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Courses

  • 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.
  • Partial Differential Equations (90915)
    • Course summary:

    Abstract:

    Derivation of the wave equation.

    D’Alembert solution for an infinite string, wave bouncing from a clamped and a free end of a string.

    Well-posedness. Classification of second order linear problems.

    Canonical forms. Laplace equation.

    Solution of the wave equation on a bounded interval by separations of variables.

    Uniqueness of the solution using the energy method. The maximum principle.

    Separation of variables to Laplace equation in a rectangular and in a circle.

    The heat equation. The maximum principle for the heat equation.

     

    Solution of the inhomogeneous problem.

    Solution of partial differential equations using Integral transforms.

     

    Waves in a rounded membrane and Bessel equation.
  • Complex Functions (90917)
    • Course summary:

    Abstract:

    Complex integration : Contour Integrals. Residue theory.

    Cauchy’s Residue Theorem and its applications: evaluation of integrals.
  • Numerical Analysis (90925)
    • Course summary:

    Abstract:

    Interpolation and approximations methods, error analysis.

    Numerical integration, differentiation.

    Ordinary differential equations solution, Solutions to non-linear equations.

    Solutions to a set of Linear equations.
  • 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.
  • Linear Algebra2 (90954)
    • Course summary:

    Abstract:

    The course consists of two major topics: Linear Operators and introduction to group theory.