Surveys and applications of numerical techniques related to matrix inversion, systems of linear equations and optimization, finite difference expressions, interpolation and approximation, numerical differentiation and integration. The problems of speed, accuracy and applicability of the topics are examined with related algorithms. The applications of these numerical methods and subjects on computers using efficient programming techniques and with necessary programming languages.
- To be able to explain effects of finite representation of real numbers for a given algorithm.
- To be able to find numerical errors in calculations and compare numerical errors of different algorithms for the same problem.
- To be able to solve numerical problems that include derivative, integral, interpolation and/or optimization.
- To be able to apply recursive solutions to numerical problems.
- To be able to implement linear/non-linear systems for the given problem.
- To be able to apply appropriate numerical algorithm for given linear/non-linear system.
|Introduction to numerical calculation methods|
|Numerical calculation errors|
|Taylor series cont.|
|Forward and backward differences|
|Central differences, polynomials|
|Interpolation & extrapolation|
|Finding roots of equations, Newton method|
|Finding roots of equations, Secant method|
The solution of simultaneous linear algebraic equations
|Least-squares curve fitting|