Abstract:

The first part of the course is dedicated to study of techniques for

solving systems of linear equations. Several basic methods are presented:

Gauss elimination, matrix solution, Cramer rule.

The last two methods involve matrix arithmetic,

which is also presented in this part. The second part discusses vector spaces and linear transformations. Most attention is given

to the matrix approach. Matrix diagonalization issues summarize this part.

Abstract:

Sorting differential equations.

First-order differential equations.

Linear differential equations of order n:

homogeneous and non-homogeneous equation, Wronskian homogeneous equations with constant coefficients. Separation into homogeneous and non-homogeneous problem, method of unknown coefficients and method of variation of parameters.

Language Problems - Sturm Liouville Theory: Defining a close-knit operator, finding the operator's self-values and self-func tions and proving their properties.

System of Linear Differential Equations Order 1: Solving the homogeneous system using eigenvalues and eigenvectors of the matrix.

Abstract:

Interpolation and approximations methods, error analysis.

Numerical integration, differentiation.

Ordinary differential equations solution, Solutions to non-linear equations.