DEPARTMENT: MATHEMATICS
MATH366 METHODS OF APPLIED MATHEMATICS (UYGULAMALI MATEMATIK)

Credits: 4

Summary:

Description:
Order symbols, asymptotic approximations and asymptotic expansions, perturbation techniques, singular perturbation, power series solutions of linear differential equations about an ordinary point, functionals and variation, the Euler-Lagrange equation and its first integrals, functionals involving several functions of a single variable, derivatives of higher order, and functions of several independent variables, variational problems with movable boundaries, variational problems of constrained extrema, isoperimetric problems, classification of linear integral equations and methods for their solution, types of kernels, reduction of multiple integrals to single and generalized Leibnitz formula, Volterra integral equations, resolvent kernel method and Neumann series, method of successive approximations, Laplace transform, the inverse transform and convolution, Laplace transform solution of linear differential equations with constant coefficients, Fredholm integral equations with degenerate kernel, Fredholm alternative, self-adjoint second order differential equations, Lagrange identity and Abel’s formula, the Sturm theory (comparison and separation theorems), boundary value problems, Sturm-Liouville boundaryvalue problems, Green’s functions. (Semboller, asimtotik yaklaşımlar, lineer diferansiyel denklemlerin adi noktalar çevresindeki seri çözümleri, fonksiyoneller, Euler-Lagrange denklemi, tek değişkenli fonksiyoneller, yüksek mertebeden türevler, çok değişkenli fonksiyonlar, değişken sınırlarda değişim problemleri, sınırlı bir küme üzerinde minimum ve maksimum değişim problemleri, izoperimetrik problemler, Lineer integral denklemlerinin sınıflandırılması ve çözüm metodları, Kümenin çekirdeği, Katlı integralin tekli integrale indirgenmesi, Leibnitz formülü, Volterra integral Denklemleri, Neuman serileri, ardışık yaklaşım metodu, Laplace dönüşümleri, ters laplace dönüşümleri, Sabit katsayılı diferansiyel denklemlerin laplace çözümleri, fredholm integral denklemleri, Fredholm ikinci dereceden özeşlenik diferansiyel denklemleri, Lagrange özdeşliği ve Abel formülü, Sturm teorisi, sınır değerleri problemi, Sturm Liouville sınır- değer problemleri, Green fonksiyonları)

Prerequisite(s):

Faculty & Department: Faculty of Arts And Sciences - Department of Mathematics

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