This course aims to provide to the students a theoretical and applied background in the numerical solution of mechanical engineering problems and to upgrade their skills in informatics including the implementation and development of engineering s/w. Following the successful completion of the course it is expected that the students are able to numerically solve linear and nonlinear algebraic systems, perform numerical interpolation and integration as well as to numerically solve ordinary and partial differential equations describing initial and boundary value problems.

• Introduction to scientific computing and numerical errors
• Solution of linear and nonlinear algebraic systems using direct methods (Gauss and Gauss
  Jordan elimination, Thomas algorithm, LU factorization) and iterative techniques (Jacobi, Gauss Seidel, SOR, Newton)
• Interpolation methods (polynomial, least squares, splines)
• Numerical differentiation (Taylor series, finite differences) and integration (Newton-Cotes formulas and Gauss quadrature)
• Solution of ordinary differential equations using Runge-Kutta methods
•  Solution of basic elliptic differential equations using finite difference methods

Suggested Literature :

• S. C. Chapra and R. P. Canade, Numerical Methods for Engineers, McGraw Hill International, 1998.
• Δ. Βαλουγεώργης, Σημειώσεις μαθήματος, Πανεπιστημιακές Εκδόσεις Πανεπιστημίου Θεσσαλίας, 2005.
• Γ. Δ. Ακρίβης και Β. Α. Δουγαλής, Εισαγωγή στην Αριθμητική Ανάλυση, Πανεπιστημιακές Εκδόσεις Κρήτης, 1998.
• B. Carnahan, H. A. Luther and J. O. Wilkes, Applied Numerical Methods, John and Wiley, 1976.
• C. Pozrikidis, Αριθμητικές Υπολογιστικές Μέθοδοι στην Επιστήμη και τη Μηχανική, Εκδόσεις Τζιόλα, 2006.
• Contantinides, Applied Numerical Methods with Personal Computers, McGraw Hill International, 1988.
• G. V. Davis, Numerical Methods in Engineering & Science, Allen & Unwin, 1978.
•  S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Taylor&Francis, 1980

Greek

Lectures, Practical Exercises