Ders 莽ok de臒i艧kenli fonksiyonlardaki iki derslik dizinin ikincisidir. Birinci ders t眉rev ve entegral kavramlar谋n谋 geli艧tirmekte ve bu konulardaki problemleri temel 莽枚zme y枚ntemlerini sunmaktad谋r. Bu ders, birinci derste geli艧tirilen temeller 眉zerine daha ileri konular谋 i艧lemekte ve daha kapsaml谋 uygulamalar ve 莽枚z眉ml眉 枚rnekler sunmaktad谋r. Ders ger莽ek ya艧amdan gelen uygulamalar谋 da tan谋tmaya 枚nem veren 鈥渋莽erikli yakla艧谋mla鈥 tasarlanm谋艧t谋r.聽

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脟ok de臒i艧kenli Fonksiyon II: Uygulamalar / Multivariable Calculus II: Applications

Instructor: Attila A艧kar
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陌ki de臒i艧kenli fonksiyonlardan hat谋rlatmalar: ikinci derece fonksiyonlar, k谋smi t眉rev ve iki katl谋 entegrallerdeki temel tan谋mlar ve geometrideki anlamlar谋; iki de臒i艧kenli fonksiyonlarda t眉rev ve entegrallerdeki temel hesaplama y枚ntemleri, iki katl谋 entegral hesaplamas谋nda s谋ran谋n 枚neminin 枚rneklerle hat谋rlat谋lmas谋; te臒et d眉zlem ve diferansiyel; tam t眉rev ve zincirleme t眉rev. Y枚ne g枚re t眉rev. Gradyan, Bu sonu莽lar谋n 眉莽 ve 鈥渘鈥 de臒i艧kenli fonksiyonlara genellenmesi.
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3 videos1 reading1 assignment
陌ki de臒i艧kenli fonksiyonlarda Koordinat d枚n眉艧眉mleri ve Jakobiyan. Diverjans, Rotasyonel ve Laplasyen. Dairesel koordinatlarda gradyan. Do臒an谋n d枚rt temel k谋smi t眉revli denklemi: dalga, s谋zma, Laplace denklemleriyle Schr枚dinger denkleminin tan谋t谋lmas谋. 陌ki de臒i艧kenli sonu莽lar谋n 眉莽 de臒i艧kene ve m眉mk眉n olan durumlarda 鈥渘鈥 de臒i艧kene genellenmesi. Karma艧谋k de臒erli fonksiyonlar谋n 枚zel yap谋s谋yla k谋smi t眉revler ve tam t眉rev.
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5 videos1 reading1 assignment
En b眉y眉k ve en k眉莽眉k de臒erler: yerel, mutlak ve k谋s谋tlama alt谋nda. K谋s谋tlama alt谋nda en iyiyi arama (optimizasyon) ve Lagrange 莽arpan谋 y枚ntemi. K谋smi t眉revlerin uygulamas谋 ile de臒i艧imler hesab谋na giri艧.
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5 videos1 reading1 assignment
Uzayda y眉zeylerin a莽谋k, kapal谋 ve parametrik fonksiyonlarla g枚sterilmeleri ve e臒risel koordinatlar. sonsuz k眉莽眉k y眉zey alanlar谋 se莽eneklerinin birle艧tirilmi艧 bir yakla艧谋mla elde edilmesi. Uzayda k眉re, koni, paraboloitler gibi temel y眉zeylerin tan谋t谋lmas谋 ve bunlar谋 i莽eren alanlarla hesaplar.
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10 videos1 reading1 assignment
Uzayda kapal谋 y眉zeylerle tan谋mlanan hac谋mlar; sonsuz k眉莽眉k hac谋mlar谋n birle艧tirilmi艧 yakla艧谋mla elde edilmesi. Jakobiyan ve sonsuz k眉莽眉k hac谋m. Kartezyen, silindir ve k眉resel koordinatlarla uzaydaki y眉zey ve cisimlerde 眉莽 katl谋 entegral hesaplamalar谋. Uzayda k眉re, koni, paraboloitler gibi temel y眉zeylerle tan谋mlanan hac谋mlardan 枚rnekler ve bunlar谋 i莽eren hac谋m hesaplar谋.
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10 videos1 reading1 assignment
Vekt枚r alanlar谋n谋n tan谋t谋lmas谋; vekt枚r alanlar谋yla t眉rev ve entegral. D眉zlem e臒rilerinde entegraller. Entegralin y枚r眉ngeye ba臒l谋 ve y枚r眉ngeden ba臒谋ms谋z olmas谋. D眉zlem e臒rilerinde birinci ve ikinci Green teoremleri. D眉zlemdeki Green teoremlerinin vekt枚rler, rotasyonel ve diverjansla g枚sterimi.
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5 videos1 reading1 assignment
D眉zlemdeki Green teoremlerinden uzayda Stokes ve Green 鈥 Gauss teoremlerine ge莽i艧. Uzayda Green 鈥 Gauss ve Stokes teoremleriyle y眉zey ve hac谋m entegralleri. Diverjans, rotasyonel ve Laplasyen鈥檌n anlam谋. Uzayda Green 鈥 Gauss ve Stokes teoremleriyle do臒adan temel korunum denklemlerinin elde edilmesi. K眉tle, elektrik y眉k眉 ve 谋s谋 enerjisinin korunmas谋nda uygulamalar.
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5 videos1 reading
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1 assignment
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