{"id":7719,"date":"2012-12-17T11:46:56","date_gmt":"2012-12-17T03:46:56","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=7719"},"modified":"2012-12-20T16:10:30","modified_gmt":"2012-12-20T08:10:30","slug":"fourier-series-interactive-graph","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/fourier-series-interactive-graph-7719","title":{"rendered":"Fourier Series interactive graph"},"content":{"rendered":"

I recently developed an interactive Fourier Series graph<\/a> that demonstrates how the series works.<\/p>\n

Fourier Series are used in various branches of engineering to solve problems involving heat, acoustics, image processing and optics. <\/p>\n

The basic idea of a Fourier Series is that we can decompose a periodic function into the sum of simpler sine and cosine curves. This was quite a revolutionary idea when French mathematician Jean-Baptiste Joseph Fourier proposed it as a solution for the heat equation in the early 19th century. His practical problem involved determining how heat is distributed through a metal plate. <\/p>\n

\"Fourier
\nStill image from interactive:
\nFourier Series terms (in pink) and resulting sum (in blue)<\/p>\n

We obtain the terms in the Fourier Series using integration. You can see the processes involved and some examples on this page: Full Range Fourier Series<\/a>. <\/p>\n

The interactive graph shows how the individual terms in the series (the sine or cosine graphs) and the result of adding those terms to some fundamental constant value.<\/p>\n

The interactive includes 3 different Fourier Series examples. <\/p>\n

Geek info<\/h2>\n

I used JXSGraph<\/a> to draw the graph, MathJax<\/a> for the equations, and stitched it together using jQuery<\/a> and other javascript.<\/p>\n

The link again: Interactive Fourier Series graph<\/a><\/p>\n

See the 2 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"

\"Fourier<\/a>
\n Here's an interactive graph that allows you to explore the concepts behind the Fourier Series.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[134,127],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/7719"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=7719"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/7719\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=7719"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=7719"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=7719"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}