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Courses

  • Differential And Integral Calculus2 (90902)
    • תקציר הקורס:

    Abstract:

    Infinite series. Convergence tests. Series of f?unctions; convergence and uniform convergence. Power series; representation of functions by power series. Taylor series. F?unctionsof 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. Polar, cylindrical and spherical coordinates. Line integrals of scalar f?unctions. Line integrals of vector fields. Independence of path and Green theorem. Surface integrals of scalar f?unctions. Oriented surfaces and surface integrals of vector fields. The divergence theorem (Gauss-Ostrogradsky). Stokes' theorem. Applications.
  • Ordinary Differential Equations (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.