MATH 1007 Lecture Notes - Lecture 19: Partial Fraction Decomposition, Lincoln Near-Earth Asteroid Research
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6 Apr 2016
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Integraion by parial fracion is a method of integraing raional funcions of the form f(x) = p(x)/q(x) , where p and q are polynomials. We will be doint things like: (5x + 2)/(3x^2 + 5x + 7) If the degree of p is less than the degree of q, then f is called proper" and it is possible to express f as a sum of simpler funcion. If instead, the degree of p is greater or equal to the degree of q, then f is called improper". Then we use per form long division. Divide q into p to get a quoient s(x) and a remainder r(x) with degree r < degree q f(x) = p(x)/q(x) = s(x) + [r(x)/q(x)] There are diferent cases of quesions we could also: when the denominator q(x) is a product of distinct linear factors, ex: (ax + b)(cx + d, not! (ax + b)2(cx + d)
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