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Analytic functions, contour integration, conformal mapping, Banach and Hilbert spaces, expansions in orthogonal functions, classical orthogonal polynomials, integral transforms, applications to partial differential equations, Green’s functions, distributions. Study of current research topics in mathematics by Ph.

Spherical functions and their applications. Characteristic function, convolution, uniqueness and inversion, convergence theorems, central limit theorem, basic properties of conditional expectation, conditional independence and Markov property. Ito’s formula, the Girsanov theorem, Markov processes, transition properties of Markov processes, examples of Markov processes, canonical process and ddiferansiyel operator, extension of filtration, strong Markov property, transience and recurrence.

Guidance of a doctoral student by a faculty member towards the preparation and presentation of a research proposal. Linear and nonlinear elliptic partial differential equations. Images, videos and audio are available under their respective licenses.

Elements of symplectic geometry. Dispersion, dissipation and nonlinearity. Uniqueness theorems for Dirichlet and Neumann problems.


The complex number system, metric spaces and topology of C, elementary properties and beometri of analytic functions, complex integration, maximum modulus theorem, Cauchy’s integral formula, properties of path integrals, conformal mapping. Three dimensional wave equation. Independence, type of convergence, almost sure convergence. Ordinary differential equations, linear systems, nonlinear systems, existence and uniqueness theorems, continuous dependence on parameters, stability.

Types of second order partial differential equations. Constructing the finite difference scheme for the model problems. Monge cones and Monge equation. Oh no, there’s been an error Please help us solve this error by emailing diiferansiyel at support wikiwand.

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Diferansiyel Geometri ( Neşe Yelkenkaya) – İKÜ – CALAMEO Downloader

Additive functions, continuity, harmonic functions, theory of general processes, predictable and optional processes, hitting times, processes with jumps, martingale decomposition, stochastic integrals. Matched asymptotic expansions, multiple scales, WKB and homogenization.

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Mathematical foundations of continuum mechanics, vectors and tensors, kinematics geoemtri deformation, conservation laws. Diferansiyel geometri My Bookmarks You have no bookmarks Add your first bookmark by selecting some text or hovering over a link.


Vector and scalar waves. Harmonic functions and properties. Linear and nonlinear equations. Differentiable manifolds, tangent and cotangent spaces, vector fields, Lie bracket, diffeomorphism, the inverse function theorem, submanifolds, hypersurfaces, standart connection of Euclidean spaces, Weingarten and Gauss maps, tensors and differential forms, Lie derivative, Riemannian connection, Riemannian manifolds, Riemannian curvature tensor.

Measure theory, classes of sets, difernsiyel measures and their distribution functions. Conformal changes of Riemannian metric.

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Diferansiyel Geometri I Ders Notu (2014 2015 Güz Dönemi)

Hahn-Banach theorem, normed linear spaces, Hilbert spaces. Direct methods of numerical linear algebra; triangular systems, Gaussian elimination and LU decomposition, pivoting, backward error analysis.

Mathematical foundations of continuum mechanics, vectors and tensors, kinematics of deformation, conservation laws. Oh no, there’s been an error Linear and nonlinear elliptic partial differential equations. Differansiyel geometri – Wikiwand Diferansiyel geometri My Bookmarks You have no bookmarks Add your first bookmark by selecting some text or hovering over a link.

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