Numerical Methods

LEARNING OUTCOMES

The objectives of this course are:

• introduction to numerical methods and their applications in engineering problems
• providing knowledge and skills necessary for the development of computational algorithms and applications in order to solve related problems

 

Upon successful completion of the course the student will be able to:

• recognize practical applications and problems of engineering science, whose solution depends on using numerical methods
• apply various methodologies of numerical analysis in order to solve fundamental mathematical problems for engineers
• use the basic principles of programming, algorithmic structures and techniques for the implementation of applications based on numerical methods and , in general, applications that solve engineering problems

 

General Competences

• Search, analysis and synthesis of data and information, using the appropriate technologies
• Individual work
• Team work
• Work in an interdisciplinary environment
• Promotion of creative and inductive thinking

 

SYLLABUS

Basic concepts. Numerical accuracy and error propagation. Matrices and determinants. Vector and matrix norms. Solving non-linear equations. Bisection method. Regula-falsi method. Newton-Raphson method. Secant method. Convergence to solutions. Multiple roots and modified Newton-Raphson method. Systems of linear equations. Stability of linear systems. Gaussian elimination. Factorization methods. Jacobi and Gauss-Seidel iterative methods. Convergence. Polynomial approaches to interpolation. Taylor polynomials. Lagrange and Newton interpolation. Interpolation and approximation with partial polynomials. Least squares method. Numerical integration. Trapezoidal and Simpson’s rule., Romberg and Gaussian quadrature rule, Numerical solutions of differential equations. Euler’s and Runge- Kutta methods. Error analysis. Implementation of numerical methods and application development in the Matlab programming environment.

 

STUDENT PERFORMANCE EVALUATION

I. Written final examination that includes:
– Short answer questions
– Problem solving
II. Midterm written examinations
III. Projects

The examination material and the evaluation process are announced to the students during the lectures and are also posted on the course’s website.

 

ATTACHED BIBLIOGRAPHY

In Greek:
1. Σαρρής Ι., Καρακασίδης Θ., 2015. Αριθμητικές Μέθοδοι και Εφαρμογές για Μηχανικούς. Εκδόσεις Τζιόλα.
2. Στεφανίδης Γ. Χ., Σαμαράς Ν.Ε., 1999. Υπολογιστικές Μέθοδοι με το Matlab. Εκδόσεις Ζυγός.
3. Chapra S., Canale R., 2016. Αριθμητικές Μέθοδοι για Μηχανικούς. Εκδόσεις Τζιόλα. In English
4. Yang W., 2005. Applied Numerical Methods Using MATLAB. Wiley-Interscience.