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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.
Write down the first few terms of each of the subsequent sequences. 1. {n+1 / n 2 } ∞ n=1 2. {(-1)n+1 / 2n} ∞ n=0 3. {bn} ∞ n=1, where bn = nth digit of ? So
Evaluate the volume and surface area of a rectangular solid: Calculate the volume & surface area of a rectangular solid along with a = 3", b = 4", & c = 5". Solution:
How do you find the distributive property any faster?
A painting was purchased 11 years ago for $26900. It has just been sold for $78000. Calculate the flat rate of appreciation p.a.
how to find the minimum distance between any two particles which are in relative motion?
Forecasting By Using Least Squares Data have been kept of sales over the last seven years Year 1 2 3 4 5 6
40.783-75
With reference to Fig. 1(a) show that the magnification of an object is given by M=SID/SOD. With reference to Fig. 1(b) show that the size of the penumbra (blur) f is given by f
(1)Derive, algebraically, the 2nd order (Simpson's Rule) integration formula using 3 equally spaced sample points, f 0 ,f 1 ,f 2 with an increment of h. (2) Using software such
Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2, Subject to the constraints: X1+ X2 = 4 X1+ X2 = 2 X1, X2 = 0
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