4 papers
A Pedagogical Introduction to the Unified Transform Method: The Heat Equation on a Finite Interval
Athanasios Paraskevopoulos
This paper presents a detailed application of the Unified Transform Method (Fokas method) to the one-dimensional heat equation on with Dirichlet boundary conditions. The an…
The unified transform for Burgers' equation: Application to unsaturated flow in finite interval
Konstantinos Kalimeris, Leonidas Mindrinos, Athanasios Paraskevopoulos
In this paper, we focus on one-dimensional vertical infiltration, assuming constant diffusivity and a quadratic relationship between hydraulic conductivity and water content. Under…
Simple Continued Fractions an Approach for High School Students
Athanasios Paraskevopoulos
This paper introduces high school students to the mathematical concept of continued fractions, encompassing both finite and infinite forms. It delves into fundamental properties, t…
Francois Viete and his contribution to mathematics
Athanasios Paraskevopoulos
This paper studies the work of the French mathematician Francois Viete, known as the "father of modern algebraic notation". Along with this fundamental change in algebra, Viete ado…