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Lecturer Mr. Bengiat Amit

Main Content

Courses

  • Fundamentals of Programming and Logical Thinking (7015)
  • Fundamentals of Computer Science and Data (7204)
  • Fundamentals of Computer Science and Data1 (7214)
  • Differential and Integral Calculus1 (90901)
    • Course summary:

    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)
    • Course summary:

    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.
  • Linear Algebra (90905)
    • Course summary:

    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)
    • Course summary:

    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.
  • Harmonic Analysis (90916)
    • Course summary:

    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.
  • Complex Functions (90917)
    • Course summary:

    Abstract:

    Complex integration : Contour Integrals. Residue theory.

    Cauchy’s Residue Theorem and its applications: evaluation of integrals.
  • Discrete Mathematics (90926)
    • Course summary:

    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.
  • Discrete Mathematics IBL (90955)
    • Course summary:

    Abstract:

    Introduction to Logic - basic concepts, Set Theory, Relations, Equivalence Relations, Order Relations, Induction, f?unctions, Cardinality, Combinatorics, Newton's Binom, Inclusion-Exclution, Pigeon hole principal, Recursion, generating f?unctions and Introduction to Graph Theory