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I am currently taking an Engineering course (differential equations), in which the concept of "Residue" has been introduced. Having missed part of the lecture, and reviewed both the class textbook (no help) and my Anton Bivens Calculus book, I have found almost no information on how to actually calculate the residue with regards to a differential equation, nor what the resulting equation (minus the residue) would look like. A Google search has been aggravating, and the Differential Equations for Dummies book I purchased does not appear to make any mention of this method either.

Could anyone explain, or point me to some idiot-level lecture notes to help explain this concept to me?

Regards, -R

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The word "residue" is typically associated with complex analysis. You would not normally find it in an ODE text. Calculation of residues would be explained in a complex analysis text in connection with evaluating integrals. –  daniel Nov 15 '11 at 10:36

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The residues typically appear when you solve the differential equations via Laplace Transformation. You can take a look at the video lectures of Arthur Mattuck for a neat introduction to the subject. If I remember correctly the relevant part starts from Lecture 19.

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