Courses

אלגברה ליניארית (90905)

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.

The last part of the course study inner product spaces and their basic properties.

משוואות דיפ' רגילות (90914)

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.

The Wronskian of the system. The non-homogeneous system.

פונקציות מרוכבות (90917)

Abstract:

Complex integration : Contour Integrals. Residue theory.

Cauchy’s Residue Theorem and its applications: evaluation of integrals.

מתמטיקה בדידה (90926)

Abstract:

Logic – basic definitions and concepts, predicate arithmetic. Set theory – basic definitions, general relations, equivalent and order relations, mathematical induction principle, f?unctions and set cardinality. Combinatorics – basic definitions and principles, Newton binomial formula, inclusion – exclusion principle, pigeonhole principle, recursions, generating f?unctions Graph theory – basic definitions and results, trees, Euler graphs.