Numerical Methods in Mechanics

Opublikowano: 29.04.2014 17:32

Subject name	Numerical Methods in Mechanics
Type of subject	Basic
Summary ECTS	3
Form of course	15h lecture, 15h laboratory
Lecturer	Prof. Mariusz Pyrz, Ph.D., D.Sc.
A brief outline:
Lecture	Introduction to numerical methods: number representation, algorithms, source of errors, modeling of typical problems in mechanics Roots of nonlinear equations: Bisection, Newton-Raphson and False-Position methods, systems of nonlinear equations Solution of linear algebraic equations: Gauss and Gauss-Jordan elimination, matrix inversion, iterative methods Interpolation: Lagrange and Newton polynomials Approximation: Least-Squares and linear regression Numerical integration: Trapezoidal rule, Newton-Cotes formulas and Gauss quadrature Numerical solution of eigenvalue problem: Power method, main idea of QR method Ordinary differential equations: Euler's method, Runge-Kutta methods, systems of equations
Laboratory	Introduction to programming in Scilab (or Matlab) Algorithms for finding roots of a nonlinear equation, test of convergence (numerical example: equilibrium of a floating object) Solution of a system of linear algebraic equations (numerical example: approximation of experimental data using the least squares approach) Determination of eigenvalues and eigenvectors of a matrix (numerical example: eigenfrequencies and eigenmodes of a system of vibrating masses) Numerical solution of a system of ordinary differential equations (numerical example: cantilever beam subjected to bending)