MHT-CET : Mathematics Entrance Exam

### MHT - CET : Mathematics - Numerical Methods Formulae Page 1

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1. Trapezoidal Rules for :

 = h [ ( y0 + yn ) + 2( y1+ y2 + y3 +….+ yn - 1 )] 2

 where h = b - a , n = Number of sub-division. n

2. Simpson's Rules for :

= [ ( y0 + yn ) + 4( y1+ y3 +…+ yn - 1 ) + 2( y2 + y4 + y6 +…+ yn - 2 )]

 where h = b - a , n = Even number of sub-division. n

3. Newton's Forward Interpolation Formula:

a)

To find the value of f(x) for given x

 f(x) = f(x0) + u.D f(x0)+ u (u - 1) D2f(x0) + u (u - 1) (u - 2) D3f(x0) + ....... + 2! 3!

 u (u - 1) (u - 2)(u - 3)......(u - n + 1) Dnf(x0) n!

 where u = x - x0 (h > 0) h = xr - xr-1, r = 1, 2, 3… h

b)

To find the polynomial f(x)

 f(x) = f(x0) + x - x0 Df(x0) + (x - x0)(x - x1) D2f(x0) + h h22!

 (x - x0)(x - x1)(x - x2) D3f(x0) + ........ where h = xr - xr-1, r = 1, 2, 3… h32!

4. Newton's Backward Interpolation Formula:

To find the value of f(x) for given x

 f(x) = f(xn) + u.Ñ f(xn)+ u (u + 1) Ñ2f(xn) + u (u + 1) (u + 2) Ñ3f(xn) + ....... 2! 3!

 where u = x - xn (h > 0) h = xr - xr-1, r = 1, 2, 3… h

5. Bisection Method:

 Formula for taking approximate root C = a + b 2

6. False position Method:

Formula for taking approximate root

 C  = af(b) - bf(a) f(b) - f(a)

7. Newton-Raphson Method:

Formula for taking approximate root

 xi =  xi - 1 - f(xi - 1) ; i = 1, 2,... f '(xi - 1)

8. Relation between D, Ñ and E:

 a) Erf(x) = f(x + rh) r is any positive or negative integer. b) D = E - 1 or E = D + 1. c) Ñ = 1 - E-1, or E-1= 1 - Ñ d) D = EÑ

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