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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'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.
  • Differential and Integral Calculus2 (90902)
    • תקציר הקורס:

    Abstract:

    Infinite series. Convergence tests. Series of f?unctions; convergence and uniform convergence. Power series; representation of f?unctions 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.
  • Linear Algebra (90905)
    • תקציר הקורס:

    Abstract:

    The first part of the course is dedicated to study of techniques for

    solving systems of linear equations. Several basic methods are presented:

    Gauss elimination, matrix solution, Cramer rule.

    The last two methods involve matrix arithmetic, which is also presented in this part. The second part discusses vector spaces and linear transformations. Most attention is given to the matrix approach. Matrix diagonalization issues summarize this part.

    The last part of the course study inner product spaces and their basic properties.
  • 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.
  • Complex Functions (90917)
    • תקציר הקורס:

    Abstract:

    Complex integration : Contour Integrals. Residue theory.

    Cauchy’s Residue Theorem and its applications: evaluation of integrals.
  • 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.