By Gupta, C.B.,Malik, A.K. , Kumar, Vipin

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**Extra resources for Advanced Mathematics As per IV Semester of RTU & Other Universities **

**Example text**

An1 x1 + an 2 x 2 + ...... + ann x n = bn Above equation can be written as x1 = U| || V| || W 1 [b1 − a12 x2 − a13 x 3 ...... a1n xn ] a11 x2 = 1 [b2 − a 21 x 1 − a23 x 3 ...... a 2 n x n ] a22 x3 = 1 [b3 − a31 x1 − a 32 x 2 ...... a3 n x n ] a33 . : xn = 1 [bn − a n1 x1 − a n 2 x 2 ...... S. 6), we get x1( 2 ) = 1 [b1 − a12 x 2(1) − a13 x3(1) ...... a1n x n(1) ] a11 45 SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS Now put x1( 2 ) x 2(1) x 3(1) ...... S. 6), we get x 2( 2 ) = 1 [b2 − a21 x1( 2 ) − a23 x 3(1) ......

309. Solution. Here h = 5. 069 39 INTERPOLATION Stirling formula is yu = y0 + 2 2 u( ∆y0 + ∆y−1 ) u 2 2 u(u 2 − 1) ( ∆3 y −1 + ∆3 y−2 ) u (u − 1) 4 + ∆ y–1 + + ∆ y–2 + ..... 2 4! 2! 3! 142) + 3! 2 2! 142) 4! 07669. 1 1. Find the missing term in the following table: x 1 2 3 4 5 y 2 5 7 — 32 2. Estimate the missing term in the following table. x 0 1 2 3 4 f (x) 1 3 9 — 81 3. 0170, find log 102. 4. Estimate the production of cotton in the year 1935 from the data given below (in millions of pales).

H 2h2 a2 = f (a + 2h) – 2ha1 – a0 a2 = = f ( a + 2h) − 2( f ( a + h) − f ( a)) − f ( a) 2 ! h2 f ( a + 2h) − 2 f ( a + h) + f ( a) ∆2 f ( a) = 2 ! h2 2 ! h2 23 INTERPOLATION Proceeding in the same way, we get a3 = ∆3 f ( a) ...... , an into (1), we get f (x) = f (a) + (x – a) ∆f ( a) ∆2 f ( a) + (x – a) (x – a – h) h 2 ! h2 + (x – a) (x – a – h) (x – a – 2h) ∆3 f ( a) + ...... 3 ! 4) + (x – a) (x – a – h) (x – a – 2h) + ..... + (x – a – (n – 1)h) ∆ f ( a) n ! hn ! 4), we get u(u − 1) 2 u(u − 1) (u − 2) .....

### Advanced Mathematics As per IV Semester of RTU & Other Universities by Gupta, C.B.,Malik, A.K. , Kumar, Vipin

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