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.

CodeΦ-152
TypeB
ECTS6
Hours6
SemesterSpring
InstructorS. Stamatiadis
ProgramMonday 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

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-Cotes formulas. Gauss quadrature methods (Legendre, Hermite, Laguerre, Chebyshev). Clenshaw–Curtis method. Other methods.
Numerical solution of initial value problems of first order ordinary differential equations (ODE). Methods: Euler (explicit/implicit), Taylor, Runge-Kutta 2nd and 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)

University of Crete - Department of Physics  - Voutes University Campus - GR-71003 Heraklion, Greece
phone: +30 2810 394300 - fax: +30 2810 394301