Related papers: A primer on Fourier Series
This is a draft of a textbook on differential forms. The primary target audience is sophmore level undergraduates enrolled in what would traditionally be a course in vector calculus. Later chapters will be of interest to advaced…
In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion…
This paper is meant to be a gentle introduction to Carleson's Theorem on pointwise convergence of Fourier series.
This is a series of short teaching papers dealing with specific topics in a standard first-year undergraduate Physics course. ----- Este texto comp\~oe-se de quatro pequenas notas -- independentes entre si -- em que se discutem alguns…
Borrowing methods and formulas from Prof. Goodman's classic Introduction to Fourier Optics textbook [1], I have developed a software package [2] that has been used in both industrial research and classroom teaching [3]. This paper briefly…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
These lecture notes were written for a mini-course that was designed to introduce students and researchers to {\it $q$-series,} which are also called {\it basic hypergeometric series} because of the parameter $q$ that is used as a base in…
In the present paper, we give a brief review of $L^{1}$-convergence of trigonometric series. Previous known results in this direction are improved and generalized by establishing a new condition.
A large number of the classical texts dealing with Fourier series more or less state that the hypothesis of periodicity is required for pointwise convergence. In this paper, we highlight the fact that this condition is not necessary.
This paper briefly describes some simple techniques for illuminating Fourier series and Fourier analysis with the Audacity sound recording program. These techniques are easily applied in the classroom and help students move beyond formula…
Course material for mathematical methods of theoretical physics intended for an undergraduate audience.
In the present paper, we deal with Fourier-transformation of Frobenius-Euler polynomials. We shall give its applications by using infinite series. Our applications possess interesting properties which we state in this paper.
Classes of simple polynomial and simple trigonometric splines given by Fourier series are considered. It is shown that the class of simple trigonometric splines includes the class of simple polynomial splines. For some parameter values, the…
The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.
These are lecture notes for a 1-semester undergraduate course (in computer science, mathematics, physics, engineering, chemistry or biology) in applied categorical meta-language. The only necessary background for comprehensive reading of…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
Using a pointwise version of Fej\'{e}r's theorem about Fourier series, we obtain two formulae related to the series representations of positive integral powers of $\pi$. We also check the correctness of our formulae by the applications of…
In this work we present new methods for transforming and solving finite series by using the Laplace transform. In addition we introduce both an alternative method based on the Fourier transform and a simplified approach. The latter allows a…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…