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Courses

  • Differential And Integral Calculus1 (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'Hopital'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.
  • 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.