Course Information

Course Information

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
Title Numerical Analysis
Category B
ECTS 6
Hours 6
Level Undergraduate
Semester Spring
Teacher S. Stamatiadis
Program Tuesday 9:00-13:00, Room 2, Computer Room 2
Course Webpage
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

Numeral systems. IEEE Standards for integer and floating point numbers.Computer representation of numbers.
Numerical solution of a nonlimear equation. Definitions,useful theorems. Methods: bisection, regula falsi, secant, Muller,fixed point, Ηοuseholder (Newton-Raphson, Halley).
Systems of linear equations. Direct methods (Gauss elimination,Gauss-Jordan, LU).Iterative methods (Gauss-Seidel, Jacobi, SOR). Other methods.Applications: calculation of the determinant of a matrix,inverse matrix, matrix eigenvalues and eigenvectors.Numerical solution of systems of nonlinear equations.
Function/set of points approximation: Interpolation of polynomial, rational, piecewise polynomial, spline. Runge phenomenon.Numerical differentiation.
Least squares approximation: line, polynomial, logarithmic and exponential. Correlation coefficient.
Numerical quadrature. Trapezoid and Simpson rules. Newton-Cotesformulas. Gauss quadrature methods (Legendre, Hermite, Laguerre,Chebyshev). Clenshaw–Curtis method. Other methods.
Numerical solution of initial value problems of first orderordinary differential equations (ODE).Methods: Euler (explicit/implicit), Taylor, Runge-Kutta 2ndand 4th orders. Systems of ODEs. Higher order ODEs.
Other topics (FFT, optimization, etc).
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)