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The linear wave equation

${\partial ^{2}u \over \partial t^{2}}=c^{2}\nabla ^{2}u$

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+The linear wave equation
-==Albums==
-All regularly released [[albums]] and their chart peak position: [[United World Chart]] ('''WW'''), [[Billboard 200|United States]] ('''U.S.'''), [[UK Albums Chart|United Kingdom]] ('''UK'''), [[Canada]] ('''CAN'''), [[ARIA Charts|Australia]] ('''AUS'''), [[Ireland]] ('''IRL'''), [[Germany]] ('''GER'''), [[France]] ('''FRA'''), [[Italy]] ('''ITA''') and [[Brazil]] ('''BRA''').
+<math>
-{| class="wikitable"
+{ \partial^2 u \over \partial t^2 }= c^2 \nabla^2 u
-! width="25" rowspan="2"| Year
+</math>
-! width="200" rowspan="2"| Album
-! colspan="10"|Chart positions<ref name="US/Canada">{{cite web | title=Billboard Data: Avril Lavigne | work=AllMusic.com | url=http://www.allmusic.com/cg/amg.dll?p=amg&sql=11:jpfpxq80ldfe~T5 | accessdate=2007-04-02}}</ref><ref name="UK">{{cite web | title=UK Singles and Albums Chart (Search) | work=EveryHit.com | url=http://www.everyhit.com/ | accessdate=2007-04-02}}</ref><ref name="Australia">{{cite web | title=Australian ARIA Albums and Singles Chart | work=[[Australian Recording Industry Association]] | url=http://australian-charts.com/showitem.asp?interpret=Avril+Lavigne&titel=Complicated&cat=s | accessdate=2007-04-02}}</ref><ref name="Germany">{{cite web | title=German Albums and Singles Chart | work=Charts-Surfer.de | url=http://www.charts-surfer.de/ | accessdate=2007-04-02}}</ref><ref name="France">{{cite web | title=French Albums and Singles Chart | work=LesCharts.com | url=http://lescharts.com/showitem.asp?interpret=Avril+Lavigne&titel=Complicated&cat=s | accessdate=2007-04-02}}</ref><ref name="ChartData">{{cite web | title=Chart Data: Avril Lavigne | work=Mariah-Charts.com | url=http://www.mariah-charts.com/chartdata/PAvrilLavigne.htm | accessdate=2007-04-02}}</ref><ref name="Ireland">{{cite web | title=Irish peak of Let Go | work=ChartTrack.co.uk | url=http://www.charttrack.co.uk/index.jsp?c=p%2Fmusicvideo%2Fmusic%2Farchive%2Findex_test.jsp&ct=240002&arch=t&lyr=2003&year=2003&week=4 | accessdate=2007-04-21}}<br>{{cite web | title=Irish peak of Under My Skin | work=ChartTrack.co.uk | url=http://www.charttrack.co.uk/index.jsp?c=p%2Fmusicvideo%2Fmusic%2Farchive%2Findex_test.jsp&ct=240002&arch=t&lyr=2004&year=2004&week=22 | accessdate=2007-04-21}}<br>{{cite web | title=Irish peak of The Best Damn Thing | work=ChartTrack.co.uk | url=http://www.charttrack.co.uk/index.jsp?c=p%2Fmusicvideo%2Fmusic%2Farchive%2Findex_test.jsp&ct=240002&arch=t&lyr=2007&year=2007&week=16 | accessdate=2007-04-21}}</ref>
-! width="200" rowspan="2"| Sales and certification
-|-
-! width="30"| <small>WW</small>
-! width="30"| <small>U.S.</small>
-! width="30"| <small>UK</small>
-! width="30"| <small>CAN</small>
-! width="30"| <small>AUS</small>
-! width="30"| <small>FRA</small>
-! width="30"| <small>ITA</small>
-! width="30"| <small>GER</small>
-! width="30"| <small>NET</small>
-! width="30"| <small>BRA</small>
-|-
-|-
-|2002
-|''[[Rotten]]''<small>
-*1st [[studio album]]
-*Released: [[2003]]
-*Formats: [[Compact Disc|CD]]</small>
-|<center>1
-|<center>2
-|<center>1
-|<center>1
-|<center>1
-|<center>13
-|<center>6
-|<center>2
-|<center>8
-|<center>1
-|<small>Worldwide sales: 16 million<ref name=officialwebsite/> <br>[[Recording Industry Association of America|RIAA]] certification: 6&times; Platinum<ref name="RIAA">{{cite web | title=RIAA Certification | work=[[Recording Industry Association of America]] | url=http://www.riaa.com/gp/database/default.asp | accessdate=2006-10-02}}</ref></small> <br><small>[[British Phonographic Industry|BPI]] certification: 5&times; Platinum<ref name="BPI">{{cite web | title=BPI Certification | work=[[British Phonographic Industry]] | url=http://www.bpi.co.uk/index.asp?Page=stats/content_file_118.shtml | accessdate=2007-04-02}}</ref></small> <br><small>[[IFPI]] certification: 2&times; Platinum<ref name="IFPI">{{cite web | title=IFPI Certification | work=[[International Federation of the Phonographic Industry]] | url=http://www.ifpi.org/content/section_news/plat_all_years.html | accessdate=2007-04-02}}</ref></small>
-|-
-|2004
-|''[[Ultraviolet Catastrophe]]''<small>
-*2nd studio album
-*Released: [[2004]]
-*Formats: CD</small>
-|<center>1
-|<center>1
-|<center>1
-|<center>1
-|<center>1
-|<center>4
-|<center>3
-|<center>1
-|<center>12
-|<center>1
-|<small>Worldwide sales: 9 million<ref name="worldchart">{{cite web | title=United World Chart: Under My Skin | work=mediatraffic.de | url=http://www.mediatraffic.de/top-album-achievements.htm | accessdate=2008-03-21}}</ref> <br>RIAA certification: 3&times; Platinum<ref name="RIAA" /></small> <br><small>BPI certification: Platinum<ref name="BPI" /></small><br><small>IFPI certification: Platinum<ref name="IFPI" /></small>
-|-
-|-
-|2007
-|''[[Ex Cathedra]]''<small>
-*3rd studio album
-*Released: [[2007]]
-*Formats: CD</small>
-|<center>1
-|<center>1
-|<center>1
-|<center>1
-|<center>2
-|<center>3
-|<center>1
-|<center>1
-|<center>8
-|<center>1
-|<small>Worldwide sales: 5.4 million<ref>[http://www.ifpi.org/content/library/top-50-albums-2007.pdf IFPI Top-Sellers 2007]</ref><br>RIAA certification: Platinum</small><br><small>BPI certification: Platinum</small><br><small>IFPI certification: Platinum</small>
-|-
-|-
-|2008
-|''[[Chimæra]]''<small>
-*4th studio album
-*Released: [[2008]]
-|-
-|-
-|2009
-|''[[Great Love]]''<small>
-*5th studio album
-*Relased: [[2009]]
-|<center>
-|<center>
-|<center>
-|<center>
-|<center>
-|<center>
-|<center>
-|<center>
-|<center>
-|<center>
-|}
-===Sales certificates===
-{| class="wikitable"
-! width="100" rowspan="2"| '''Country'''
-! colspan="3"| '''Certificate'''<sup>
-! width="220" rowspan="2"| '''Notes'''<ref>[http://www.ifpi.org/content/library/Certification%20Awards%20Full%20List%20-%20OCTOBER%2007.pdf IFPI Table on Certifications]</ref>
-|-
-! width="110"|<small>'''[[Let Go (Avril Lavigne album)|Let Go]]'''</small>
-! width="110"|<small>'''[[Under My Skin]]'''</small>
-! width="110"|<small>'''[[The Best Damn Thing]]'''</small>
-|-----
-| [[Australian Recording Industry Association|Australia]]
-| <center>7× Platinum
-| <center>Platinum
-| <center>2× Platinum
-|<sup>Platinum = 70,000 / Gold = 35,000</sup>
-|-
-|-----
-| [[Brazil]]<ref>[http://www.abpd.org.br/certificados_interna.asp ABPD - Brazilian Certifications - Searchable database]</ref>
-| <center>2× Platinum
-| <center>1× Platinum
-| <center>Platinum
-| <sup>Platinum= 125,000 / Gold= 50,000</sup>
-|-
-|-----
-| [[Canadian Recording Industry Association|Canada]]
-| <center>1× diamond
-| <center>5× Platinum
-| <center>3× Platinum
-|<sup>Diamond = 1 million / Platinum = 100,000</sup>
-|-
-| [[IFPI|Europe]]
-| <center>2× Platinum
-| <center>Platinum
-| <center>Platinum
-|<sup>Platinum = 1 million<ref name="IFPI albums">IFPI. [http://www.ifpi.org/site-content/platinum/plat_all_years.html List of European sales certificates]. [[International Federation of the Phonographic Industry]]. Retrieved 27 August 2006.</ref></sup><br />
-|-
-|-----
-| [[France]]
-| <center>2× Platinum
-| <center>Platinum
-| <center>Gold
-|<sup>Platinum = 200,000 / Gold = 75,000</sup>
-|-
-| [[Germany]]
-| <center>2× Platinum
-| <center>Gold
-| <center>Platinum
-|<sup>Platinum = 200,000 / Gold = 100,000</sup>
-|-
-|-----
-| [[Switzerland]]
-| <center>
-| <center>Platinum
-| <center>Platinum
-|<sup>Platinum = 30,000 / Gold = 15,000</sup>
-|-
-|-----
-| [[British Phonographic Industry|United Kingdom]]
-| <center>5× Platinum
-| <center>Platinum
-| <center>Platinum
-|<sup>Platinum = 300,000 / Gold = 100,000</sup>
-|-
-|-----
-| [[RIAA|United States]]
-| <center>6× Platinum
-| <center>3× Platinum
-| <center>Platinum
-|<sup>Platinum = 1 million / Gold = 500,000</sup>
-|-
-|}