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# 12: Argument Principle

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The argument principle (or principle of the argument) is a consequence of the residue theorem. It connects the winding number of a curve with the number of zeros and poles inside the curve. This is useful for applications (mathematical and otherwise) where we want to know the location of zeros and poles.

• 12.1: Principle of the Argument
• 12.2: Nyquist Criterion for Stability
The Nyquist criterion is a graphical technique for telling whether an unstable linear time invariant system can be stabilized using a negative feedback loop. We will look a little more closely at such systems when we study the Laplace transform in the next topic. For this topic we will content ourselves with a statement of the problem with only the tiniest bit of physical context.
• 12.3: A Bit on Negative Feedback
In a negative feedback loop the output of the system is looped back and subtracted from the input.

12: Argument Principle is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jeremy Orloff via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.