## Numerical Analysis

Errors calculations: Basic concepts, types of errors, error propagation in numerical calculations. Approximate expressions functions: The coincident polynomial and polynomials of Taylor and Mc Laurin, applications in numerical problem solving methods - complete functions in non-closed form. Numerical solution of algebraic equations: Finding roots - method of regula falsi, method of Newton-Raphson. Numerical interpolation: Linear interpolation full insertion by the method of Newton. Dual linear interpolation. Numerical differentiation: Linear derivation, complete derivatization by means of coincident polynomial Newton. Numerical integration: trapezoidal method, method of Cotes. Numerical solution of first-order differential equations: The method of Euler, the method of Taylor, the method of Runge-Kutta 2nd and 4th order.

### Objectives

After successful completion of the course students should: To know the basic concepts regarding the types of errors and their transmission by numerical calculations. To adequately manage the concepts of coincident polynomial, and the polynomial of Taylor and Mc Laurin (related to "unwieldy" functions), with emphasis on their applications in numerical problem solving methods (integrals whose calculated in closed form is not feasible et. al.). To solve numerically algebraic equations (finding the roots), the methods of regula falsi and Newton-Raphson. To handle interference problems between numerical values ​​of functions of one variable, either linearly or in full, the method (polynomial) of Newton. The linear method can be applied to functions of two variables, using double entry table. Perform numerically acts of derivation - linear and Newton, and integration - to the method of the trapezium and that of Cotes (either via price list, or by using the analytical type). To solve numerically first order differential equations, with the methods: Euler, Taylor (up to third order) and Runge-Kutta 2nd and 4th order.

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### Syllabus

Errors calculations: Basic concepts, types of errors, error propagation in numerical calculations. Approximate expressions functions: The coincident polynomial and polynomials of Taylor and Mc Laurin, applications in numerical problem solving methods - complete functions in non-closed form. Numerical solution of algebraic equations: Finding roots - method of regula falsi, method of Newton-Raphson. Numerical interpolation: Linear interpolation full insertion by the method of Newton. Dual linear interpolation. Numerical differentiation: Linear derivation, complete derivatization by means of coincident polynomial Newton. Numerical integration: trapezoidal method, method of Cotes. Numerical solution of first-order differential equations: The method of Euler, the method of Taylor, the method of Runge-Kutta 2nd and 4th order.

COURSE DETAILS
 Level: Type: Undergraduate (A-) Instructors: Konstantinos Kleidis Department: Department of Mechanical Engineering Institution: TEI of Central Macedonia Subject: Mathematics Rights: CC - Attribution-ShareAlike