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 Numerical Methods Calculators 1. Find a root an equation using 1. Bisection Method 2. False Position Method 3. Iteration Method 4. Newton Raphson Method 5. Secant Method 6. Muller Method 7. Birge-Vieta method (for n^(th) degree polynomial equation) 8. Bairstow method 2. Find roots of non-linear equations using Modified Newton Raphson method (Multivariate Newton Raphson method) 3. Numerical Interpolation using 1. Best suitable formula (among 2 to 10) 2. Newton's Forward Difference formula 3. Newton's Backward Difference formula 4. Newton's Divided Difference Interpolation formula 5. Langrange's formula 6. Gauss Forward formula 7. Gauss Backward formula 8. Stirling's formula 9. Bessel's formula 10. Everett's formula 11. Hermite's formula 4. Numerical Differentiation using 1. Best suitable formula (among 2 to 7) 2. Newton's Forward Difference formula 3. Newton's Backward Difference formula 4. Newton's Divided Difference formula 5. Langrange's formula 6. Stirling's formula 7. Bessel's formula 5. Numerical Integration using 1. Trapezoidal Rule 2. Simpson's 1/3 Rule 3. Simpson's 3/8 Rule 4. Boole's Rule 5. Weddle's Rule 6. Solve numerical differential equation using 1. Euler method 2. Runge-Kutta 2 method 3. Runge-Kutta 3 method 4. Runge-Kutta 4 method 5. Improved Euler method 6. Modified Euler method 7. Taylor Series method 8. Adams bashforth predictor method 9. Milne's simpson predictor corrector method
 1. Bisection, False Position, Iteration, Newton Raphson, Secant Method Find a real root an equation using 1. Bisection Method 2. False Position Method 3. Iteration Method 4. Newton Raphson Method 5. Secant Method 6. Muller Method 7. Birge-Vieta method (for n^(th) degree polynomial equation) 8. Bairstow method Enter an equation like... f(x) = 2x^3-2x-5 f(x) = x^3-x-1 f(x) = x^3+2x^2+x-1 f(x) = x^3-2x-5 f(x) = x^3-x+1 f(x) = cos(x)
2. Numerical Differentiation
Numerical Differentiation using Newton's Forward, Backward Method
1. From the following table of values of x and y, obtain (dy)/(dx) and (d^2y)/(dx^2) for x = 1.2 .
 x 1 1.2 1.4 1.6 1.8 2 2.2 y 2.7183 3.3201 4.0552 4.953 6.0496 7.3891 9.025

2. From the following table of values of x and y, obtain (dy)/(dx) and (d^2y)/(dx^2) for x = 2.2 .
 x 1 1.2 1.4 1.6 1.8 2 2.2 y 2.7183 3.3201 4.0552 4.953 6.0496 7.3891 9.025

3. Numerical Integration
Numerical Integration using Trapezoidal, Simpson's 1/3, Simpson's 3/8 Rule

1. From the following table, find the area bounded by the curve and x axis from x=7.47 to x=7.52 using trapezodial, simplson's 1/3, simplson's 3/8 rule.
 x 7.47 7.48 7.49 7.5 7.51 7.52 f(x) 1.93 1.95 1.98 2.01 2.03 2.06

2. Evaluate I = int_0^1 (1)/(1+x) dx by using simpson's rule with h=0.25 and h=0.5
 5. Solve numerical differential equation using Euler, Runge-kutta 2, Runge-kutta 3, Runge-kutta 4 methods 1. Find y(0.1) for y'=x-y^2, y(0) = 1, with step length 0.1 2. Find y(0.5) for y'=-2x-y, y(0) = -1, with step length 0.1 3. Find y(2) for y'=(x-y)/2, y(0) = 1, with step length 0.2 4. Find y(0.3) for y'=-(x*y^2+y), y(0) = 1, with step length 0.1 5. Find y(0.2) for y'=-y, y(0) = 1, with step length 0.1

4. Numerical Interpolation
Numerical Interpolation using Forward, Backward Method

1. The population of a town in decimal census was as given below. Estimate population for the year 1895.
 Year 1891 1901 1911 1921 1931 Population (in Thousand) 46 66 81 93 101

2. Let y(0) = 1, y(1) = 0, y(2) = 1 and y(3) = 10. Find y(4) using newtons's forward difference formula.

3. In the table below  the values of y are consecutive terms of a series of which the number 21.6 is the 6th term. Find the 1st and 10th terms of the series.
 X 3 4 5 6 7 8 9 Y 2.7 6.4 12.5 21.6 34.3 51.2 72.9

4. The population of a town in decimal census was as given below. Estimate population for the year 1895.
 X 0.1 0.15 0.2 0.25 0.3 tan(X) 0.1003 0.1511 0.2027 0.2553 0.3073
Find (1) tan 0.12    (2) tan 0.26

5. Certain values of x and log10x are (300,2.4771), (304,2.4829), (305,2.4843) and (307,2.4871). Find log10 301.

6. Find lagrange's Inerpolating polynomial of degree 2 approximating the function y = ln x defined by the following table of values. Hence find ln 2.7
 X 2 2.5 3 ln(X) 0.69315 0.91629 1.09861

7. Using the following table find f(x) as polynomial in x
 x -1 0 3 6 7 f(x) 3 -6 39 822 1611

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