Partial fraction expansion

In summary, partial fraction expansion is a method used in mathematics to decompose a rational function into simpler fractions, commonly used in calculus and other areas of mathematics. It involves breaking down a rational function into simpler fractions with distinct denominators and has benefits such as simplifying complex functions and identifying individual components. However, it can only be used for rational functions with certain limitations.
  • #1
xzibition8612
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Homework Statement



I'm taking the Laplace transform of F(s), and the first thing is to expand it by partial fraction or something so that I can match F(s) with a table of laplace transforms.

Homework Equations





The Attempt at a Solution


Does partial fraction even work? I've got two variables s and w so I doubt it. How do I do this? Just brute force trying to factor it out or something?
 

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  • #2
Your fractions should be for the form A/s + B/s^2 + [Cs+D]/(s^2+w^2)
 

1. What is partial fraction expansion?

Partial fraction expansion is a method used in mathematics to decompose a rational function into simpler fractions. This method is particularly useful for integration, as it allows us to break down complex functions into smaller, more manageable parts.

2. When is partial fraction expansion used?

Partial fraction expansion is commonly used in calculus, particularly in the integration of rational functions. It is also used in other areas of mathematics, such as in solving systems of linear equations or in finding the inverse Laplace transform of a function.

3. How is partial fraction expansion done?

The process of partial fraction expansion involves breaking down a rational function into simpler fractions with distinct denominators. This is accomplished by using algebraic manipulation and solving for the coefficients of the simpler fractions.

4. What are the benefits of using partial fraction expansion?

Partial fraction expansion allows us to simplify complex functions and make them easier to integrate. It also helps us to identify and understand the individual components of a function, which can be useful in further analysis or applications.

5. Are there any limitations to partial fraction expansion?

Partial fraction expansion can only be used for rational functions, which are functions with polynomial expressions in both the numerator and denominator. It also requires that the degree of the numerator is less than the degree of the denominator. Additionally, it may not always be possible to fully decompose a rational function into simpler fractions, especially if it has repeated or complex roots.

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