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Ayrıca şifreli dizilere erişim için proxy kullanımı da gösterilmektedir. 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üniversite matematiği derslerinden calculus-II dersine ait \" Vektör Alanlarının Curl ve Diverjansını Bulma (Curl and Divergence)\" videosudur. Hazırlayan: Kemal Duran (Matematik Öğretmeni)...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/222140/bada03e826a2946215c69c560bde6d03/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/Y0Un3gAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"17","reqid":"1770055071364975-15917786914754786194-balancer-l7leveler-kubr-yp-sas-184-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1770055071364975-15917786914754786194-balancer-l7leveler-kubr-yp-sas-184-BAL&text=videoid:16551999045765604366","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik eğitimi formatında bir ders anlatımıdır.","Videoda üç boyutlu vektör alanlarının curl ve diverjansı kavramları detaylı şekilde ele alınmaktadır. Eğitmen önce teorik bilgileri vererek curl'un vektörel, diverjansın ise skaler bir büyüklük olduğunu açıklar, ardından hesaplama formüllerini gösterir. Daha sonra örnek problemler üzerinden konuyu pekiştirir ve korumalı vektör alanının nasıl tespit edileceğini adım adım anlatır.","Videoda ayrıca curl'un sıfır çıkması durumunda vektör alanının tutarlı (korumalı) olduğu, diverjansın sıfır çıkması durumunda ise curl'un diverjansının sıfır çıkması gerektiği gibi önemli özellikler vurgulanmaktadır. Eğitmen, verilen bir vektör alanının korumalı olup olmadığını test etmek için curl ve diverjans hesaplamalarını göstererek konuyu pekiştirmektedir."]},"endTime":1307,"title":"Vektör Alanlarının Curl ve Diverjansı Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Vektör Alanlarının Curl ve Diverjansı","list":{"type":"unordered","items":["Vektör alanlarının curl ve diverjansı, üç boyutlu vektör alanlarının yorumlanmasında kullanılan iki temel kavramdır.","Üç boyutlu vektör alanı F(x,y,z) = p(x,y,z)i + q(x,y,z)j + r(x,y,z)k şeklinde ifade edilir.","Curl vektörel bir büyüklükken, diverjans skaler bir büyüklüktür."]},"beginTime":1,"endTime":254,"href":"/video/preview/16551999045765604366?parent-reqid=1770055071364975-15917786914754786194-balancer-l7leveler-kubr-yp-sas-184-BAL&text=Curls+-+Topic&t=1&ask_summarization=1"},{"index":1,"title":"Curl ve Diverjansın Matematiksel Tanımları","list":{"type":"unordered","items":["Curl F = (r_y - q_z)i + (p_z - r_x)j + (q_x - p_y)k formülüyle hesaplanır.","Diverjans F = div F = p_x + q_y + r_z formülüyle hesaplanır.","Curl, vektör alanının herhangi bir (x,y,z) noktasındaki hareketinin eğilimsel yönünü gösterirken, diverjans bu değişim oranının büyüklüğünü gösterir."]},"beginTime":254,"endTime":493,"href":"/video/preview/16551999045765604366?parent-reqid=1770055071364975-15917786914754786194-balancer-l7leveler-kubr-yp-sas-184-BAL&text=Curls+-+Topic&t=254&ask_summarization=1"},{"index":2,"title":"Örnek Hesaplama","list":{"type":"unordered","items":["F = 2yi + xyj + yzk vektör alanı için curl F = (x + 2yz)i + yz²k olarak hesaplanır.","Aynı vektör alanı için diverjans F = x + y olarak bulunur.","Curl F'in diverjansı sıfır çıkması, curl hesabının doğruluğunu test etmek için kullanılabilir."]},"beginTime":493,"endTime":763,"href":"/video/preview/16551999045765604366?parent-reqid=1770055071364975-15917786914754786194-balancer-l7leveler-kubr-yp-sas-184-BAL&text=Curls+-+Topic&t=493&ask_summarization=1"},{"index":3,"title":"Önemli Özellikler","list":{"type":"unordered","items":["Eğer curl F vektörü sıfır ise, F vektör alanı korumalı (tutarlı) bir vektör alanıdır.","Curl F'in diverjansı her zaman sıfırdır.","Korumalı vektör alanının belirlenmesinde curl F'in sıfır olup olmadığı kontrol edilir."]},"beginTime":763,"endTime":1103,"href":"/video/preview/16551999045765604366?parent-reqid=1770055071364975-15917786914754786194-balancer-l7leveler-kubr-yp-sas-184-BAL&text=Curls+-+Topic&t=763&ask_summarization=1"},{"index":4,"title":"Korumalı Vektör Alanı Testi","list":{"type":"unordered","items":["Bir vektör alanının korumalı olup olmadığını anlamak için curl (çöp) hesaplanır ve sonuç sıfır vektörü çıkarsa korumalı vektör alanıdır.","Verilen vektör alanının curl hesaplanırken kısmi türevler alınır ve sonuç sıfır vektörü çıkmadığı için korumalı bir vektör alanı değildir.","Diverjans hesaplanarak (div F) test edildiğinde, p'nin x'e göre, q'nun y'ye göre ve r'nin z'ye göre kısmi türevleri alınarak sonuç sıfır çıkması, 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