# complex analysis

Published articles for complex analysis.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## The Fourier Series--A Primer

DevFeed: [The Fourier Series--A Primer](<https://devfeed.tech/articles/the-fourier-series-a-primer-40271.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/04/25/the-fourier-series/>)

Published: 2012-04-25T21:43:06Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [function](<https://devfeed.tech/topics/function.md>)

Tags: [analysis](<https://devfeed.tech/tags/analysis.md>), [classification](<https://devfeed.tech/tags/classification.md>), [complex-analysis](<https://devfeed.tech/tags/complex-analysis.md>), [foundation](<https://devfeed.tech/tags/foundation.md>), [fourier-analysis](<https://devfeed.tech/tags/fourier-analysis.md>), [heat-equation](<https://devfeed.tech/tags/heat-equation.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [orthogonality](<https://devfeed.tech/tags/orthogonality.md>), [primer](<https://devfeed.tech/tags/primer.md>)

### AI overview

This primer introduces the mathematics of Fourier series, beginning with periodic functions and explaining how sine and cosine functions serve as building blocks for representing functions. It establishes foundational concepts for later work involving Fourier transforms, sound and image analysis, classification, and machine vision.

### Source excerpt

Overview In this primer we'll get a first taste of the mathematics that goes into the analysis of sound and images. In the next few primers, we'll be building the foundation for a number of projects in this domain: extracting features of music for classification, constructing so-called hybrid images, and other image manipulations for machine vision problems (for instance, for use in neural networks or support vector machines; we're planning on covering these topics in due time as well).

## Fundamental Theorem of Algebra (With Picard's Little Theorem)

DevFeed: [Fundamental Theorem of Algebra (With Picard's Little Theorem)](<https://devfeed.tech/articles/fundamental-theorem-of-algebra-with-picard-s-little-theorem-40261.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/02/07/fundamental-theorem-of-algebra-with-picards-little-theorem/>)

Published: 2012-02-07T21:30:12Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>)

Tags: [complex-analysis](<https://devfeed.tech/tags/complex-analysis.md>), [fundamental-theorem-of-algebra](<https://devfeed.tech/tags/fundamental-theorem-of-algebra.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>)

### AI overview

This post proves the Fundamental Theorem of Algebra using Picard's Little Theorem. Assuming basic complex analysis, it argues that a nonconstant polynomial cannot omit both zero and a suitable reciprocal value, because continuity and boundedness would force a zero.

### Source excerpt

This post assumes familiarity with some basic concepts in complex analysis, including continuity and entire (everywhere complex-differentiable) functions. This is likely the simplest proof of the theorem (at least, among those that this author has seen), although it stands on the shoulders of a highly nontrivial theorem. The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way.