# Important questions of algorithmic mathematics.

- How can you solve the system of nonlinear equations? Explain the importance of Jacobian Matrix. Write down its algorithm and explain the steps.
- If the date is not evenly spaced, which interpolation method you apply? Explain it with suitable example and algorithm.
- What are the advantages of Least Square Method? Derive the equation for quadratic curve fitting. Write down its algorithm and explain it.
- Why Numerical Integration is required? Explain it with suitable example. Derive the general quadrature formula. Write down its algorithm and explain it.
- 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.
- 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.
- Justify the Measure of Central Tendency, Dispersion, and Direction are important in the statistics. Explain with suitable equations and examples.
- Why distribution is important in the probability? Explain Poisson's distribution with suitable example and write down its algorithm.
- Why do you require optimization? Explain the steps for Simplex method with suitable example and write down its algorithm. Compare it with dynamic programming.
- Why we require Discrete Fourier Transformation? Explain with suitable example. Compare it with Fast Fourier Transformation and write its algorithm.

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