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Courses

  • Mathematical Logic (90913)
    • תקציר הקורס:

    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
  • Partial Differential Equations (90915)
    • תקציר הקורס:

    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.
  • Numerical Analysis (90925)
    • תקציר הקורס:

    Abstract:

    Interpolation and approximations methods, error analysis.

    Numerical integration, differentiation.

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

    Solutions to a set of Linear equations.
  • Discrete Mathematics (90926)
    • תקציר הקורס:

    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.