- #1
icesalmon
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Homework Statement
use partial fraction decomposition to re-write 1/(s2(s2+4)
The Attempt at a Solution
I thought it would break down into (A/s) + (B/s2) + ((cx+d)/(s2+4)
but it doesn't.
The only thing wrong is that the last term should be (cs + d)/(s2 + 4). Otherwise, your decomposition is correct.icesalmon said:Homework Statement
use partial fraction decomposition to re-write 1/(s2(s2+4)
The Attempt at a Solution
I thought it would break down into (A/s) + (B/s2) + ((cx+d)/(s2+4)
but it doesn't.
icesalmon said:Homework Statement
use partial fraction decomposition to re-write 1/(s2(s2+4)
The Attempt at a Solution
I thought it would break down into (A/s) + (B/s2) + ((cx+d)/(s2+4)
but it doesn't.
Because -1/4 has no imaginary part. You can think of your equation as being written like this:icesalmon said:okay I had this problem solved, but I went back after changing my variable from x to s
and I get A(s)(s2+4) + B(s2+4) +(cs+d)(s2) = 1 (1)
if I let s = 0 then B(4) = 1 -> B = 1/4
if I let s = +/-2i then +/-2iC + D = -1/4 (2)
where as before I equate coefficients it's obvious to me that +/-2iXC != -1/4 and D = -1/4 so C = 0
Letting s = 1 after I get A = 0 also,
my questions are how do I come to the conclusion that C = 0 in (2)?
It doesn't matter what values you choose for s. The only thing to be concerned with is how convenient a particular value is.icesalmon said:Should I keep plugging values into (1) and try to create a system? Also, how do I pick values for A, once I've actually calculated D, C, and B. What would cause me to choose 1 for S as opposed to any other value?
Partial Fraction Decomposition is a mathematical process used to break down a rational expression into simpler fractions. It is often used in integration, solving linear differential equations, and simplifying complex algebraic expressions.
Partial Fraction Decomposition allows us to solve problems that involve rational expressions more easily. It also helps us to identify and understand the behavior of complex functions.
To perform Partial Fraction Decomposition, you first need to factor the denominator of the rational expression. Then, you write the partial fraction decomposition in the form A/(x-a) + B/(x-b) + ... where A, B, etc. are constants to be determined. You can use various methods such as equating coefficients or the cover-up method to determine the values of the constants.
There are three types of Partial Fraction Decomposition: proper, improper, and mixed. In proper decomposition, the degree of the numerator is less than the degree of the denominator. In improper decomposition, the degree of the numerator is equal to or greater than the degree of the denominator. In mixed decomposition, the rational expression has both proper and improper terms.
Partial Fraction Decomposition is used in various fields of science and engineering, including physics, chemistry, and electrical engineering. It is particularly useful in solving differential equations, evaluating integrals, and simplifying complex mathematical expressions.