Important questions of algorithmic mathematics.

1. How can you solve the system of nonlinear equations? Explain the importance of Jacobian Matrix. Write down its algorithm and explain the steps.
2. If the date is not evenly spaced, which interpolation method you apply? Explain it with suitable example and algorithm.
3. What are the advantages of Least Square Method? Derive the equation for quadratic curve fitting. Write down its algorithm and explain it.
4. Why Numerical Integration is required? Explain it with suitable example. Derive the general quadrature formula.  Write down its algorithm and explain it.
5. Differentiate between direct and iterative method for these solution of liner system of equations. Derive the equation for Gauss Seideal Method, explain it with suitable example and write its algorithm. 
6. Write down the general form of second order partial differential equation and derive the Poission's equation. Explain the equation and write down its algorithm. 
7. Justify the Measure of Central Tendency, Dispersion, and Direction are important in the statistics. Explain with suitable equations and examples. 
8. Why distribution is important in the probability? Explain Poisson's distribution with suitable example and write down its algorithm.
9. Why do you require optimization? Explain the steps for Simplex method with suitable example and write down its algorithm. Compare it with dynamic programming. 
10. Why we require Discrete Fourier Transformation? Explain with suitable example. Compare it with Fast Fourier Transformation and write its algorithm.