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Item #:
264397465
Diferensiyel Denklemler
Item #:
264397465
AUD 37
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Diferensiyel Denklemler provides detailed examinations and a variety of solution methods for both simple and complex differential equations, empowering readers with practical examples and theoretical insights.
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Product Details
- Bu kitap on bölüm halinde hazırlanmış olup çalışılan bölümlerin detaylı olarak incelenmesine gayret edilmiştir. Bir çözüm metodu incelenirken, denklemin şekline göre olması muhtemel olan her bir durum için örnek sorular çözülmüştür. Birinci mertebeden denklemler ile birinci mertebeden ve yüksek dereceden denklemlerin genel ve özel durumları ayrıntılı olarak incelenmiştir. Çözümün var ve tek olma şartları bir bölüm olarak konuya ait teoremler yardımıyla ele alınmıştır. Bağımlı değişkene, bağımsız değişkene ve türeve göre çözülebilen denklemler ile türeve göre çözülemeyen denklemlerin genel ve tekil çözümlerinin elde edilişi farklı konularda ayrı ayrı çalışılmıştır. Yüksek mertebeden denklemlerin çözüm metotları ayrıntılı olarak ele alınmış, sabitlerin değişimi metodu ile belirsiz katsayılar metodu üzerinde ağırlıklı olarak durulmuş ve operatör metodunun uygulamasına yer verilmiştir. Denklemin değişken katsayılı olması halinde hem regüler hem de singüler noktalar için genel çözümünün nasıl bulunacağı kuvvet serileri yardımıyla açıklanmıştır. Lineer denklem sistemleri, matrislere ait özellikler kullanılarak oldukça ayrıntılı çalışılmıştır. Burada özellikle karakteristik polinomun kökleri olan özdeğerlerin farklı ve katlı olması durumları, özdeğerlere karşılık gelen özvektörlerin ve özuzayların elde edilişi ve özdeğerlerin katlı olması halinde genelleştirilmiş özvektörlerin nasıl bulunacağı üzerinde durulmuştur. Daha sonra özdeğerlerin farklı ve katlı olması hallerine göre denklem sistemlerinin genel çözümünü elde etme metotları incelenmiştir. Sınır değer problemleri çalışılırken problemin ürettiği diferensiyel operatör üzerine vurgu yapılmış ve operatöre ait bazı özellikler üzerinde durulmuştur. Burada diferensiyel operatöre ait oluşacak izlenimden sonra farklı problemlerin ürettiği diferensiyel operatörlerin farklı özelliklerinin çalışılabileceği öngörüsünün oluşması hedeflenmiştir. Laplace dönüşümünün incelenmesindeki amaç klasik başlangıç değer problemlerin çözümüne farklı bir yaklaşım sunmak ve klasik olmayan yani fonksiyonun parçalı sürekli olması halinde bile problemin burada verilen çözüm metotları yardımıyla çözülebileceğini ifade etmektir. Daha fazla göster
| Yayıncı | Pegem Akademi Yayıncılık |
| Yayınlanma Tarihi | 18 Aralık 2015 |
| Baskı | 1. |
| Dil | Türkçe |
| Baskı Uzunluğu | 736 sayfa |
| ISBN-10 | 6053183210 |
| ISBN-13 | 978-6053183211 |
| Boyutlar | 15 x 2 x 21.5 cm |
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Diferensiyel Denklemler
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Features & Benefits
- Comprehensive breakdown of differential equations across ten chapters.
- Examples for each solution method tailored to specific equation forms.
- Thorough exploration of first-order and higher-order equations.
- Techniques for finding general and particular solutions highlighted.
- In-depth study of boundary value problems and differential operators.
- Innovative approaches like Laplace transformations for diverse problem-solving.
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