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Available in 61 language" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-61" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">61 kalba</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%8B%E1%8D%95%E1%88%8B%E1%88%B5_%E1%88%BD%E1%8C%8D%E1%8C%8D%E1%88%AD" title="ላፕላስ ሽግግር – amharų" lang="am" hreflang="am" data-title="ላፕላስ ሽግግር" data-language-autonym="አማርኛ" data-language-local-name="amharų" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AD%D9%88%D9%8A%D9%84_%D9%84%D8%A7%D8%A8%D9%84%D8%A7%D8%B3" title="تحويل لابلاس – arabų" lang="ar" hreflang="ar" data-title="تحويل لابلاس" data-language-autonym="العربية" data-language-local-name="arabų" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Tresformada_de_Laplace" title="Tresformada de Laplace – asturianų" lang="ast" hreflang="ast" data-title="Tresformada de Laplace" data-language-autonym="Asturianu" data-language-local-name="asturianų" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%BD%D0%B0_%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81" title="Преобразование на Лаплас – bulgarų" lang="bg" hreflang="bg" data-title="Преобразование на Лаплас" data-language-autonym="Български" data-language-local-name="bulgarų" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B2%E0%A6%BE%E0%A6%AA%E0%A7%8D%E0%A6%B2%E0%A6%BE%E0%A6%B8_%E0%A6%B0%E0%A7%82%E0%A6%AA%E0%A6%BE%E0%A6%A8%E0%A7%8D%E0%A6%A4%E0%A6%B0" title="লাপ্লাস রূপান্তর – bengalų" lang="bn" hreflang="bn" data-title="লাপ্লাস রূপান্তর" data-language-autonym="বাংলা" data-language-local-name="bengalų" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Laplaceova_transformacija" title="Laplaceova transformacija – bosnių" lang="bs" hreflang="bs" data-title="Laplaceova transformacija" data-language-autonym="Bosanski" data-language-local-name="bosnių" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Transformada_de_Laplace" title="Transformada de Laplace – katalonų" lang="ca" hreflang="ca" data-title="Transformada de Laplace" data-language-autonym="Català" data-language-local-name="katalonų" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Laplaceova_transformace" title="Laplaceova transformace – čekų" lang="cs" hreflang="cs" data-title="Laplaceova transformace" data-language-autonym="Čeština" data-language-local-name="čekų" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Laplacetransformation" title="Laplacetransformation – danų" lang="da" hreflang="da" data-title="Laplacetransformation" data-language-autonym="Dansk" data-language-local-name="danų" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Laplace-Transformation" title="Laplace-Transformation – vokiečių" lang="de" hreflang="de" data-title="Laplace-Transformation" data-language-autonym="Deutsch" data-language-local-name="vokiečių" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B5%CF%84%CE%B1%CF%83%CF%87%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CF%83%CE%BC%CF%8C%CF%82_%CE%9B%CE%B1%CF%80%CE%BB%CE%AC%CF%82" title="Μετασχηματισμός Λαπλάς – graikų" lang="el" hreflang="el" data-title="Μετασχηματισμός Λαπλάς" data-language-autonym="Ελληνικά" data-language-local-name="graikų" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Laplace_transform" title="Laplace transform – anglų" lang="en" hreflang="en" data-title="Laplace transform" data-language-autonym="English" data-language-local-name="anglų" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Laplaca_transformo" title="Laplaca transformo – esperanto" lang="eo" hreflang="eo" data-title="Laplaca transformo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Transformada_de_Laplace" title="Transformada de Laplace – ispanų" lang="es" hreflang="es" data-title="Transformada de Laplace" data-language-autonym="Español" data-language-local-name="ispanų" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Laplace%27i_teisendus" title="Laplace'i teisendus – estų" lang="et" hreflang="et" data-title="Laplace'i teisendus" data-language-autonym="Eesti" data-language-local-name="estų" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Laplaceren_transformazio" title="Laplaceren transformazio – baskų" lang="eu" hreflang="eu" data-title="Laplaceren transformazio" data-language-autonym="Euskara" data-language-local-name="baskų" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A8%D8%AF%DB%8C%D9%84_%D9%84%D8%A7%D9%BE%D9%84%D8%A7%D8%B3" title="تبدیل لاپلاس – persų" lang="fa" hreflang="fa" data-title="تبدیل لاپلاس" data-language-autonym="فارسی" data-language-local-name="persų" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Laplace-muunnos" title="Laplace-muunnos – suomių" lang="fi" hreflang="fi" data-title="Laplace-muunnos" data-language-autonym="Suomi" data-language-local-name="suomių" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Transformation_de_Laplace" title="Transformation de Laplace – prancūzų" lang="fr" hreflang="fr" data-title="Transformation de Laplace" data-language-autonym="Français" data-language-local-name="prancūzų" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Transformada_de_Laplace" title="Transformada de Laplace – galisų" lang="gl" hreflang="gl" data-title="Transformada de Laplace" data-language-autonym="Galego" data-language-local-name="galisų" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/L%C3%A0-ph%C3%BA-l%C3%A0-s%E1%B9%B3%CC%82_pien-von" title="Là-phú-là-sṳ̂ pien-von – kinų kalbos hakų tarmė" lang="hak" hreflang="hak" data-title="Là-phú-là-sṳ̂ pien-von" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="kinų kalbos hakų tarmė" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%AA%D7%9E%D7%A8%D7%AA_%D7%9C%D7%A4%D7%9C%D7%A1" title="התמרת לפלס – hebrajų" lang="he" hreflang="he" data-title="התמרת לפלס" data-language-autonym="עברית" data-language-local-name="hebrajų" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B2%E0%A4%BE%E0%A4%AA%E0%A5%8D%E0%A4%B2%E0%A4%BE%E0%A4%B8_%E0%A4%B0%E0%A5%82%E0%A4%AA%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4%E0%A4%B0" title="लाप्लास रूपान्तर – hindi" lang="hi" hreflang="hi" data-title="लाप्लास रूपान्तर" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Laplaceova_transformacija" title="Laplaceova transformacija – kroatų" lang="hr" hreflang="hr" data-title="Laplaceova transformacija" data-language-autonym="Hrvatski" data-language-local-name="kroatų" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Laplace-transzform%C3%A1ci%C3%B3" title="Laplace-transzformáció – vengrų" lang="hu" hreflang="hu" data-title="Laplace-transzformáció" data-language-autonym="Magyar" data-language-local-name="vengrų" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BC%D5%A1%D5%BA%D5%AC%D5%A1%D5%BD%D5%AB_%D5%B1%D6%87%D5%A1%D6%83%D5%B8%D5%AD%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Լապլասի ձևափոխություն – armėnų" lang="hy" hreflang="hy" data-title="Լապլասի ձևափոխություն" data-language-autonym="Հայերեն" data-language-local-name="armėnų" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Transformation_de_Laplace" title="Transformation de Laplace – tarpinė" lang="ia" hreflang="ia" data-title="Transformation de Laplace" data-language-autonym="Interlingua" data-language-local-name="tarpinė" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Transformasi_Laplace" title="Transformasi Laplace – indoneziečių" lang="id" hreflang="id" data-title="Transformasi Laplace" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziečių" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Trasformata_di_Laplace" title="Trasformata di Laplace – italų" lang="it" hreflang="it" data-title="Trasformata di Laplace" data-language-autonym="Italiano" data-language-local-name="italų" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%A9%E3%83%97%E3%83%A9%E3%82%B9%E5%A4%89%E6%8F%9B" title="ラプラス変換 – japonų" lang="ja" hreflang="ja" data-title="ラプラス変換" data-language-autonym="日本語" data-language-local-name="japonų" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Transformasi_Laplace" title="Transformasi Laplace – javiečių" lang="jv" hreflang="jv" data-title="Transformasi Laplace" data-language-autonym="Jawa" data-language-local-name="javiečių" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tabeddilt_n_Lapla%E1%B9%A3" title="Tabeddilt n Laplaṣ – kebailų" lang="kab" hreflang="kab" data-title="Tabeddilt n Laplaṣ" data-language-autonym="Taqbaylit" data-language-local-name="kebailų" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81_%D1%82%D2%AF%D1%80%D0%BB%D0%B5%D0%BD%D0%B4%D1%96%D1%80%D1%83%D1%96" title="Лаплас түрлендіруі – kazachų" lang="kk" hreflang="kk" data-title="Лаплас түрлендіруі" data-language-autonym="Қазақша" data-language-local-name="kazachų" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%94%E1%9F%86%E1%9E%9B%E1%9F%82%E1%9E%84%E1%9E%A1%E1%9E%B6%E1%9E%94%E1%9F%92%E1%9E%9B%E1%9E%B6%E1%9E%9F" title="បំលែងឡាប្លាស – khmerų" lang="km" hreflang="km" data-title="បំលែងឡាប្លាស" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="khmerų" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%9D%BC%ED%94%8C%EB%9D%BC%EC%8A%A4_%EB%B3%80%ED%99%98" title="라플라스 변환 – korėjiečių" lang="ko" hreflang="ko" data-title="라플라스 변환" data-language-autonym="한국어" data-language-local-name="korėjiečių" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B2%E0%B4%BE%E0%B4%AA%E0%B5%8D%E0%B4%B2%E0%B5%87%E0%B4%B8%E0%B5%8D_%E0%B4%AA%E0%B4%B0%E0%B4%BF%E0%B4%B5%E0%B5%BC%E0%B4%A4%E0%B5%8D%E0%B4%A4%E0%B4%A8%E0%B4%82" title="ലാപ്ലേസ് പരിവർത്തനം – malajalių" lang="ml" hreflang="ml" data-title="ലാപ്ലേസ് പരിവർത്തനം" data-language-autonym="മലയാളം" data-language-local-name="malajalių" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B2%E0%A5%85%E0%A4%AA%E0%A5%8D%E0%A4%B2%E0%A5%87%E0%A4%B8_%E0%A4%AA%E0%A4%B0%E0%A4%BF%E0%A4%B5%E0%A4%B0%E0%A5%8D%E0%A4%A4%E0%A4%A8" title="लॅप्लेस परिवर्तन – maratų" lang="mr" hreflang="mr" data-title="लॅप्लेस परिवर्तन" data-language-autonym="मराठी" data-language-local-name="maratų" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Laplacetransformatie" title="Laplacetransformatie – olandų" lang="nl" hreflang="nl" data-title="Laplacetransformatie" data-language-autonym="Nederlands" data-language-local-name="olandų" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Laplace-transformasjon" title="Laplace-transformasjon – naujoji norvegų" lang="nn" hreflang="nn" data-title="Laplace-transformasjon" data-language-autonym="Norsk nynorsk" data-language-local-name="naujoji norvegų" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Laplacetransformasjon" title="Laplacetransformasjon – norvegų bukmolas" lang="nb" hreflang="nb" data-title="Laplacetransformasjon" data-language-autonym="Norsk bokmål" data-language-local-name="norvegų bukmolas" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Transformacja_Laplace%E2%80%99a" title="Transformacja Laplace’a – lenkų" lang="pl" hreflang="pl" data-title="Transformacja Laplace’a" data-language-autonym="Polski" data-language-local-name="lenkų" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Trasform%C3%A0_%C3%ABd_Laplace" title="Trasformà ëd Laplace – italų kalbos Pjemonto tarmė" lang="pms" hreflang="pms" data-title="Trasformà ëd Laplace" data-language-autonym="Piemontèis" data-language-local-name="italų kalbos Pjemonto tarmė" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Transformada_de_Laplace" title="Transformada de Laplace – portugalų" lang="pt" hreflang="pt" data-title="Transformada de Laplace" data-language-autonym="Português" data-language-local-name="portugalų" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Transformat%C4%83_Laplace" title="Transformată Laplace – rumunų" lang="ro" hreflang="ro" data-title="Transformată Laplace" data-language-autonym="Română" data-language-local-name="rumunų" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B5%D0%BE%D0%B1%D1%80%D0%B0%D0%B7%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81%D0%B0" title="Преобразование Лапласа – rusų" lang="ru" hreflang="ru" data-title="Преобразование Лапласа" data-language-autonym="Русский" data-language-local-name="rusų" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Laplaceova_transformacija" title="Laplaceova transformacija – serbų-kroatų" lang="sh" hreflang="sh" data-title="Laplaceova transformacija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbų-kroatų" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Laplace_transform" title="Laplace transform – Simple English" lang="en-simple" hreflang="en-simple" data-title="Laplace transform" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Laplaceova_transformacija" title="Laplaceova transformacija – slovėnų" lang="sl" hreflang="sl" data-title="Laplaceova transformacija" data-language-autonym="Slovenščina" data-language-local-name="slovėnų" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Transformimi_i_Laplasit" title="Transformimi i Laplasit – albanų" lang="sq" hreflang="sq" data-title="Transformimi i Laplasit" data-language-autonym="Shqip" data-language-local-name="albanų" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81%D0%BE%D0%B2%D0%B0_%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Лапласова трансформација – serbų" lang="sr" hreflang="sr" data-title="Лапласова трансформација" data-language-autonym="Српски / srpski" data-language-local-name="serbų" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Transformasi_Laplace" title="Transformasi Laplace – sundų" lang="su" hreflang="su" data-title="Transformasi Laplace" data-language-autonym="Sunda" data-language-local-name="sundų" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Laplacetransform" title="Laplacetransform – švedų" lang="sv" hreflang="sv" data-title="Laplacetransform" data-language-autonym="Svenska" data-language-local-name="švedų" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%B2%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BF%E0%AE%B3%E0%AE%BE%E0%AE%9A%E0%AF%81_%E0%AE%AE%E0%AE%BE%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AF%81" title="இலப்பிளாசு மாற்று – tamilų" lang="ta" hreflang="ta" data-title="இலப்பிளாசு மாற்று" data-language-autonym="தமிழ்" data-language-local-name="tamilų" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%81%E0%B8%9B%E0%B8%A5%E0%B8%87%E0%B8%A5%E0%B8%B2%E0%B8%9B%E0%B8%A5%E0%B8%B1%E0%B8%AA" title="การแปลงลาปลัส – tajų" lang="th" hreflang="th" data-title="การแปลงลาปลัส" data-language-autonym="ไทย" data-language-local-name="tajų" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Laplace_d%C3%B6n%C3%BC%C5%9F%C3%BCm%C3%BC" title="Laplace dönüşümü – turkų" lang="tr" hreflang="tr" data-title="Laplace dönüşümü" data-language-autonym="Türkçe" data-language-local-name="turkų" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D0%B5%D1%80%D0%B5%D1%82%D0%B2%D0%BE%D1%80%D0%B5%D0%BD%D0%BD%D1%8F_%D0%9B%D0%B0%D0%BF%D0%BB%D0%B0%D1%81%D0%B0" title="Перетворення Лапласа – ukrainiečių" lang="uk" hreflang="uk" data-title="Перетворення Лапласа" data-language-autonym="Українська" data-language-local-name="ukrainiečių" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A9p_bi%E1%BA%BFn_%C4%91%E1%BB%95i_Laplace" title="Phép biến đổi Laplace – vietnamiečių" lang="vi" hreflang="vi" data-title="Phép biến đổi Laplace" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamiečių" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF%E5%8F%98%E6%8D%A2" title="拉普拉斯变换 – kinų kalbos vu tarmė" lang="wuu" hreflang="wuu" data-title="拉普拉斯变换" data-language-autonym="吴语" data-language-local-name="kinų kalbos vu tarmė" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%8B%89%E6%99%AE%E6%8B%89%E6%96%AF%E5%8F%98%E6%8D%A2" title="拉普拉斯变换 – kinų" lang="zh" hreflang="zh" data-title="拉普拉斯变换" data-language-autonym="中文" data-language-local-name="kinų" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Laplace_pi%C3%A0n-o%C4%81%E2%81%BF" title="Laplace piàn-oāⁿ – kinų kalbos pietų minų tarmė" lang="nan" hreflang="nan" data-title="Laplace piàn-oāⁿ" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="kinų kalbos pietų minų tarmė" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Straipsnis iš Vikipedijos, laisvosios enciklopedijos.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="lt" dir="ltr"><p><b>Laplaso transformacija</b> – <a href="/wiki/Pjeras_Simonas_Laplasas" title="Pjeras Simonas Laplasas">Pjero Simono Laplaso</a> sukurtas <a href="/wiki/Tiesinis_operatorius" title="Tiesinis operatorius">tiesinis operatorius</a>, transformuojantis <a href="/wiki/Realusis_skai%C4%8Dius" title="Realusis skaičius">realiųjų skaičių</a> <a href="/wiki/Funkcija" class="mw-disambig" title="Funkcija">funkcijas</a> į <a href="/wiki/Kompleksinis_skai%C4%8Dius" title="Kompleksinis skaičius">kompleksinių skaičių</a> funkcijas. Tokiu atveju realiojo kintamojo funkcija vadinama vaizdu, o ją atitinkanti kompleksinio kintamojo funkcija – atvaizdu. </p><p>Laplaso transformacija apibrėžiama taip: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(s)={\mathcal {L}}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow> <mo>{</mo> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>}</mo> </mrow> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>s</mi> <mi>t</mi> </mrow> </msup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(s)={\mathcal {L}}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5cac69d45b381b379f6d9d500978d560c1446f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:34.783ex; height:5.843ex;" alt="{\displaystyle F(s)={\mathcal {L}}\left\{f(t)\right\}=\int _{0^{-}}^{\infty }e^{-st}f(t)\,dt.}"></span></dd></dl> <p>Čia <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> – <a href="/wiki/Menamasis_vienetas" title="Menamasis vienetas">menamasis vienetas</a>, o <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0^{-}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0^{-}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb153c3e2b753e4b1627d97a00817d6ecab67eca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.673ex; height:2.509ex;" alt="{\displaystyle 0^{-}}"></span> yra <font style="vertical-align:-20%;"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{\epsilon \rightarrow +0}-\epsilon \ }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>ϵ</mi> <mo stretchy="false">→</mo> <mo>+</mo> <mn>0</mn> </mrow> </munder> <mo>−</mo> <mi>ϵ</mi> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{\epsilon \rightarrow +0}-\epsilon \ }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd8ee790a78f3f38c374afaf99fcbfc4485fc6a5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:8.131ex; height:4.009ex;" alt="{\displaystyle \lim _{\epsilon \rightarrow +0}-\epsilon \ }"></span> </font>. Tokia riba reiškia, kad į integravimo intervalą patenka visa <a href="/w/index.php?title=Dirako_delta_funkcija&action=edit&redlink=1" class="new" title="Dirako delta funkcija (puslapis neegzistuoja)">Dirako delta funkcija</a>. </p><p>Atvirkštinė Laplaso transformacija yra tokia: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(t)={\mathcal {L}}^{-1}\{F(s)\}={\frac {1}{2\pi i}}\int _{\gamma -i\cdot \infty }^{\gamma +i\cdot \infty }e^{st}F(s)\,ds.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo fence="false" stretchy="false">{</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo fence="false" stretchy="false">}</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>π</mi> <mi>i</mi> </mrow> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> <mo>−</mo> <mi>i</mi> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>γ</mi> <mo>+</mo> <mi>i</mi> <mo>⋅</mo> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>t</mi> </mrow> </msup> <mi>F</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>s</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(t)={\mathcal {L}}^{-1}\{F(s)\}={\frac {1}{2\pi i}}\int _{\gamma -i\cdot \infty }^{\gamma +i\cdot \infty }e^{st}F(s)\,ds.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5028e71fcf3dae75bc6f3f5e083bb266e7a31a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:44.13ex; height:6.509ex;" alt="{\displaystyle f(t)={\mathcal {L}}^{-1}\{F(s)\}={\frac {1}{2\pi i}}\int _{\gamma -i\cdot \infty }^{\gamma +i\cdot \infty }e^{st}F(s)\,ds.}"></span></dd></dl> <p>Čia γ yra tam tikras realusis skaičius, su kuriuo atvaizdas visame integravimo intervale <a href="/w/index.php?title=Konvergavimas&action=edit&redlink=1" class="new" title="Konvergavimas (puslapis neegzistuoja)">konverguoja</a> absoliučiai. </p><p>Laplaso transformacijoje pakeitus <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> į <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -iw}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>i</mi> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -iw}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5c13c6eea752c82eff6744b658a8447fd2011b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:4.275ex; height:2.343ex;" alt="{\displaystyle -iw}"></span>, ši pasidaro panaši į <a href="/wiki/Furj%C4%97_transformacija" title="Furjė transformacija">Furjė transformaciją</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Šaltiniai"><span id=".C5.A0altiniai"></span>Šaltiniai</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Laplaso_transformacija&veaction=edit&section=1" title="Redaguoti skyrelį: Šaltiniai" class="mw-editsection-visualeditor"><span>redaguoti</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Laplaso_transformacija&action=edit&section=1" title="Edit section's source code: Šaltiniai"><span>redaguoti vikitekstą</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Algirdas Matulis. 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