Computational Mathematics II
General
Code: ΜΥ03
Language: Greek
Delivery: Face-to-face
Prerequisites: Basic math concepts
Workload
- Lectures: 39.0 hours
- Lab: 0.0 hours
- Study: 86.0 hours
- Project: 0.0 hours
Course Content
Errors in numerical calculaitons
-Representation of numbers in memory, rounding error,s propagating error.
Numerical solution of nonlinear equations
- Dividing method
- Fixed point problem
- Newton Rapshon method
- Cutting method
- Horner shape
Numerical methods for solving linear systems
- Gaussian elimination method
- Jordan elimination method
- Three-diagonal system solution
- Basic iterative methods
Numerical calculation of eigenvalues and eigenvectors
- Method of forces
- Reverse method of forces.
Approximation of functions
- Finite differences
- Interpolation polynomial
Numerical derivation and integration
- Types of numerical derivation for equidistant points
- Numerical derivation by the method of determinable factors
- Error in arithmetic derivation
Numerical solution of ordinary differential equations
- Euler method
- Taylor series method
- Numerical solution of ordinary differential equations with boundary conditions
Learning Outcomes
The course belongs to the wider area of Scientific Computing. Scientific calculations are the basis for many fields and an important tool for the study of scientific problems arising from many sciences such as Physics, Chemistry, Biology, Economics etc. Most of these problems lead to the solution of a mathematical problem, for which either there is not always an analytical solution, or if there is it requires complex calculations. The course also includes the implementation of algorithms in a laboratory environment, based on the programming language Python.
Skills
Search, analysis and synthesis of data and information with the use of the assorted technologies
Adaptation in new conditions
Decision Making
Independent work
Team work
Promoting free, creative and deductive reasoning