Courses: 4th Year 2nd Sem., B. Sc. Mathematics

MTH412: Partial Differential Equations
(3 credit units)First and second order Partial Differential Equations. Solutions of Heat, Wave, and Laplace equations by the method of characteristics, separation of variables, eigenfunctions expansions and Fourier series and transforms SturmLiouville problems orthogonal polynomials and functions

MTH422: Applied Functional Analysis II
(3 credit units)Separability and compactness. Algebraic structure of linear vector spaces, normed spaces and continuous operators, linear products spaces and Hilbert spaces. Minimization of quadratic functionals

MTH432: General Topology
(3 credit units)Topological spaces, definition, open and closed sets, neighborhoods. Coarser, and finer topologies. Basis and sub bases.Separatic axioms, compactness, local compactness, connectedness. Construction of new topological spaces from given ones; subspaces, quotient spaces. Continuous functions homoeomorphous topological invariants, spaces of continuous functions: point wise and uniform convergence.

MTH492: Project
(6 credit units) 
MTH442: Abstract Algebra III
(3 credit units)Minimal polynomial of an algebraic number.Eisentein’s irreducibility criterion.Splitting fields and normal extension.Primitive element theorem.Galois group of a polynomial.Field degrees and group orders.The Galois correspondence.The fundamental theorem of Galois Theory.

MTH452: Field Theory
(3 credit units)Gradient, divergence and curl: further treatment and application of the differential definitions. The integral definition of gradient, divergence and curl: line, surface and volume integrals: green’s gauss` and stroke’s theorems. Curvilinear Coordinates.Simple notion of tensors.The use of tensor notation.

MTH462: Complex Analysis III
(3 credit units)The algebra of complex numbers.Geometric representation of complex numbers and the spherical representation. Analytic functions, power series. The Exponential and logarithm function. Analytical function as mappings.Cauchy’s theorem and the cauchy Integral formula.Local properties of Analytic functions.The general form of cauchy’stheorem.The calculus of Residues.Harmonic functions.

MTH472: Numerical analysis III
(3 credit units)Numerical quadrature: Romberg, Gauss, Integrable singular integrands, infinite range, multiple integrands. Discrete and continuous Collocation Tau methods for solving Ode’s.Error analysis. Partial differential equations: finite difference methods. Stability, convergence and error, orthogonal expansion.

MTH482: Quantum Mechanics
(3 credit units)Particle wave duality. Quantum postulates. Schroedinger equation of motion. Potential steps and wells in 1 dim Heisenberg formulation. Classical limits of quantum mechanic. Computer brackets.Linear harmonic oscillator.Angular momentum.3dim square well potential.The hydrogen atom collision in 3dim.Approximation methods for stationary problems.
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