This module focuses on the presentation and the discussion of the basis methods for the numerical resolution of problems, and notably for the numerical resolution of equations. The module presents the construction of numerical method from principles of basis, the introduction to the analysis of the errors and to the assessment of the efficiency of the methods in terms of computation. It deals with good understanding of writing algorithm for different numerical methods implemented using a symbolic computer analysis package Matlab to program the numerical methods.
he laws of physics are generally down as differential equations.
A Differential Equation (DE) is an equation containing one or more derivatives of a single unknown function. If the unknown function is depending with one independent variable, then the DE is called Ordinary Differential Equation (ODE). If the unknown function is depending with two or more independent variables, then the DE is called Partial Differential Equation (PDE). The DEs are taught to undergraduate students who are science majors, including mathematics, physics, and engineering. ODEs are taught to undergraduate students during the first year while PDEs are taught to third year undergraduate students.
Here we will concentrate on introduction to ODEs describing the main ideas for finding analytical solutions to certain odes, such as first-order ODEs, second-order ODEs, higher-order linear ODEs, and systems of first-order linear ODEs.
The prerequisites for studying ODEs are Calculus (Differentiation and Integration), Linear Algebra (Matrices, Determinants of matrices, Systems of linear algebraic equations, and eigenvalues and eigenvectors) and they are taught during the first semester.