# Courses Catalogue

### Syllabus of the course: * Numerical Analysis *

In this web page we provide the syllabus of the course Numerical Analysis, offered by the Department of Physics.

The list of the courses offered during the current accademic year is available here.

The list of all courses offered by the Department of Physics is available here.

Code | Φ-152 |
---|---|

Type | B |

ECTS | 6 |

Hours | 6 |

Semester | Spring |

Instructor | S. Stamatiadis |

Program | Monday 09:00-11:00, Room 2 Monday 16:00-19:00, Computer Room 2 |

Web page | |

Goal of the course | The course is addressed to second year students. It is an introduction to numerical analysis and covers numerical techniques and algorithms for the solution of mathematical problems which are encountered in physics. |

Syllabus | Representation of numbers on the computer. Numerical errors. Machine accuracy. Experimental data errors. Truncation, roundoff, and algorithm errors. Under- and over-flow. Error propagation in calculations. Definition of algorithm stability. Numerical solution of nonlinear equations. Bisection method. Fixed point method. Newton-Raphson and secant methods. Algorithms and convergence issues. Systems of linear equations. Gauss elimination with backsubstitution. Stability. Partial and full pivoting. Determinant calculation with Gauss elimination. Inverse matrix calculation using the Gauss-Jordan method. Iterative methods for the solution of systems of linear equations. Calculation of matrix eigenvalues. Numerical interpolation. Lagrange interpolation method for non-equidistant points. Maximum interpolation error. Least square fit to a straight line. Polynomial, logarithmic, and exponential curve fitting. General linear least squares. Numerical integration. Trapezoidal and Simpson rules. Algorithms, step choice, methods accuracy and errors. Numerical solution of differential equations. Review of ordinary differential equations. Euler, 2nd and 4th order Runge-Kutta methods. Algorithms, comparison, errors. Systems of 1st order differential equations. |

Bibliography | Grammatikakis M., Kopidakis G., Papadakis N., Stamatiadis S.- Introduction to Numerical Analysis, Lecture and Lab Notes (in Greek)
http://www.edu.physics.uoc.gr/~tety213/notes.pdf Forsythe G.E., Malcom M.A., Moler C.B.- Computer Methods for Mathematical Computations. Akrivis G.D., Dougalis V.A.- Introduction to Numerical Analysis (in Greek) |

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