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*** Qualifying Exams are conducted in accordance with the rules and regulations specified by the Department and announced before each exam. **** Additional requirement for graduation: An article related to doctoral studies published (or accepted for publication) in a scientific journal indexed by SCIE/SSCI. CE 501 The Boundary Element Method (3+0+0) 3 ECTS 8 (S?n?r Elemanlar? Yontemi) Green's functions; the BEM for Laplace's equation; constant, linear and higher order elements; numerical analysis and integration; application to ground water flows; Poisson's equation, Monte Carlo integration; methods for the transformation of domain integrals to boundary integrals, particular solutions, Galerkin vector approach, multiple reciprocity, Fourier expansions; the dual reciprocity method, application to convective problems, Helmholtz equation, Burger's equation and the Navier-Stokes equation. CE 503 Mathematical Methods in Engineering (4+0+0) 4 ECTS 10 (Muhendislikte Matematik Yontemler) Mathematical and experimental modeling in engineering. Tensor analysis. Extrema of a function and functionals. Differential mathematical models and solution methods. Weighted residual methods. Perturbation methods. Integral equations. Finite difference method.