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The functions
{sinmx; cosmx}; m = 0,....∞
form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these with a unique set of coecients. For f(x) = x, we have
To show that the above holds for x = 1, study the dierence between the left- and right-hand sides of the equality as a function of the number of terms included in the sum. Write an octave program to compute and plot the truncated sum approximation (expansion vs x) for n =4 and 16 together with the function x. Make a table showing the error (dierence between two sides) for n =1, 2, 4, 16, 64, 256, 1024. Plot the result of the expansion for 2 values of n together with the original function. Comment on your results. You should submit an octave script or function le I can use to reproduce your results and a separate document (plain text le preferred) for your comments.
The backwards Euler difference operator is given by for differential equation y′ = f(t, y). Determine the order of the local truncation error. Explain why this difference o
Michael made 19 out of 30 free-throws this basketball season. Larry's freethrow average was 0.745 and Charles' was 0.81. John made 47 out of 86 free-throws. Who is the best free-th
Example: Find out which of the following equations functions are & which are not functions. y= 5x + 1 Solution The "working" definition of fu
Solving Trig Equations with Calculators, Part I : The single problem along with the equations we solved out in there is that they pretty much all had solutions which came from a
The order of a differential equation is the huge derivative there in the differential equation. Under the differential equations as listed above in equation (3) is a first order di
General approach of Exponential Functions : Before getting to this function let's take a much more general approach to things. Let's begin with b = 0 , b ≠ 1. Then an exponential f
AREAS RELATED TO CIRCLES The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. In t
the circumference of a circle C of radius r is given by C=2pR.taking p to be 22/7 a)find the circumference when the radius is 28 cm b)find the radius when the circumference is 484
why minimum three coplanar vectors are required to give zero resultant and not two?
The equation ax2 + 2hxy + by2 =0 represents a pair of straight lines passing through the origin and its angle is tan q = ±2root under h2-ab/(a+b) and even the eqn ax2+2hxy+by2+2gx+
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