krypto problem

Using the numbers 3, 3, 8 and 8 once and only once, obtain the target number of 24. (use have to use 3 twice and 8 twice - 3 x 8 = 24 is not acceptable). You may use only addition, subtraction, multiplication and division (eg. no factorial). Hint: no addition in the equation.

Use Monte Carlo integration to estimate the value of the double integral, try to find....

Use Monte Carlo integration to estimate the value of the double integral (x^2+y^2)/(1+y^2) over the unit circle. Try to find a 95% confidence interval in which the true value lies? What is the exact value?

Mathematical Methods

(a) Describe how the weights for the order 4 closed Newton-Cotes quadrature formula could be found. Do NOT calculate the weights. (b) What are composite quadrature rules and why are they preferred to using higher order quadrature rules? (c) What are the main characteristics of a predictor-corrector method for solving an initial value problem. (d) In general, there are 3 conditions for stopping an iterative algorithm, describe each of them, and give an example of each by considering the problem of finding a solution of f(x) = 0.

Monte Carlo integration

Describe how to use the Monte Carlo method to estimate the double integral of xydxdy over the area 0

use the RK4 method, with a step size of h=0.5, to obtain an approximation...

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