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It is the last case that we need to take a look at. Throughout this section we will look at solutions to the system,
x?' = A x?
Here the eigenvalues of the matrix A are complex. By using complex eigenvalues we are going to have similar problem that we had back while we were looking at second order differential equations. We need our solutions to only have real numbers in them, though as our solutions to systems are of the form,
x?1 = ?h elt
We are going to contain complex numbers come in our solution from both the eigenvector and the eigenvalue. Getting rid of the complex numbers now will be same to how we did this back in the second order differential equation case, although will include a little more work this time around. It's simple to see how to do it in an example.
Differentials : In this section we will introduce a notation. We will also look at an application of this new notation. Given a function y = f ( x ) we call dy & dx differen
If α,β are the zeros of the polynomial 2x 2 - 4x + 5 find the value of a) α 2 + β 2 b) (α - β) 2 . Ans : p (x) = 2 x 2 - 4 x + 5 (Ans: a) -1 , b) -6) α + β =
if .77x + x = 8966.60, what is the value of x?
Children Learn By Experiencing Things : One view about learning says that children construct knowledge by acting upon things. They pick up things, throw them, break them, join the
real life applications of lengrange''s mean value theorem
1+2x
What is Multiplying Fractions ? The rule for multiplying fractions is to "multiply across": Multiply the numerators to get the numerator of the answer. Multiply the den
Circles In this section we are going to take a rapid look at circles. Though, prior to we do that we have to give a quick formula that expectantly you'll recall seeing at som
(x^2)y-(y^2)x
Poisson Mathematical Properties 1. The expected or mean value = np = λ Whereas; n = Sample Size p = Probability of success 2. The variance = np = ? 3. Standard dev
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