🕷️ Crawler Inspector

URL Lookup

Direct Parameter Lookup

Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 77 (from laksa044)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa077.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://medium.com/the-mathsy-way/using-laplace-transforms-f8148e0e6986\')), getAhrefsUnparsedNoserviceFromURL(\'https://medium.com/the-mathsy-way/using-laplace-transforms-f8148e0e6986\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/medium.com\/the-mathsy-way\/using-laplace-transforms-f8148e0e6986","crawl_time":1755350066,"first_indexed_time":0,"http_code":200,"src_unparsed":"com,medium!\/the-mathsy-way\/using-laplace-transforms-f8148e0e6986 s443","src_root_hash":"13179037029838926277","history_drop_reason":null,"meta_title":"Using Laplace Transforms. What are Laplace transforms and how do… | by William Keens | The Mathsy Way | Medium","meta_descriptions":["Laplace transforms are an amazing tool that you need in your arsenal for solving differential equations. They are a foolproof way of solving for the solution and allow you to bypass all wasted time…"],"attrs_boilerpipe_text":"Photo by  Michael Dziedzic  on  Unsplash Laplace transforms are an amazing tool that you need in your arsenal for solving differential equations. They are a foolproof way of solving for the solution and allow you to bypass all wasted time in trying to guess a solution to any random equation. Here it is: Laplace transform equation ( made with Latex ) It works by enabling you to convert differential equations into algebraic equations that we know how to solve. This transform from what is known as t-space to s-space allows us to then reverse the process to find the general solution equation. (We also often use just the capital letter to mean the Laplace transform of a given function which you may see later) Let’s see how it can be used to turn a derivative of a function into an algebraic expression involving it. Laplace of derivative ( made with Latex ) Solution of derivative, when transformed ( made with Latex ) Now this may be a lot to unpack if you are not used to it, but I shall try to explain. First, we use integration by parts to get y(x) on its own inside the integral with no other factors of the given function. The just by simplifying we can see that this integral is s multiplied by the Laplace transform of y(x). This gives us a general rule: Derivative rule ( made with Latex ) Now there is only one thing to see before we get started on our first differential equation. What are some Laplace transforms?","attrs_markdown":"[Sitemap](https:\/\/medium.com\/sitemap\/sitemap.xml)\n\n[Open in app](https:\/\/rsci.app.link\/?%24canonical_url=https%3A%2F%2Fmedium.com%2Fp%2Ff8148e0e6986&~feature=LoOpenInAppButton&~channel=ShowPostUnderCollection&~stage=mobileNavBar&source=post_page---top_nav_layout_nav-----------------------------------------)\n\nSign up\n\n[Sign in](https:\/\/medium.com\/m\/signin?operation=login&redirect=https%3A%2F%2Fmedium.com%2Fthe-mathsy-way%2Fusing-laplace-transforms-f8148e0e6986&source=post_page---top_nav_layout_nav-----------------------global_nav------------------)\n\n[Medium Logo](https:\/\/medium.com\/?source=post_page---top_nav_layout_nav-----------------------------------------)\n\n[Write](https:\/\/medium.com\/m\/signin?operation=register&redirect=https%3A%2F%2Fmedium.com%2Fnew-story&source=---top_nav_layout_nav-----------------------new_post_topnav------------------)\n\nSign up\n\n[Sign in](https:\/\/medium.com\/m\/signin?operation=login&redirect=https%3A%2F%2Fmedium.com%2Fthe-mathsy-way%2Fusing-laplace-transforms-f8148e0e6986&source=post_page---top_nav_layout_nav-----------------------global_nav------------------)\n\n![](https:\/\/miro.medium.com\/v2\/resize:fill:64:64\/1*dmbNkD5D-u45r44go_cf0g.png)\n\n[The Mathsy Way](https:\/\/medium.com\/the-mathsy-way?source=post_page---publication_nav-c5c2f93fae70-f8148e0e6986---------------------------------------)\n\n·\n\n[![The Mathsy Way](https:\/\/miro.medium.com\/v2\/resize:fill:76:76\/1*0LSRHPPAHLgm4lZTDMYzTQ.png)](https:\/\/medium.com\/the-mathsy-way?source=post_page---post_publication_sidebar-c5c2f93fae70-f8148e0e6986---------------------------------------)\n\nMaths Concepts explained simply.\n\n# Using Laplace Transforms\n[![William Keens](https:\/\/miro.medium.com\/v2\/resize:fill:64:64\/1*WWjR7GqHyjSVCcZIGbucog.png)](https:\/\/medium.com\/@william-k?source=post_page---byline--f8148e0e6986---------------------------------------)\n\n[William Keens](https:\/\/medium.com\/@william-k?source=post_page---byline--f8148e0e6986---------------------------------------)\n\n4 min read\n\n·\n\nJun 28, 2023\n\n\\--\n\nListen\n\nShare\n\nPress enter or click to view image in full size\n\n![]()\n\nPhoto by [Michael Dziedzic](https:\/\/unsplash.com\/@lazycreekimages?utm_source=medium&utm_medium=referral) on [Unsplash](https:\/\/unsplash.com\/?utm_source=medium&utm_medium=referral)\n\nLaplace transforms are an amazing tool that you need in your arsenal for solving differential equations. They are a foolproof way of solving for the solution and allow you to bypass all wasted time in trying to guess a solution to any random equation. Here it is:\n\n![]()\n\nLaplace transform equation ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nIt works by enabling you to convert differential equations into algebraic equations that we know how to solve. This transform from what is known as t-space to s-space allows us to then reverse the process to find the general solution equation. (We also often use just the capital letter to mean the Laplace transform of a given function which you may see later)\n\nLet’s see how it can be used to turn a derivative of a function into an algebraic expression involving it.\n\n![]()\n\nLaplace of derivative ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nPress enter or click to view image in full size\n\n![]()\n\nSolution of derivative, when transformed ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nNow this may be a lot to unpack if you are not used to it, but I shall try to explain.\n\n1. First, we use integration by parts to get y(x) on its own inside the integral with no other factors of the given function.\n2. The just by simplifying we can see that this integral is s multiplied by the Laplace transform of y(x).\n\nThis gives us a general rule:\n\n![]()\n\nDerivative rule ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nNow there is only one thing to see before we get started on our first differential equation. What are some Laplace transforms?\n\n# **1\\) Constant**\n![]()\n\nConstant rule ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\n# 2\\) Exponential\n![]()\n\nExponential Rule ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nIf you want to get more examples please consult the Wikipedia page on this very topic\n\n> <https:\/\/en.wikipedia.org\/wiki\/Laplace_transform#Table_of_selected_Laplace_transforms>\n\nNow we are ready to tackle our first equation\\!\n\n# Solving a Differential Equation\nWe shall start out with this equation below.\n\n![]()\n\n1st Order ODE ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nNow as we have done before we can take the Laplace transform of this equation. Now due to the fact the Laplace transform is an Integral it has a nice property that we can split all things added inside it into added outside the Function.\n\n![]()\n\nLaplace of everything ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nNow we have learnt all of these and can evaluate this expression.\n\n![]()\n\nEvaluate it ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nThis expression can now be rearranged to find Y(s).\n\n![]()\n\nSimplify ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\n![]()\n\nSimplify further ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nPress enter or click to view image in full size\n\n![]()\n\nPartial fractions ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nHere now that we have a ‘nice’ expression for Y(s) we can perform the inverse Laplace transform by pattern spotting.\n\n![]()\n\nInverse Laplace transform ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\n![]()\n\nEvaluated the ODE ([made with Latex](https:\/\/latexeditor.lagrida.com\/))\n\nAnd by that we have solved the equation.\n\nIf you would like to learn more about Laplace Transforms, I would extremely encourage you to do your own research and find whatever quirky equation floats your boat and as always.\n\nHave fun and never stop solving.\n\n[5 Laplace Transforms with Solutions A Guide to how to evaluate different Laplace Transforms. william-k.medium.com](https:\/\/william-k.medium.com\/5-laplace-transforms-with-solutions-92722efebf77?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Piecewise Laplace Transforms The Lego Bricks of the maths world medium.com](https:\/\/medium.com\/the-mathsy-way\/piecewise-laplace-transforms-c6ece20e27c2?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Differential Equations](https:\/\/medium.com\/tag\/differential-equations?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Laplace Transforms](https:\/\/medium.com\/tag\/laplace-transforms?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Mathematics](https:\/\/medium.com\/tag\/mathematics?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Laplace](https:\/\/medium.com\/tag\/laplace?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Calculus](https:\/\/medium.com\/tag\/calculus?source=post_page-----f8148e0e6986---------------------------------------)\n\n\\--\n\n\\--\n\n[![The Mathsy Way](https:\/\/miro.medium.com\/v2\/resize:fill:96:96\/1*0LSRHPPAHLgm4lZTDMYzTQ.png)](https:\/\/medium.com\/the-mathsy-way?source=post_page---post_publication_info--f8148e0e6986---------------------------------------)\n\n[![The Mathsy Way](https:\/\/miro.medium.com\/v2\/resize:fill:128:128\/1*0LSRHPPAHLgm4lZTDMYzTQ.png)](https:\/\/medium.com\/the-mathsy-way?source=post_page---post_publication_info--f8148e0e6986---------------------------------------)\n\n[Published in The Mathsy Way](https:\/\/medium.com\/the-mathsy-way?source=post_page---post_publication_info--f8148e0e6986---------------------------------------)\n\n[82 followers](https:\/\/medium.com\/the-mathsy-way\/followers?source=post_page---post_publication_info--f8148e0e6986---------------------------------------)\n\n·[Last published Jun 15, 2025](https:\/\/medium.com\/the-mathsy-way\/crack-the-code-of-optimization-simplex-method-for-students-and-analysts-9d45c62ec0c3?source=post_page---post_publication_info--f8148e0e6986---------------------------------------)\n\nMaths Concepts explained simply.\n\n[![William Keens](https:\/\/miro.medium.com\/v2\/resize:fill:96:96\/1*WWjR7GqHyjSVCcZIGbucog.png)](https:\/\/medium.com\/@william-k?source=post_page---post_author_info--f8148e0e6986---------------------------------------)\n\n[![William Keens](https:\/\/miro.medium.com\/v2\/resize:fill:128:128\/1*WWjR7GqHyjSVCcZIGbucog.png)](https:\/\/medium.com\/@william-k?source=post_page---post_author_info--f8148e0e6986---------------------------------------)\n\n[Written by William Keens](https:\/\/medium.com\/@william-k?source=post_page---post_author_info--f8148e0e6986---------------------------------------)\n\n[1\\.2K followers](https:\/\/medium.com\/@william-k\/followers?source=post_page---post_author_info--f8148e0e6986---------------------------------------)\n\n·[31 following](https:\/\/medium.com\/@william-k\/following?source=post_page---post_author_info--f8148e0e6986---------------------------------------)\n\nI have three Passions : Maths, Maths, Maths. Are these yours?\n## No responses yet\n[Help](https:\/\/help.medium.com\/hc\/en-us?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Status](https:\/\/medium.statuspage.io\/?source=post_page-----f8148e0e6986---------------------------------------)\n\n[About](https:\/\/medium.com\/about?autoplay=1&source=post_page-----f8148e0e6986---------------------------------------)\n\n[Careers](https:\/\/medium.com\/jobs-at-medium\/work-at-medium-959d1a85284e?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Press](mailto:pressinquiries@medium.com)\n\n[Blog](https:\/\/blog.medium.com\/?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Privacy](https:\/\/policy.medium.com\/medium-privacy-policy-f03bf92035c9?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Rules](https:\/\/policy.medium.com\/medium-rules-30e5502c4eb4?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Terms](https:\/\/policy.medium.com\/medium-terms-of-service-9db0094a1e0f?source=post_page-----f8148e0e6986---------------------------------------)\n\n[Text to speech](https:\/\/speechify.com\/medium?source=post_page-----f8148e0e6986---------------------------------------)","attrs_readable_markdown":null,"meta_canonical":null}

3. Robots.txt Check

Query:

Response:

4. Spam/Ban Check

Query:

Response:

5. Seen Status Check

ℹ️ Skipped - page is already crawled

🚫

NOT INDEXABLE

✅

CRAWLED

8 months ago

🤖

ROBOTS ALLOWED

Page Info Filters

Filter	Status	Condition	Details
HTTP status	PASS	`download_http_code = 200`	HTTP 200
Age cutoff	FAIL	`download_stamp > now() - 6 MONTH`	8.1 months ago
History drop	PASS	`isNull(history_drop_reason)`	No drop reason
Spam/ban	PASS	`fh_dont_index != 1 AND ml_spam_score = 0`	ml_spam_score=0
Canonical	PASS	`meta_canonical IS NULL OR = '' OR = src_unparsed`	Not set

Page Details

Property	Value
URL	https://medium.com/the-mathsy-way/using-laplace-transforms-f8148e0e6986
Last Crawled	2025-08-16 13:14:26 (8 months ago)
First Indexed	not set
HTTP Status Code	200
Meta Title	Using Laplace Transforms. What are Laplace transforms and how do… \| by William Keens \| The Mathsy Way \| Medium
Meta Description	Laplace transforms are an amazing tool that you need in your arsenal for solving differential equations. They are a foolproof way of solving for the solution and allow you to bypass all wasted time…
Meta Canonical	null
Boilerpipe Text	Photo by Michael Dziedzic on Unsplash Laplace transforms are an amazing tool that you need in your arsenal for solving differential equations. They are a foolproof way of solving for the solution and allow you to bypass all wasted time in trying to guess a solution to any random equation. Here it is: Laplace transform equation ( made with Latex ) It works by enabling you to convert differential equations into algebraic equations that we know how to solve. This transform from what is known as t-space to s-space allows us to then reverse the process to find the general solution equation. (We also often use just the capital letter to mean the Laplace transform of a given function which you may see later) Let’s see how it can be used to turn a derivative of a function into an algebraic expression involving it. Laplace of derivative ( made with Latex ) Solution of derivative, when transformed ( made with Latex ) Now this may be a lot to unpack if you are not used to it, but I shall try to explain. First, we use integration by parts to get y(x) on its own inside the integral with no other factors of the given function. The just by simplifying we can see that this integral is s multiplied by the Laplace transform of y(x). This gives us a general rule: Derivative rule ( made with Latex ) Now there is only one thing to see before we get started on our first differential equation. What are some Laplace transforms?
Markdown	[Sitemap](https://medium.com/sitemap/sitemap.xml) [Open in app](https://rsci.app.link/?%24canonical_url=https%3A%2F%2Fmedium.com%2Fp%2Ff8148e0e6986&~feature=LoOpenInAppButton&~channel=ShowPostUnderCollection&~stage=mobileNavBar&source=post_page---top_nav_layout_nav-----------------------------------------) Sign up [Sign in](https://medium.com/m/signin?operation=login&redirect=https%3A%2F%2Fmedium.com%2Fthe-mathsy-way%2Fusing-laplace-transforms-f8148e0e6986&source=post_page---top_nav_layout_nav-----------------------global_nav------------------) [Medium Logo](https://medium.com/?source=post_page---top_nav_layout_nav-----------------------------------------) [Write](https://medium.com/m/signin?operation=register&redirect=https%3A%2F%2Fmedium.com%2Fnew-story&source=---top_nav_layout_nav-----------------------new_post_topnav------------------) Sign up [Sign in](https://medium.com/m/signin?operation=login&redirect=https%3A%2F%2Fmedium.com%2Fthe-mathsy-way%2Fusing-laplace-transforms-f8148e0e6986&source=post_page---top_nav_layout_nav-----------------------global_nav------------------) ![](https://miro.medium.com/v2/resize:fill:64:64/1dmbNkD5D-u45r44go_cf0g.png) [The Mathsy Way](https://medium.com/the-mathsy-way?source=post_page---publication_nav-c5c2f93fae70-f8148e0e6986---------------------------------------) · [![The Mathsy Way](https://miro.medium.com/v2/resize:fill:76:76/10LSRHPPAHLgm4lZTDMYzTQ.png)](https://medium.com/the-mathsy-way?source=post_page---post_publication_sidebar-c5c2f93fae70-f8148e0e6986---------------------------------------) Maths Concepts explained simply. # Using Laplace Transforms [![William Keens](https://miro.medium.com/v2/resize:fill:64:64/1WWjR7GqHyjSVCcZIGbucog.png)](https://medium.com/@william-k?source=post_page---byline--f8148e0e6986---------------------------------------) [William Keens](https://medium.com/@william-k?source=post_page---byline--f8148e0e6986---------------------------------------) 4 min read · Jun 28, 2023 \-- Listen Share Press enter or click to view image in full size ![]() Photo by [Michael Dziedzic](https://unsplash.com/@lazycreekimages?utm_source=medium&utm_medium=referral) on [Unsplash](https://unsplash.com/?utm_source=medium&utm_medium=referral) Laplace transforms are an amazing tool that you need in your arsenal for solving differential equations. They are a foolproof way of solving for the solution and allow you to bypass all wasted time in trying to guess a solution to any random equation. Here it is: ![]() Laplace transform equation ([made with Latex](https://latexeditor.lagrida.com/)) It works by enabling you to convert differential equations into algebraic equations that we know how to solve. This transform from what is known as t-space to s-space allows us to then reverse the process to find the general solution equation. (We also often use just the capital letter to mean the Laplace transform of a given function which you may see later) Let’s see how it can be used to turn a derivative of a function into an algebraic expression involving it. ![]() Laplace of derivative ([made with Latex](https://latexeditor.lagrida.com/)) Press enter or click to view image in full size ![]() Solution of derivative, when transformed ([made with Latex](https://latexeditor.lagrida.com/)) Now this may be a lot to unpack if you are not used to it, but I shall try to explain. 1. First, we use integration by parts to get y(x) on its own inside the integral with no other factors of the given function. 2. The just by simplifying we can see that this integral is s multiplied by the Laplace transform of y(x). This gives us a general rule: ![]() Derivative rule ([made with Latex](https://latexeditor.lagrida.com/)) Now there is only one thing to see before we get started on our first differential equation. What are some Laplace transforms? # 1\) Constant* ![]() Constant rule ([made with Latex](https://latexeditor.lagrida.com/)) # 2\) Exponential ![]() Exponential Rule ([made with Latex](https://latexeditor.lagrida.com/)) If you want to get more examples please consult the Wikipedia page on this very topic > <https://en.wikipedia.org/wiki/Laplace_transform#Table_of_selected_Laplace_transforms> Now we are ready to tackle our first equation\! # Solving a Differential Equation We shall start out with this equation below. ![]() 1st Order ODE ([made with Latex](https://latexeditor.lagrida.com/)) Now as we have done before we can take the Laplace transform of this equation. Now due to the fact the Laplace transform is an Integral it has a nice property that we can split all things added inside it into added outside the Function. ![]() Laplace of everything ([made with Latex](https://latexeditor.lagrida.com/)) Now we have learnt all of these and can evaluate this expression. ![]() Evaluate it ([made with Latex](https://latexeditor.lagrida.com/)) This expression can now be rearranged to find Y(s). ![]() Simplify ([made with Latex](https://latexeditor.lagrida.com/)) ![]() Simplify further ([made with Latex](https://latexeditor.lagrida.com/)) Press enter or click to view image in full size ![]() Partial fractions ([made with Latex](https://latexeditor.lagrida.com/)) Here now that we have a ‘nice’ expression for Y(s) we can perform the inverse Laplace transform by pattern spotting. ![]() Inverse Laplace transform ([made with Latex](https://latexeditor.lagrida.com/)) ![]() Evaluated the ODE ([made with Latex](https://latexeditor.lagrida.com/)) And by that we have solved the equation. If you would like to learn more about Laplace Transforms, I would extremely encourage you to do your own research and find whatever quirky equation floats your boat and as always. Have fun and never stop solving. [5 Laplace Transforms with Solutions A Guide to how to evaluate different Laplace Transforms. william-k.medium.com](https://william-k.medium.com/5-laplace-transforms-with-solutions-92722efebf77?source=post_page-----f8148e0e6986---------------------------------------) [Piecewise Laplace Transforms The Lego Bricks of the maths world medium.com](https://medium.com/the-mathsy-way/piecewise-laplace-transforms-c6ece20e27c2?source=post_page-----f8148e0e6986---------------------------------------) [Differential Equations](https://medium.com/tag/differential-equations?source=post_page-----f8148e0e6986---------------------------------------) [Laplace Transforms](https://medium.com/tag/laplace-transforms?source=post_page-----f8148e0e6986---------------------------------------) [Mathematics](https://medium.com/tag/mathematics?source=post_page-----f8148e0e6986---------------------------------------) [Laplace](https://medium.com/tag/laplace?source=post_page-----f8148e0e6986---------------------------------------) [Calculus](https://medium.com/tag/calculus?source=post_page-----f8148e0e6986---------------------------------------) \-- \-- [![The Mathsy Way](https://miro.medium.com/v2/resize:fill:96:96/10LSRHPPAHLgm4lZTDMYzTQ.png)](https://medium.com/the-mathsy-way?source=post_page---post_publication_info--f8148e0e6986---------------------------------------) [![The Mathsy Way](https://miro.medium.com/v2/resize:fill:128:128/10LSRHPPAHLgm4lZTDMYzTQ.png)](https://medium.com/the-mathsy-way?source=post_page---post_publication_info--f8148e0e6986---------------------------------------) [Published in The Mathsy Way](https://medium.com/the-mathsy-way?source=post_page---post_publication_info--f8148e0e6986---------------------------------------) [82 followers](https://medium.com/the-mathsy-way/followers?source=post_page---post_publication_info--f8148e0e6986---------------------------------------) ·[Last published Jun 15, 2025](https://medium.com/the-mathsy-way/crack-the-code-of-optimization-simplex-method-for-students-and-analysts-9d45c62ec0c3?source=post_page---post_publication_info--f8148e0e6986---------------------------------------) Maths Concepts explained simply. [![William Keens](https://miro.medium.com/v2/resize:fill:96:96/1WWjR7GqHyjSVCcZIGbucog.png)](https://medium.com/@william-k?source=post_page---post_author_info--f8148e0e6986---------------------------------------) [![William Keens](https://miro.medium.com/v2/resize:fill:128:128/1WWjR7GqHyjSVCcZIGbucog.png)](https://medium.com/@william-k?source=post_page---post_author_info--f8148e0e6986---------------------------------------) [Written by William Keens](https://medium.com/@william-k?source=post_page---post_author_info--f8148e0e6986---------------------------------------) [1\.2K followers](https://medium.com/@william-k/followers?source=post_page---post_author_info--f8148e0e6986---------------------------------------) ·[31 following](https://medium.com/@william-k/following?source=post_page---post_author_info--f8148e0e6986---------------------------------------) I have three Passions : Maths, Maths, Maths. Are these yours? ## No responses yet [Help](https://help.medium.com/hc/en-us?source=post_page-----f8148e0e6986---------------------------------------) [Status](https://medium.statuspage.io/?source=post_page-----f8148e0e6986---------------------------------------) [About](https://medium.com/about?autoplay=1&source=post_page-----f8148e0e6986---------------------------------------) [Careers](https://medium.com/jobs-at-medium/work-at-medium-959d1a85284e?source=post_page-----f8148e0e6986---------------------------------------) [Press](mailto:pressinquiries@medium.com) [Blog](https://blog.medium.com/?source=post_page-----f8148e0e6986---------------------------------------) [Privacy](https://policy.medium.com/medium-privacy-policy-f03bf92035c9?source=post_page-----f8148e0e6986---------------------------------------) [Rules](https://policy.medium.com/medium-rules-30e5502c4eb4?source=post_page-----f8148e0e6986---------------------------------------) [Terms](https://policy.medium.com/medium-terms-of-service-9db0094a1e0f?source=post_page-----f8148e0e6986---------------------------------------) [Text to speech](https://speechify.com/medium?source=post_page-----f8148e0e6986---------------------------------------)
Readable Markdown	null
Shard	77 (laksa)
Root Hash	13179037029838926277
Unparsed URL	com,medium!/the-mathsy-way/using-laplace-transforms-f8148e0e6986 s443