{"id":815,"date":"2020-02-09T21:19:43","date_gmt":"2020-02-09T21:19:43","guid":{"rendered":"https:\/\/tutorials.retopall.com\/?p=815"},"modified":"2020-10-28T09:16:09","modified_gmt":"2020-10-28T09:16:09","slug":"taylor-series-visualization","status":"publish","type":"post","link":"https:\/\/tutorials.retopall.com\/index.php\/2020\/02\/09\/taylor-series-visualization\/","title":{"rendered":"Taylor series visualization"},"content":{"rendered":"\n

Taylor series is a representation of a function as an infinite sum of a polynomial expression. These series are really helpful for programming because of the complexity of different functions. Consequently, is really helpful in terms of optimization and also gives a really good approximation of a function.<\/p>\n\n\n\n

Taylor series of a function $f(x)$ centered in a is:<\/p>\n\n\n\n

$ f(x)=P(a)=\\displaystyle\\sum_{n=0}^{\\infty} \\frac{f^{(n)}(a)}{n!}(x-a)^n $<\/p>\n\n\n\n

However, computers can’t do an infinit sum so the taylor series will be an aproximation of a determined function <\/p>\n\n\n\n

$ f(x) \\approx P(a,n)=f(a)+f'(a)(x-a)+\\frac{f”(a)}{2}(x-1)^2+…+\\frac{f^{(n)}}{n!}(x-1)^n \\quad n\\in{ \\mathbb{N}}$ <\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

When $a=0$ the series are called Mac-Laurin series<\/p>\n\n\n\n

It’s also very important to manage the error of the taylor series and we can calculate it with the Lagrange theorem where $b$ is the x point we want to calculate the error<\/p>\n\n\n\n

$|ERROR|\\leq sup{\\frac{f(c)^{(n+1)}}{(n+1)!}(b-a)^n} \\quad c\\in(a,b)$<\/p>\n\n\n\n

I have developed a simulation about the taylor series where you can visualize the taylor series of different function such as cosine, sine, logarithm and exponential.<\/p>\n\n\n\n

\n
Taylor series visualization<\/strong><\/span><\/a><\/div>\n<\/div>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Taylor series is a representation of a function as an infinite sum of a polynomial expression. These series are really helpful for programming because of […]<\/p>\n","protected":false},"author":1,"featured_media":817,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,4,10,6],"tags":[128,127],"class_list":["post-815","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","category-programming","category-simulation","category-tutorial","tag-lagrange-theorem","tag-taylor-series"],"_links":{"self":[{"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/posts\/815","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/comments?post=815"}],"version-history":[{"count":27,"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/posts\/815\/revisions"}],"predecessor-version":[{"id":1003,"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/posts\/815\/revisions\/1003"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/media\/817"}],"wp:attachment":[{"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/media?parent=815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/categories?post=815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tutorials.retopall.com\/index.php\/wp-json\/wp\/v2\/tags?post=815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}