INSTITUTE OF APPLIED MATHEMATICS

MSc without Thesis in Scientific Computing

  • Compulsory Courses

    Credit: 3(3-0); ECTS: 8.0

    Computer Arithmetic; Linear Equations: Gauss elimination, LU decomposition; Linear Least Squares: data fitting, normal equations, orthogonal transformations; Eigenvalue Problems; Singular Value Decomposition; Nonlinear Equations: bisection, fixed-point iteration, Newton’s method, optimization; Interpolation: polynomials, piecewise polynomials; Numerical Differentiation and Integration.

    See the course in IAM Catalogue or METU Catalogue

    Credit: 3(3-0); ECTS: 8.0

    Ordinary Differential Equations: Euler’s method, multistep methods, Runge-Kutta methods, stiff equations, adaptivity; Boundary Value Problems: shooting, collocation, Galerkin; Partial Differential Equations: parabolic, elliptic, and hyperbolic equations; Iterative Methods for Sparse Linear Systems: splitting methods, descent methods, conjugate gradients, preconditioners, multigrid methods.

    See the course in IAM Catalogue or METU Catalogue

    Credit: 3(3-0); ECTS: 8.0

    Unconstrained Optimization: steepest descent, line search methods, trust-region methods, conjugate gradient methods, Newton and quasi-Newton methods, large-scale unconstrained optimization, least-square problems; Theory of Constrained Optimization; Linear Programming: simplex method, interior point method; Quadratic Programming; Active Set Methods; Interior Point Methods; Penalty, Barrier and Augmented Lagrangian Methods; Sequential Quadratic Programming.

    See the course in IAM Catalogue or METU Catalogue

    Credit: 3(3-0); ECTS: 8.0

    Abstract Finite Element Analysis: weak derivatives, Sobolev spaces, Lax-Milgram lemma; Piecewise Polynomials Approximations 1D and 2D: interpolation, projection; Finite Element Method 1D and 2D: weak formulation, derivation of linear system of equations, a priori estimates; Time Dependent Problems: finite differences for systems of ODE, stability estimates; Semi-elliptic equations; a posteriori Error Analysis: estimator, mesh Refinement

    See the course in IAM Catalogue or METU Catalogue

    Credit: 0(0-2); ECTS: 20.0

    M.S. students working on a common area choose a research topic to study and present to a group under the guidance of a faculty member.

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    Credit: 0(0-2); ECTS: 10.0

    This course is designed to provide students with a chance to prepare and present a professional seminar on subjects of their own choice.

    See the course in IAM Catalogue or METU Catalogue

    Credit: 3(3-0); ECTS: 8.0

    Classification of inverse problems, linear regression, discretizing continuous inverse problems, rank-deficiency, Tikhonov regularization, iterative methods, other regularization techniques, Fourier techniques, nonlinear inverse problems, Bayesian methods. Computer applications and MATLAB exercises are important elements of the course.

    See the course in IAM Catalogue or METU Catalogue

    5 Elective Courses (Total 30 credits)

See IAM Catalogue for possible elective courses.

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