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(UCY-UW):



Fall 2021: ΜΑΣ 301

Fall 2021: ΜΑΣ 131

Spring 2020: No teaching

Fall 2020: ΜΑΣ 301

Spring 2020: ΜΑΣ 202

Fall 2019: ΜΑΣ 603 (Graduate)

Fall 2019: ΜΑΣ 303

Spring 2019: ΜΑΣ 203

Spring 2019: ΜΑΣ 029

Fall 2018: ΜΑΣ 606 (Graduate)

Fall 2018: ΜΑΣ 102

Spring 2018: ΜΑΣ 101

Spring 2018: ΜΑΣ 002

Fall 2017: ΜΑΣ 603 (Graduate)

Fall 2017: ΜΑΣ 303

Academic year 2016-17: No teaching

Spring 2016: ΜΑΣ 033/043/024/027

Spring 2016: ΜΑΣ 605 (Graduate)

Fall 2015: ΜΑΣ 033/043/024/027

Spring 2015: ΜΑΣ 304

Spring 2015: ΜΑΣ 604 (Graduate)

Fall 2014: ΜΑΣ 033

Fall 2014: ΜΑΣ 043

Fall 2014: ΜΑΣ 024

Fall 2014: ΜΑΣ 617 (Graduate)

Spring 2014: ΜΑΣ 302

Fall 2013: ΜΑΣ 121

Fall 2013: ΜΑΣ 606 (Graduate)

Spring 2013: ΜΑΣ 302

Fall 2012: ΜΑΣ 603 (Graduate)

Fall 2012: ΜΑΣ 303

Fall 2012: ΜΑΣ 023

Fall 2012: ΜΑΣ 605 (Graduate)

Spring 2012: ΜΑΣ 302

Spring 2012: ΜΑΣ 024

Fall 2011: ΜΑΣ 603 (Graduate)

Spring 2011: ΜΑΣ 603 (Graduate)

Spring 2011: ΜΑΣ 121

Fall 2010: ΜΑΣ 303

Fall 2010: ΜΑΣ 023

Spring 2010: ΜΑΣ 122

Spring 2010: ΜΑΣ 101

Fall 2009: ΜΑΣ 023

Spring 2009: Math 126 A

Winter 2009: Math 126 A&B

Autumn 2008: Math 424 B

Summer 2008: Math 324 B&C

Spring 2008: Math 308 D

Winter 2008: Math 308 D&E

Autumn 2007: Math 308 D&E

Spring 2007: Math 126 A&B

Winter 2007: Math 308 D and Math 308 H

Autumn 2006: No teaching


Graduate Courses Courses Description (Selection)


MAS 603 Partial Differential Equations


First order quasi-linear equations, the method of characteristics. Classification and normal forms. Existence theorem of Cauchy- Kovalevskaya and uniqueness theorem of Holmgren. Distributions and weak solutions. Hyperbolic theory, characteristics, propagation of singularities. Wave equation in one, two and three space dimensions. Conservation laws and shock waves. Elliptic theory, Laplace and Poisson equations, fundamental solutions, harmonic functions. Variational formulation of elliptic boundary value problems. Parabolic theory, heat equation, parabolic initial/boundary value problems.


MAS 605 Elliptic Partial Differential Equations of 2nd order


Laplace equation, fundamental solutions, Green's function, maximum principle, Poisson kernel, Harmonic functions and their properties, Harnack inequalities, equations with variable coefficients, Dirichlet problem, existence and regularity of solutions. Sobolev Spaces


MAS 617 Topics in Analysis


Free Boundary problems, the thick obstacle problem, the thin obstacle problem, two phase problems, Alt-Caffarelli-Friedman monotonicity formula, Almgren’s monotonicity formula, optimal regularity in elliptic and parabolic problems.


MAS 606 Function Theory of One Complex Variable


Basic facts about complex functions of one complex variable. Differentiation. Cauchy-Riemann equations. Elementary complex functions. Complex integration and the Cauchy Theorem. Applications of Cauchy Theorem. Meromorphic functions. Power series and Laurent series. Residues. Entire functions and Conformal mappings.


MAS 604 Functional Analysis


Compact operators. Spectral theory. Self adjoint operators. Closed and orthonormal operators. Spectral theorem. Semigroups.



Undergraduate Courses Description (Selection)


MAS 303 Partial Differential Equations


Separation of variables – Fourier series. First order Partial Differential Equations. Nonlinear first order Partial Differential Equations. Linear second order Partial Differential Equations. Elliptic, Parabolic and Hyperbolic Partial Differential Equations.


MAS 302 Complex Analysis


Complex numbers, Basic complex functions, Cauchy- Riemann equations, holomorphic functions, harmonic functions. (Exponential, trigonometric and logarithmic functions). Contontintegration, Cauchy’s theorem, Cauchy’s integral formula. Morera’s theorem, Liouville’s theorem, the fundamental theorem of algebra. The Maximum modulus theorem. Taylor series, Laurent series, calculus of residues. Conformal mapping, linear fractional transformation.


MAS 304 Functional Analysis


Metric spaces: Examples and elements of the theory of metric
spaces. Banach spaces: Norm, dimension and compactness,
bounded operators, linear functionals, dual space, the spaces

,
1≤ p ≤ ∞, Hilbert spaces: Inner products, orthogonal sums,
orthonormal bases, the Riesz representation theorem, the adjoint
operator, self – adjoint, unitary and normal operators.
Fundamental theorems for Banach spaces: the Hahn–Banach
theorem, reflexive spaces, the uniform boundedness theorem,
weak and strong convergence, the open mapping and closed graph theorems. Applications:

The fixed point theorem and its applications to the theory of linear, integral and differential

equations, applications to the theory of approximation.