הודעה מהמערכת

Lecturer Mrs. Zelekman Smirin Olga

Courses

  • חשבון דיפרנציאלי אי (90901)
    • תקציר הקורס:

    Abstract:

    Real numbers. Sequences. Limit of a sequence. Limits and continuity of f?unctions. Intermediate value theorem. Weierstrass's theorem. The derivative. Techniques of differentiation. Fermat, Rolle and Lagrange theorems. L'H?pital's rule. Taylor polynomial approximations. The derivative in graphing and applications. The definite and indefinite integral. Principles on integral evaluation: integration by parts and by substitution. The fundamental theorem of calculus (Newton-Leibniz). Improper integral.
  • חשבון דיפרנציאלי אי (90902)
    • תקציר הקורס:

    Abstract:

    Infinite series. Convergence tests. Series of f?unctions; convergence; (uniform convergence-optional). Power series; representation of f?unction by power series. Taylor series. F?unctions of several variables- limits and continuity, partial and directional derivatives. Linear approximation. Gradient. The chain rule. Higher order partial derivatives and second-degree Taylor polynomial. Relative/absolute maximum and minimum values. Lagrange multipliers. Multiple integrals. Fubini's theorem. Change of variables and Jacobian. Polar, cylindrical and spherical coordinates. Line integrals of scalar f?unctions. Line integrals of vector fields. Independence of path and Green’s theorem. Surface integrals of scalar f?unctions. Oriented surfaces and surface integrals of vector fields. The divergence theorem (Gauss-Ostrogradsky). Stokes' theorem. Applications.
  • משוואות דיפ' רגילות (90914)
    • תקציר הקורס:

    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.
  • משוואות דיפ' חלקיות (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.
  • אנליזה הרמונית (90916)
    • תקציר הקורס:

    Abstract:

    Fourier series: expansion to Fourier series on a finite interval,

    Fourier coefficients. Complex representation of Fourier series,

    the convergence of the series, Dirichlet function, convergence in a jump discontinuity. Gibbs phenomena.

    Parseval’s identity. Differentiation and integration of Fourier series.

    Fourier transform, definition, properties and the transform table.

    Applications of Fourier transform in signal processing and

    in solutions of differential equations. Laplace transform and its applications in solving ordinary differential equations.

    Solution in cases where the forcing term is a step function or a delta function.
  • פונקציות מרוכבות (90917)
    • תקציר הקורס:

    Abstract:

    Complex integration : Contour Integrals. Residue theory.

    Cauchy’s Residue Theorem and its applications: evaluation of integrals.
  • אנליזה נומרית (90925)
  • מתמטיקה בדידה (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.
  • אלגברה ליניארית2 (90954)
    • תקציר הקורס:

    Abstract:

    The course consists of two major topics: Linear Operators and introduction to group theory.