Proof of a partial fraction theorem

In summary, The conversation is about someone looking for a proof of a theorem called the "Heaviside method" which involves partial fractions and integration. They have been searching for it online but have been unable to find it. They ask for someone to show them a proof or provide a link to it. Another person responds by asking for clarification on which specific proof they are looking for and suggests that if they need it for class, they should try to prove it themselves. The conversation ends with the suggestion to prove that the algorithm works as advertised.
  • #1
Kinsama
4
0
I've been looking all over the net since yesterday for a PROOF of a theorem called the "heaviside method" it involves partial fractions and itegration of such. If anyone could show me a proof of it or send me a link of it I would gladly appreciate it, thanks!
 
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  • #2
Of what, specifically, do you want a proof?

P.S. if you have an algorithm that does something, that is a proof that you can do that something.
 
  • #3
i want a proof of a theorem called the Heaviside Method, my book tells how to do it, but i need a proof of it for class and its almost impossible to find.
 
  • #4
Well, if you need it for class, shouldn't you prove it yourself? :-p And I don't even know the theorem you're trying to prove -- I can find references to the algorithm called "Heaviside's method", but you can't prove an algorithm. (The very idea is nonsensical)

My best guess is that you want a proof that the algorithm works as advertised, and I've already given you a hint: just prove that the output of the algorithm is what it claims to be
 

FAQ: Proof of a partial fraction theorem

What is the partial fraction theorem?

The partial fraction theorem is a mathematical concept that states that any rational function can be expressed as a sum of simpler fractions, called partial fractions. This theorem is often used in calculus and algebra to simplify complex expressions.

How is the partial fraction theorem used in mathematics?

The partial fraction theorem is used to simplify complex rational expressions, making it easier to work with them in mathematical calculations. It is also used to solve integrals and to find the roots of polynomials.

Can you provide an example of using the partial fraction theorem?

Sure, let's say we have the rational function f(x) = (x+2)/(x^2+3x+2). Using the partial fraction theorem, we can express this as f(x) = A/(x+1) + B/(x+2), where A and B are constants. This makes it easier to integrate or find the inverse of f(x).

Are there any limitations to the partial fraction theorem?

Yes, the partial fraction theorem can only be applied to rational functions, which are functions where the numerator and denominator are polynomials. It also assumes that the denominator can be factored into linear and irreducible quadratic factors.

How is the partial fraction theorem related to other mathematical concepts?

The partial fraction theorem is closely related to the concept of factorization in algebra. It is also used in conjunction with integration techniques such as substitution and u-substitution. Additionally, it is related to other theorems in calculus, such as the Cauchy residue theorem and the Cauchy integral theorem.

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