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Consider the differential equation give by
y′ = -10(y - sin t)
(a) Derive by hand exact solution that satis?es the initial condition y(0) = 1.
(b) Numerically obtain the solution to the IVP using Forward Euler with a step size of h = 0.1 from t = 0 to t = 3. Print the value of the approximate solution at time t = 3. Also plot the exact solution (with a solid line) and the approximate solution (with square markers) on the same plot.
(c) Numerically determine the relative global error,
of your approximate solution at t = 3 when h = h, h/2, h/4, h/8 and h/16.
Plot the log of the relative error vs. the log of the spacing h. Explain why this veri?es your scheme is convergent to order 1.
Standard form of a complex number So, let's start out with some of the basic definitions & terminology for complex numbers. The standard form of a complex number is
If A be the area of a right triangle and b one of the sides containing the right angle, prove that the length of the altitude on the hypotenuse is 2 Ab /√ b 4 +4A 2 . An
1. Consider the model Y t = β 0 + β 1 X t + ε t , where t = 1,..., n. If the errors ε t are not correlated, then the OLS estimates of β 0 and β
If ABCD isaa square of side 6 cm find area of shaded region
example and about this
if one side of a square is increased 4 inches and an adjacement side is multiplied by 4, the perimeter of the resulting rectangle is 3 times the perimeter of the square. find the s
how do you slove 4u-5=2u-13
The Lognormal Distribution If ln(X) is a normally distributed random variable, then X is said to be a lognormal variable. If P1, P2, P3, ... are the prices of a scrip in per
Solving Trig Equations with Calculators, Part II : Since this document is also being prepared for viewing on the web we split this section into two parts to keep the size of the
Next we have to talk about evaluating functions. Evaluating a function is in fact nothing more than asking what its value is for particular values of x. Another way of looking at
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