Related papers: A primer on Fourier Series

This primer is a brief introduction to the technologies used in particle detectors designed for high-energy particle physics experiments. The intended readers are students, especially undergraduates, starting laboratory work.

The properties of curl and gradient of divergence operators in the domain $G$ of three-dimensional space are described. The self-conjugacy of these operators in the subspaces $\mathbf{L}_{2}(G) $ and the basis property of the system of…

We consider the systems of rational functions $\{\Phi_n(z)\}, ~n \in \mathbb{Z}$, defined by fixed set points ${\bf a}:=\{a_k\}_{k=0}^{\infty}, ~ (\mathop{\rm Im} a_k>0)$, ${\bf b}:=\{b_k\}_{k=1}^{\infty}, ~ (\mathop{\rm Im} b_k<0)$ and is…

The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple…

This work presents an introduction to feature-based time-series analysis. The time series as a data type is first described, along with an overview of the interdisciplinary time-series analysis literature. I then summarize the range of…

We discuss the formal aspects of the factorial polynomials and of the associated series. We develop the theory using the formalism of quasi-monomials and prove the usefulness of the method for the solutions of nontrivial difference…

In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].

In this chapter we present an overview of the main ideas and methods in the fractional integration and cointegration literature. We do not attempt to give a complete survey of this enormous literature, but rather a more introductory…

This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by…

In this note we consider the Fourier expansion of the Ferrers function P of the first kind. We determine its mode of convergence.

This is a collection of teaching materials used in several Russian universities, schools, and mathematical circles. Most problems are chosen in such a way that in the course of the solution and discussion a reader learns important…

In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out very easily calculating for the analytic Fourier-Feynman transform of…

We present a simple, closed formula which gives all the primes in order. It is a simple product of integer floor and ceiling functions.

This review article was first published in 2008 as chapter 11 in the book "Fast Fourier Transforms," edited by C. S. Burrus, for the Connexions project at Rice University, which is sadly no longer online. It gives a high-level overview of…

The following is the very first set of the series in 'Problems and Solutions in a Graduate Course in Classical Electrodynamics'. In each of the sets of the problems we intend to follow a theme, which not only makes it unique but also deals…

In this work, I present an automatic system for the evaluation of closed-type exercises in physics at the high school level or in the first year of a degree where physics is a mandatory course. It is expected that this will allow students…

We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…

While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…

This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results…

In this work we derive results concerning Elliptic Functions using as tools general formulas from previus work.