Courses

משוואות דיפ' חלקיות (90915)

Abstract:

Derivation of the wave equation.

D’Alembert solution for an infinite string, wave bouncing from a clamped and a free end of a string.

Well-posedness. Classification of second order linear problems.

Canonical forms. Laplace equation.

Solution of the wave equation on a bounded interval by separations of variables.

Uniqueness of the solution using the energy method. The maximum principle.

Separation of variables to Laplace equation in a rectangular and in a circle.

The heat equation. The maximum principle for the heat equation.

Solution of the inhomogeneous problem.

Solution of partial differential equations using Integral transforms.

Waves in a rounded membrane and Bessel equation.

לוגיקה מתמטית למדעי מחשב (90923)

Abstract:

Propositional logic: syntax. Semantics, propositional calculus. Interpretations. Deductions systems: L system , Deduction theorem, consistence, soundness and

completeness theorems.

Predicate Logic: syntax: terms and formulas, Semantic predicate calculus.

Deduction systems: K system, deduction theorem. Consistence, soundness and completeness theorem. Relationship between system L and the system K. G?del incompleteness theorems

אנליזה נומרית (90925)
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.