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üniversite matematiği derslerinden calculus-I dersine ait \"Kuvvet Serileri (Power Series) \" videosudur. Hazırlayan: Kemal Duran (Matematik Öğretmeni) http://www.buders.com/kadromuz.html...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3780447/d78706d1d3b142eecdeb98d896edc06c/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/uCvJDAAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"6","reqid":"1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=videoid:4337887614401758007","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Eğitmen, kuvvet serileri (power series) konusunu açıklamaktadır.","Video, kuvvet serilerinin ne olduğunu, normal serilerden nasıl ayırt edileceğini ve kuvvet serilerinin açılımlarını örneklerle anlatmaktadır. Eğitmen, kuvvet serilerinin yakınsaklık aralığı, yakınsaklık yarıçapı ve yakınsaklık merkezi gibi önemli kavramlarını bir sonraki videoda ele alacağını belirtmektedir. Ayrıca, kuvvet serilerinin Taylor ve Maclaurin açılımları ile nasıl elde edildiğini de inceleyeceğini ifade etmektedir."]},"endTime":566,"title":"Kuvvet Serileri Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Kuvvet Serilerinin Tanımı","list":{"type":"unordered","items":["Kuvvet serileri, serinin özel bir halidir ve bu videoda kuvvet serilerinin ne olduğu anlatılacaktır.","Seriler, herhangi bir başlangıç değeri ile üstü sonsuzluğa giden toplam sembolleridir ve içlerinde sadece sayısal ifadeler bulunur.","Kuvvet serisi, serinin içine x-a üzeri n biçiminde x'e bağlı üslü bir ifadenin gelmesiyle oluşur."]},"beginTime":1,"endTime":151,"href":"/video/preview/4337887614401758007?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=1&ask_summarization=1"},{"index":1,"title":"Seri ve Kuvvet Serisi Arasındaki Fark","list":{"type":"unordered","items":["Normal seri ile kuvvet serisini ayırt etmek önemlidir; kuvvet serisinde x'e bağlı 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Video, iki farklı kardioid örneği üzerinden (r = 1 + cosθ ve r = 1 + sinθ) çizim sürecini detaylı şekilde gösteriyor."]},"endTime":692,"title":"Kardioid Nedir ve Nasıl Çizilir?","beginTime":0}],"fullResult":[{"index":0,"title":"Kardioid Nedir","list":{"type":"unordered","items":["Kardioid, kutupsal denklemlerin grafiklerinin özel bir şekline verilen isimdir.","Kutupsal denklemler r ve theta yazı denklemlerdir; r orijine olan uzaklığı, theta ise noktanın x ekseni ile yaptığı açıyı temsil eder.","Bir kutupsal denklemin grafiği kalp şeklini verirse, bu grafiğe kardioid denir."]},"beginTime":1,"endTime":160,"href":"/video/preview/4213204199098599651?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=1&ask_summarization=1"},{"index":1,"title":"Kardioidin Çizimi","list":{"type":"unordered","items":["Kardioid çizimi için ilk adım, teta ve r'nin alacağı değerleri gösteren bir tablo üretmektedir.","Kutupsal grafik çizmek için derece değerleri (0, 90, 180, 270, 360) ve bunların kosinüs veya sinüs değerleri hesaplanır.","İkinci adım, bu noktaları analitik düzleme yerleştirmektir; r değeri orijine olan uzaklığı temsil eder."]},"beginTime":160,"endTime":183,"href":"/video/preview/4213204199098599651?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=160&ask_summarization=1"},{"index":2,"title":"Örnek Çizimler","list":{"type":"unordered","items":["r = 1 + cos(teta) denklemi için tablo oluşturulup, 0 derecede r = 2, 90 derecede r = 1, 180 derecede r = 0, 270 derecede r = 1, 360 derecede r = 2 değerleri bulunur.","r = 1 + sin(teta) denklemi için tablo oluşturulup, 0 derecede r = 1, 90 derecede r = 2, 180 derecede r = 1, 270 derecede r = 0, 360 derecede r = 1 değerleri bulunur.","Kardioid grafikleri x eksenine göre simetrik olup kalp şeklini verir."]},"beginTime":183,"endTime":685,"href":"/video/preview/4213204199098599651?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=183&ask_summarization=1"}],"linkTemplate":"/video/preview/4213204199098599651?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Calculus-II : Kardioid Nedir ve Nasıl Çizilir? 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2 videolarına değişken değiştirme yöntemiyle giriş yapıyoruz. metodu,öabt integral,öabt analiz Oynatma Listesi Linki : • Kalkülüs 2 Kalkülüs 2 Oynatma Listesi Videoları: Değişken...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/397852/55effa3e9a315bf053cbd88d37d5be82/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/40PF5gAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"14","reqid":"1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=videoid:2900491046475357600","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeni tarafından sunulan eğitim içeriğidir. Öğretmen, integral alma tekniklerinden biri olan değişken değiştirme yöntemini anlatmaktadır.","Videoda, değişken değiştirme yönteminin temel prensipleri açıklanmakta ve çeşitli örneklerle uygulamalı olarak gösterilmektedir. Öğretmen, \"ud eşittir dx\" şeklinde bir değişken değiştirme yaparak, x² + 1 üzeri 8, 3e üzeri 3x gibi zor integrallerin nasıl çözüleceğini adım adım anlatmaktadır.","Ayrıca videoda, değişken değiştirme yaparken dikkat edilmesi gereken noktalar, katsayıların ayarlanması ve farklı durumlarda (köklü ifadeler, trigonometrik fonksiyonlar) u değişkeninin nasıl seçileceği gibi konulara da değinilmektedir. Kök içindeki ifadelerin nasıl değiştirileceği ve sonucun nasıl elde edileceği detaylı olarak açıklanmaktadır."]},"endTime":963,"title":"İntegral Alma Teknikleri: Değişken Değiştirme","beginTime":0}],"fullResult":[{"index":0,"title":"İntegral Alma Teknikleri - Değişken Değiştirme","list":{"type":"unordered","items":["İntegral alma tekniklerinden biri olan değişken değiştirme, zor integralleri çözmek için kullanılır.","Değişken değiştirme yönteminde, integralin içindeki bir ifadeyi \"u\" olarak seçip, bu ifadenin türevinin de integralin içinde görünmesi gerekir.","Köklü ifadeler, üstel ifadeler veya parantez içindeki karmaşık ifadeler genellikle \"u\" olarak seçilmeye adaydır."]},"beginTime":0,"endTime":83,"href":"/video/preview/2900491046475357600?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=0&ask_summarization=1"},{"index":1,"title":"İlk Örnek - Değişken Değiştirme Uygulaması","list":{"type":"unordered","items":["İlk örnekte, x²+1 ifadesi \"u\" olarak seçilir çünkü türevi 2x dx şeklinde integralin içinde görünür.","İntegral, 2x dx = du şeklinde yazılır ve x²+1 üzeri 8 ifadesi u üzeri 8 olarak değiştirilir.","İntegral hesaplandıktan sonra, u yerine x²+1 yazarak cevap bulunur: (x²+1)⁹/9 + C."]},"beginTime":83,"endTime":273,"href":"/video/preview/2900491046475357600?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=83&ask_summarization=1"},{"index":2,"title":"İkinci Örnek - Değişken Değiştirme Uygulaması","list":{"type":"unordered","items":["İkinci örnekte, e^(3x) ifadesi \"u\" olarak seçilir çünkü türevi 3 dx şeklinde integralin içinde görünür.","İntegral, 3 dx = du şeklinde yazılır ve e^(3x) ifadesi u olarak değiştirilir.","İntegral hesaplandıktan sonra, u yerine 3x yazarak cevap bulunur: 3e^(3x) + C."]},"beginTime":273,"endTime":447,"href":"/video/preview/2900491046475357600?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=273&ask_summarization=1"},{"index":3,"title":"Değişken Değiştirme Uygulamaları ve Özel Durumlar","list":{"type":"unordered","items":["Değişken değiştirme yönteminde, hangi ifadelerin \"u\" olarak seçileceği önemlidir; örneğin x³+1, sin(x)+4 veya tan(x)+3 gibi ifadeler tercih edilebilir.","İçerideki ifadenin türevi dışarıda aynı şekilde gelmezse, integrali çarpıp bölerek veya x² dx'i yalnız bırakarak çözüm yapılabilir.","Köklü ifadelerde, değişken olarak değiştirilen ifade kökün içindeyse, u² şeklinde yazmak akıllıca bir yöntemdir."]},"beginTime":447,"endTime":736,"href":"/video/preview/2900491046475357600?parent-reqid=1766983933478491-2281034663371718861-balancer-l7leveler-kubr-yp-klg-205-BAL&text=K+Calculus&t=447&ask_summarization=1"},{"index":4,"title":"İntegral 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