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A lemniscate is a curve defined by two foci, F1 and F2. If the distance between the focal points of F1 - F2 is 2a (a: constant), then any point P on the lemniscate curve satisfy the equation PF1 PF2 = a^2. Jacob Bernoulli first described…
Hyperbolism of a given curve with respect to a point and a line is an interesting construct, a special kind of geometric locus, not frequent in the literature. While networking between two different kinds of mathematical software, we…
In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new…
The humble pendulum is often invoked as the archetype of a simple, gravity driven, oscillator. Under ideal circumstances, the oscillation frequency of the pendulum is independent of its mass and swing amplitude. However, in most real-world…
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation.…
An elastic double pendulum subject to a force acting along a fixed straight line, the so-called "Reut's column problem", is a structure exhibiting flutter and divergence instability, which was never realized in practice and thus debated…
The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
The Looping pendulum phenomenon was first introduced in 2019 at the 32nd edition of the IYPT, wherein a lighter bob sweeps around a cylindrical rod to support the weight of a heavier bob. In this paper, the phenomenon was divided based on…
Bernoulli's free boundary problem is an overdetermined problem in which one seeks an annular domain such that the capacitary potential satisfies an extra boundary condition. There exist two different types of solutions called elliptic and…
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…
In our previous paper, Real Polynomials with a Complex Twist [see http://archives.math.utk.edu/ICTCM/VOL28/A040/paper.pdf], we used advancements in computer graphics that allow us to easily illustrate more complete graphs of polynomial…
The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to the average first-year physics student. However, deriving this expression from first principles involves solving a non-linear differential…
In this article we discuss an important students' misconception about derivatives, that the expression of the derivative of the function contains the information as to whether the function is differentiable or not where the expression is…
A heuristic but pedagogical derivation is given of an explicit formula which accurately reproduces the period of a simple pendulum even for large amplitudes. The formula is compared with others in the literature.
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
A novel third order nonlinear evolution equation governing the dynamics of high frequency electrostatic drift waves has been derived in the framework of a plasma fluid model in an inhomogeneous magnetized plasma. The linear dispersion…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
Interest in inverse dynamical, spectral and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguides and by a variety of other classical and quantum…
We study the angular derivative problem for petals of one-parameter semigroups of holomorphic self-maps of the unit disk. For hyperbolic petals we prove a necessary and sufficient condition for the conformality of the petal in terms of the…