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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 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.
  • Introduction to Probability (90911)
    • תקציר הקורס:

    Abstract:

    Basic concepts in probability theory: sample space, elementary theorems, combinatorial calculations, conditional probability and independence, random discrete variables, expected value and variance, special random variables,

     multivariate variables, central limit theorem. Basic concepts in statistics: statistical estimation and testing, confidence intervals.
  • Harmonic Analysis (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 func tion,

    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 func tion or a delta func tion.
  • Complex Functions (90917)
    • תקציר הקורס:

    Abstract:

    Complex integration : Contour Integrals. Residue theory.

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