NO Q.1 RGPV QUESTIONS Year Marks Apply gauss Jordan method to find the solution of the RGPV DEC 7 following system of equation: x+y+z=12, 2x+10y+z=13, x+y+5z=7
18 Unit-02/Lecture-07 Crouts method
19 Unit-02/Lecture-07 S.NO Q.1 RGPV QUESTIONS Solve the following equations by crouts method 10x+y+z=12, 2x+10y+z=13, 2x+2y+10z=14 Q.2 Solve the following equations by the application of crouts RGPV triangularization(lu) method : x-3y+10z=3, -x+4y+2z=20, 5x+2y+z=-12 Year Marks RGPV DEC DEC 7
20 Unit-02/Lecture-08 Jacobi s method
21 Unit-02/Lecture-08 S.NO Q.1 RGPV QUESTIONS Solve the following equations by crouts method 10x+y+z=12, 2x+10y+z=13, 2x+2y+10z=14 Q.2 Solve the following equations by the application of crouts RGPV triangularization(lu) method : x-3y+10z=3, -x+4y+2z=20, 5x+2y+z=-12 Year Marks RGPV DEC DEC 7
22 Unit-02/Lecture-09 Gauss-seidel iterative method
23 S.NO Q.1 RGPV QUESTIONS Solve the following equations by gauss seidal method 20x+y-2z=17, 3x+20y-z=-18, 2x-3y+20z=25 Year Marks RGPV DEC Q.2 Solve the following equations by gauss seidal method : 8x-y+z=18, 2x+5y-2z=3, x+2y-3z=-6 Solve the following equations by using gauss seidal method : 27x+6y-z=85, 6x+15y+2z=72, x+y+54z=110 RGPV 2014 RGPV 2011 Q. 3 DEC 7 JUNE 7
24 Unit-02/Lecture-10 Error and approximations Absolute error, relative error and percentage errors. Absolute error is the numerical difference between the true value and approximate value of a quantity. If X is true value and X is approximate value then X X is called absolute error. Truncation and round off error in numerical calculations. Truncation errors : They are caused by using approximate results or on replacing an infinite process by a finite one. Round off errors : They arise when a calculated figure is rounded off to a fixed number of digits to represent the exact figure, the difference between such rounded figure and exact figure is called round off error. e.g. Round off correct to four significant digits. Number rounded off to four significant digits = Types of errors arise in numerical calculations. In numerical calculations we come across following types of errors (a) Inherent errors (b) Rounding errors (c) Truncation errors (d) Absolute errors (e) Relative errors (J) Percentage errors.
25 Unit-02/Lecture-10 Q Explain rounding off errors and explain how to reduce it. Sol. Rounding off errors-these errors arise from The process of rounding off the numbers during the computation. These errors can be reduced: (a) By changing the calculation procedure so as to avoid subraction of nearly equal number or division by a small number. (b) By retairing at least one more significant digit at each step and rounding off at last step. Q Define absolute, relative and percentage errors by giving suitable example. Sol. Absolute error: 2. If the first significant figure of no. is K and the no. is correct to n significant
26 Unit-02/Lecture-10 Q Find the no. of terms of logarithm series such that value of log 1.02 is correct to three decimals. Q The error in the measurement of area of circle is not allowed to exceed 0.1 % How accurately should the diameter be measured? Q Differentiate inherent errors and Truncation errors. Ans. Inherent Errors : The interent error is that quantity which is already present in the statement of problem before its solution. These errors arise either due to limitations of Mathematical tables, calculators and computers. The inherent errors further classified as (a) Data Errors (b) Conversion Error. Truncation Error : The truncation error arised by using approximate results or on replacing infinite process by finite one. Suppose we have
27 Reference Book Author Higher Engg. Mathematics B.S.Grewal Engg. Mathematics - III Dr. D.C.Agarwal
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