Numerical Methods
Instructor: Perdiou Angela
Course code: 5302
Semester: 3ο
Course content:

  1. Roots of nonlinear equations using successive approximation methods (Newton-Raphson, Secant, Taylor, Muller).
  2. Real and complex roots of polynomials (Bairstow method).
  3. Systems of nonlinear algebraic equations (Newton-Raphson method).
  4. Systems of linear algebraic equations (Thomas algorithm, Gauss Elimination, Crout and Cholesky methods).
  5. Eigenvalue problems (Power and Krylov methods). Curve fitting (Lagrange interpolating polynomials, Finite differences, Aitken acceleration, Least Squares method, use of Cubic Splines). Numerical integration (Trapezoidal rule, Romberg formula, Newton-Cotes algorithms, Gauss quadrature).
  6. Numerical differentiation (High-accuracy differentiation formulas, use of interpolation polynomials).
  7. Ordinary differential equations of boundary-value problems (Taylor, Euler, Midpoint and Runge-Kutta methods). Applications using FORTRAN programming and MATLAB software.

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