Vector operator

A vector operator is a differential operator used in vector calculus. Vector operators include the gradient, divergence, and curl:

  • Gradient is a vector operator that operates on a scalar field, producing a vector field.
  • Divergence is a vector operator that operates on a vector field, producing a scalar field.
  • Curl is a vector operator that operates on a vector field, producing a vector field.

Defined in terms of del:

The Laplacian operates on a scalar field, producing a scalar field:

Vector operators must always come right before the scalar field or vector field on which they operate, in order to produce a result. E.g.

yields the gradient of f, but

is just another vector operator, which is not operating on anything.

A vector operator can operate on another vector operator, to produce a compound vector operator, as seen above in the case of the Laplacian.

See also

Further reading

  • H. M. Schey (1996) Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, ISBN 0-393-96997-5.

Read other articles:

Willem Einthoven

Dutch physiologist Willem EinthovenWillem Einthoven in 1906Born(1860-05-21)21 May 1860Semarang, Dutch East IndiesDied29 September 1927(1927-09-29) (aged 67)Leiden, NetherlandsNationalityDutchAlma materUniversity of UtrechtKnown for First practical electrocardiogram machine Clinical electrocardiography Einthoven's triangle AwardsNobel Prize in Medicine in 1924Scientific careerFieldsPhysiologyInstitutionsUniversity of Leiden Willem Einthoven (21 May 1860 – 29 September 1927) wa...

 

Da Derrty Versions: The Reinvention

2003 remix album by NellyDa Derrty Versions: The ReinventionRemix album by NellyReleasedNovember 25, 2003Recorded2002–03GenreHip hopLength77:53LabelUniversalProducerNellyNelly chronology Nellyville(2002) Da Derrty Versions: The Reinvention(2003) Sweat(2004) Professional ratingsReview scoresSourceRatingAllmusic linkRapReviews link Da Derrty Versions: The Reinvention is a remix album by American rapper Nelly, released on November 25, 2003. Track listing Intro (1:25) Country Gramma...

 

غليبيتشيفو (لينينغراد)

غليبيتشيفو الإحداثيات 60°27′14″N 28°43′09″E / 60.453888888889°N 28.719166666667°E / 60.453888888889; 28.719166666667  تقسيم إداري  البلد روسيا[2][1]  معلومات أخرى 188917  رمز الهاتف 81378  رمز جيونيمز 561251  تعديل مصدري - تعديل   غليبيتشيفو (بالروسية: Глебычево) هي مدينة في مقاطعة...

الدوري النمساوي 1911–12

يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (نوفمبر 2019) الدوري النمساوي 1911–12 تفاصيل الموسم الدوري النمساوي  النسخة 1  البلد النمسا  التاريخ بداية:3 سبتمب...

 

Haftevan

Village in West Azerbaijan province, Iran For other places with a similar name, see Haftvan. Village in West Azerbaijan, IranHaftevan Persian: هفتوانVillageSt. George Church, a 13th century Armenian churchHaftevanCoordinates: 38°10′04″N 44°45′24″E / 38.16778°N 44.75667°E / 38.16778; 44.75667[1]CountryIranProvinceWest AzerbaijanCountySalmasDistrictCentralRural DistrictZulachayPopulation (2016)[2] • Total8,203Time zoneUT...

 

Ringworld

1970 science fiction novel by Larry Niven Not to be confused with Discworld. Ringworld Paperback first editionAuthorLarry NivenIllustratorDean EllisCountryUnited StatesLanguageEnglishSeriesRingworld storyline from Known SpaceGenreScience fictionPublisherBallantine BooksPublication dateOctober 1970Media typePrint (hardcover, paperback), audiobookPages342 pagesAwardsLocus Award for Best Novel (1971)ISBN0-345-02046-4Followed byThe Ringworld Engineers, 1979  Ringworld is a 1970 sci...

André Devaux

Questa voce sull'argomento atleti francesi è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. André Devaux Nazionalità  Francia Atletica leggera Specialità 400 metri piani Palmarès Competizione Ori Argenti Bronzi Giochi olimpici 0 0 1 Per maggiori dettagli vedi qui   Modifica dati su Wikidata · Manuale Jean André Devaux (Laon, 4 agosto 1894 – Chaumont, 28 febbraio 1981) è stato un ...

 

Pescadores campaign (1895)

This article relies excessively on references to primary sources. Please improve this article by adding secondary or tertiary sources. Find sources: Pescadores campaign 1895 – news · newspapers · books · scholar · JSTOR (April 2023) (Learn how and when to remove this message) Battle of the First Sino-Japanese War Pescadores campaignPart of the First Sino-Japanese War and the Japanese invasion of Taiwan (1895)The Rising Sun Flag flying over Yuweng ...

 

Their Own Desire

1929 American pre-Code romantic drama film by E. Mason Hopper Their Own DesireLobby cardDirected byE. Mason HopperScreenplay byFrances MarionJames Forbes (dialogue)Lucille Newmark (titles)Based onTheir Own Desire1929 novelby Sarita FullerStarringNorma ShearerBelle BennettLewis StoneRobert MontgomeryHelene MillardCinematographyWilliam H. DanielsEdited byHarry ReynoldsDistributed byMetro-Goldwyn-MayerRelease date December 27, 1929 (1929-12-27) Running time65 minutesCountryUnited ...

الاستجابة لجائحة فيروس كورونا 2019–20 في مارس 2020

هذه مقالة غير مراجعة. ينبغي أن يزال هذا القالب بعد أن يراجعها محرر؛ إذا لزم الأمر فيجب أن توسم المقالة بقوالب الصيانة المناسبة. يمكن أيضاً تقديم طلب لمراجعة المقالة في الصفحة المخصصة لذلك. (أبريل 2020) الاستجابة لجائحة فيروس كورونا 2019–20 في مارس 2020معلومات عامةصنف فرعي من response ...

 

Aylmer Haldane

British Army general (1862–1950) Sir Aylmer HaldaneSir Aylmer Haldane, photographed around 1900Born(1862-11-17)17 November 1862Gleneagles, ScotlandDied19 April 1950(1950-04-19) (aged 87)London, EnglandBuriedBrookwood CemeteryService/branch British ArmyYears of service1882–1925RankGeneralUnitGordon HighlandersCommands held10th Infantry Brigade3rd Division6th Army CorpsBattles/warsNorth West FrontierRusso-Japanese War - Military AttacheSecond Boer WarWorld War IInsurrection of Mes...

 

Daftar makhluk dan benda yang disebut namanya dalam Al-Qur'an

Al-Qur'an Sejarah Wahyu Kesejarahan Asbabunnuzul Nuzululqur'an Manuskrip Samarkand Sanaa Birmingham Topkapi Pembagian Hizb Juz Manzil Muqatta'at Surah Daftar Makiyah Madaniyah Isi Eskatologi Hewan Keajaiban Ketuhanan Ilmu pengetahuan Legenda Nabi dan Rasul Nama lain Perumpamaan Wanita Membaca Taawuz Basmalah Hafiz Qiraat Qari Tajwid Tartil Khatam Terjemahan Daftar terjemahan Al-Qur'an Tafsir Daftar karya tafsir Hermeneutika Takwil Nasakh Hubungan dengan kitab lain Orang yang disebut namanya K...

1790 Footprints

East Hawaiʻi Battles of 1790Part of Unification of HawaiiAsh layer from 1790 eruption.Date1790LocationEastern Hawaiʻi IslandResult inconclusiveBelligerents Kamehameha I's army Keōua KuahuʻulaCommanders and leaders Kamehameha IKeawemauhili Keōua Kuahuʻula vteUnification of Hawaiʻi Mokuʻōhai Olowalu Kaʻūpūlehu Kepaniwai East Hawaiʻi Kawaihae Kawela Nuʻuanu Namakeha's rebellion Kauaʻi United States historic place1790 FootprintsU.S. National Register of Historic Places Location9.1 ...

 

The quiet Australians

Concept in politics This article is part of a series aboutScott Morrison Early life and career Member for Cook (2007–2024) Abbott government Abbott Ministry Turnbull government First Turnbull Ministry Second Turnbull Ministry 2018 Liberal Party leadership spills Prime Minister of Australia(International trips) First Ministry Second Ministry 2019–20 Australian fires Sports rorts affair COVID-19 pandemic in Australia Brereton Report Parliament House sexual misconduct allegations AUKUS 2022 ...

 

1886 United Kingdom general election

1886 United Kingdom general election ← 1885 1–27 July 1886 (1886-07-01 – 1886-07-27) 1892 → ← outgoing memberselected members →All 670 seats in the House of Commons336 seats needed for a majorityTurnout74.2%   First party Second party Third party   Leader Marquess of Salisbury William Ewart Gladstone Charles Stewart Parnell Party Conservative and Liberal Unionist Liberal Irish Parliamentary Leader since April ...

رودولفو كوتا

رودولفو كوتا معلومات شخصية الميلاد 3 يوليو 1987 (العمر 36 سنة)مازاتلان  الطول 1.83 م (6 قدم 0 بوصة) مركز اللعب حارس مرمى الجنسية المكسيك  معلومات النادي النادي الحالي كلوب ليون الرقم 30 المسيرة الاحترافية1 سنوات فريق م. (هـ.) 2007–2018 باتشوكا 74 (0) 2014–2015 ← بويبلا (إعارة) 31 (0) ...

 

Petar Bajalović

Cet article est une ébauche concernant un architecte serbe. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants. Petar Bajalović Présentation Naissance 27 mai 1876Šabac, Principauté de Serbie Décès 14 avril 1947 (à 70 ans)Belgrade, Yougoslavie Nationalité Serbe Activités Architecte modifier  Petar Bajalović (en serbe cyrillique : Петар Бајаловић ; né le 27 mai 1876 à Ša...

 

Elections in Slovenia

Politics of Slovenia UN Member State(UNSC Member · ECOSOC Member)EU Member State(Eurozone Member · Schengen Area Member)NATO Member StateCouncil of Europe Member StateOECD Member State Constitution Constitutional Court Constitution of Slovenia Executive President of the Republic Nataša Pirc Musar Prime Minister Robert Golob Government Golob Cabinet Legislature Parliament National Council President Marko Lotrič National Assembly Speaker Urška Klakočar Zupančič 9th National Assembly Ju...

Site d'initiation de la transcription

Pour les articles homonymes, voir TSS. Le site d'initiation de la transcription (en anglais, transcription start site, TSS) est le premier nucléotide de l'ADN qui est transcrit en ARN. Identification du site d'initiation de la transcription Le site d'initiation de la transcription ne correspond pas au premier acide aminé de la protéine correspondante (si cet ARN est traduit). Il est difficile de déterminer sa position exacte par bio-informatique, mais il existe plusieurs méthodes expér...

 

Planetensystem

Symbolische Darstellung des Planeten­systems der Sonne, nicht maßstabsgetreu Ein Planetensystem ist die Gesamtheit nicht selbstleuchtender größerer Himmelskörper – der Planeten –, die sich – durch die Gravitationskraft gebunden – um mindestens einen gemeinsamen zentralen Stern (oder einen sternähnlichen Himmelskörper wie einen Braunen Zwerg, ein Kompaktes Objekt oder ein Schwarzes Loch)[1] bewegen. Im weiteren Sinn ist es die Gesamtheit des physikalischen ...