explain xkcd - User contributions [en]

2117: Differentiation and Integration

2019-02-27T19:24:19Z

Ozmandias42: /* Integration */

{{comic
| number = 2117
| date = February 27, 2019
| title = Differentiation and Integration
| image = differentiation_and_integration.png
| titletext = "Symbolic integration" is when you theatrically go through the motions of finding integrals, but the actual result you get doesn't matter because it's purely symbolic.
}}

==Explanation==
{{incomplete|Created by a BESSEL FUNCTION? Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
This comic provides a {{w|flowchart}} purporting to show the process of differentiation, and another for integration.

{{w|Derivative|Differentiation}} and {{w|Antiderivative|Integration}} are two major components of {{w|calculus}}. As many Calculus 2 students are painfully aware, integration is much more complicated than the differentiation it undoes.

However, Randall dramatically overstates this point here. After the first step of integration, Randall assumes that any integration can not be solved so simply, and then dives into a step named "????", suggesting that it is unknowable how to proceed. (The four ?s are not all on the same line, which implies further chaos and confusion.) The rest of the flowchart is (we can assume deliberately) even harder to follow, and does not reach a conclusion. This is in contrast to the simple, straightforward flowchart for differentiation.

It should be noted that Randall slightly undermines his point by providing four different methods, and an "etc", for attempting differentiation with no guidelines for selecting between them. (The "etc" in particular should not be here, as lists like this should name every single element without relying on the reader to be able to fill in unstated parts.)

===Differentiation===
'''{{w|Chain rule}}'''

For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx}(f(g(x)))=f'(g(x))*g'(x)</math>.

'''{{w|Power Rule}}'''

For any <math> f(x)=x^a </math>, it follows that <math> \frac{d}{dx}f(x)=a*x^{a-1} </math>.

'''{{w|Quotient rule}}'''

For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx} \frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}</math> if <math>g(x)\ne 0</math>.

'''{{w|Product rule}}'''

For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx}(f(x)*g(x))=f'(x)*g(x)+f(x)*g'(x)</math>.

===Integration===
'''{{w|Integration by parts}}'''
???

'''{{w|Integration by substitution|Substitution}}'''
???

'''{{w|Cauchy's integral formula|Cauchy's Formula}}'''
???

'''{{w|Partial_fraction_decomposition#Application_to_symbolic_integration|Partial Fractions}}'''

'''Install Mathematica'''

{{w|Mathematica}} is a modern technical computing system spanning most areas. One of its features is to compute mathematical functions. This step in the flowchart is install and use Mathematica to compute to do the integration for you.

'''{{w|Riemann integral|Riemann Integration}}'''
???

'''{{w|Stokes' Theorem}}'''
???

'''{{w|Risch Algorithm}}'''
???

'''{{w|Bessel function}}'''
???

'''{{w|Symbolic integration}}'''
Mentioned in the title text. ???

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Two flow charts are shown.]

:[The first flow chart has four steps in simple order, one with multiple recommendations.]
:DIFFERENTIATION
:Start
:Try applying
::Chain Rule
::Power Rule
::Quotient Rule
::Product Rule
::Etc.
:Done?
::Yes
::No
:Done!

[The second flow chart begins like the first, then descends into chaos.]
:INTEGRATION
:Start
:Try applying
::Integration by Parts
::Substitution
:Done?
:Haha, Nope!

:[Chaos, Roughly from left to right, top to bottom, direction arrows not included.]
::Cauchy's Formula
::????
::???!?
::???
::???
::?
::Partial Fractions
::??
::?
::Install Mathematica
::?
::Riemann Integration
::Stokes' Theorem
::???
::?
::Risch Algorithm
::???
::[Sad face.]
::?????
::???
::What the heck is a Bessel Function??
::Phone calls to mathematicians
::Oh No
::Burn the Evidence


{{comic discussion}}

2117: Differentiation and Integration

2019-02-27T19:19:26Z

Ozmandias42: /* Differentiation */

{{comic
| number = 2117
| date = February 27, 2019
| title = Differentiation and Integration
| image = differentiation_and_integration.png
| titletext = "Symbolic integration" is when you theatrically go through the motions of finding integrals, but the actual result you get doesn't matter because it's purely symbolic.
}}

==Explanation==
{{incomplete|Created by a BESSEL FUNCTION? Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
This comic provides a {{w|flowchart}} purporting to show the process of differentiation, and another for integration.

{{w|Derivative|Differentiation}} and {{w|Antiderivative|Integration}} are two major components of {{w|calculus}}. As many Calculus 2 students are painfully aware, integration is much more complicated than the differentiation it undoes.

However, Randall dramatically overstates this point here. After the first step of integration, Randall assumes that any integration can not be solved so simply, and then dives into a step named "????", suggesting that it is unknowable how to proceed. (The four ?s are not all on the same line, which implies further chaos and confusion.) The rest of the flowchart is (we can assume deliberately) even harder to follow, and does not reach a conclusion. This is in contrast to the simple, straightforward flowchart for differentiation.

It should be noted that Randall slightly undermines his point by providing four different methods, and an "etc", for attempting differentiation with no guidelines for selecting between them. (The "etc" in particular should not be here, as lists like this should name every single element without relying on the reader to be able to fill in unstated parts.)

===Differentiation===
'''{{w|Chain rule}}'''

For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx}(f(g(x)))=f'(g(x))*g'(x)</math>.

'''{{w|Power Rule}}'''

For any <math> f(x)=x^a </math>, it follows that <math> \frac{d}{dx}f(x)=a*x^{a-1} </math>.

'''{{w|Quotient rule}}'''

For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx} \frac{f(x)}{g(x)}=\frac{g(x)f'(x)-f(x)g'(x)}{(g(x))^2}</math> if <math>g(x)\ne 0</math>.

'''{{w|Product rule}}'''

For any <math> \frac{d}{dx}f(x)=f'(x)</math> and <math> \frac{d}{dx}g(x)=g'(x) </math>, it follows that <math> \frac{d}{dx}(f(x)*g(x))=f'(x)*g(x)+f(x)*g'(x)</math>.

===Integration===
'''{{w|Integration by parts}}'''
???

'''{{w|Integration by substitution|Substitution}}'''
???

'''{{w|Cauchy's integral formula|Cauchy's Formula}}'''
???

'''{{w|Partial_fraction_decomposition#Application_to_symbolic_integration|Partial Fractions}}'''

'''Install Mathematica'''

{{w|Mathematica}} is a modern technical computing system spanning most areas. One of its features is to compute mathematical functions. This step in the flowchart is install and use Mathematica to compute to do the integration for you.

'''{{w|Riemann integral|Riemann Integration}}'''
???

'''{{w|Stokes' Theorem}}'''
???

'''{{w|Risch Algorithm}}'''
???

'''{{w|Bessel Function}}'''
???

'''{{w|Symbolic integration}}'''
Mentioned in the title text. ???

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Two flow charts are shown.]

:[The first flow chart has four steps in simple order, one with multiple recommendations.]
:DIFFERENTIATION
:Start
:Try applying
::Chain Rule
::Power Rule
::Quotient Rule
::Product Rule
::Etc.
:Done?
::Yes
::No
:Done!

[The second flow chart begins like the first, then descends into chaos.]
:INTEGRATION
:Start
:Try applying
::Integration by Parts
::Substitution
:Done?
:Haha, Nope!

:[Chaos, Roughly from left to right, top to bottom, direction arrows not included.]
::Cauchy's Formula
::????
::???!?
::???
::???
::?
::Partial Fractions
::??
::?
::Install Mathematica
::?
::Riemann Integration
::Stokes' Theorem
::???
::?
::Risch Algorithm
::???
::[Sad face.]
::?????
::???
::What the heck is a Bessel Function??
::Phone calls to mathematicians
::Oh No
::Burn the Evidence


{{comic discussion}}

Talk:1891: Obsolete Technology

2017-09-18T20:30:57Z

Ozmandias42:

Wasn't DOS still running behind Win95, and integrated into the OS similarly to the Linux shell? [[Special:Contributions/162.158.59.154|162.158.59.154]] 14:48, 18 September 2017 (UTC)

This reminds me of this Raganwald article on Blub: [http://weblog.raganwald.com/2006/10/are-we-blub-programmers.html Are we blub programmers?] Adequate doesn't mean best for the job; this comic presents the other side of the coin, don't upgrade just for upgrade's sake. --[[User:Jgt|Jgt]] ([[User talk:Jgt|talk]]) 14:51, 18 September 2017 (UTC)

The computer doesn't look like an early PC from the MS-DOS era. Reminds me more of the previous generation: à so-called mini-computer or a terminal connected to a mainframe.
Zetfr 15:32, 18 September 2017 (UTC)

:You are right, but I think we should make allowances to the look as this is stated to be an 'industrial' computer. Sebastian --[[Special:Contributions/172.68.110.52|172.68.110.52]] 16:24, 18 September 2017 (UTC)

https://www.cpsc.gov/Safety-Education/Safety-Education-Centers/Fireworks has a link to the 2016 Fireworks Annual Report, which has some useful statistics on page 2, the executive summary.
--[[User:Ozmandias42|Ozmandias42]] ([[User talk:Ozmandias42|talk]]) 20:08, 18 September 2017 (UTC)