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: line search methods, steepest descent, Newton and quasi Newton methods, the conjugate gradient method constrained optimization: equality and inequality constraints, linear constraints and duality, linear programming, the simplex method, Lagrange multiplier algorithms, interior point methods, penalty methods, large scale optimization.

    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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