Summary A result is discussed which permits the summing of series whose terms have more complicated sign patterns than simply alternating plus and minus. The Alternating Series Test, commonly taught in beginning calculus courses, is a corollary. This result, which is not difficult to prove, widens the series summable by beginning students and paves the way for understanding more advanced questions such as convergence of Fourier series. An elementary exposition is given of Dirichlet’s Test for the convergence of a series and an elementary example suitable for a beginning calculus class and a more advanced example involving a Fourier series which is appropriate for an advanced calculus class are provided. Finally, two examples are discussed for which Dirichlet’s Test does not apply and a general procedure is given for deciding the convergence or divergence of these and similar examples.

This thesis is intended as an introduction to the study of one type of trigonometric series, the Fourier series.

No description available.

No description available.

Thesis (D.A.)--Illinois State University, 1991. / Title from title page screen, viewed December 9, 2005. Dissertation Committee: Arnold J. Insel (chair), John A. Dossey, Robert G. Hathway, Patricia H. Klass, Robert K. Ritt. Includes bibliographical references (leaves 17-18) and abstract. Also available in print.

Thesis (Ph. D.)--University of Wisconsin, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf 83).

The thesis is divided into four chapters. The first contains notation and fundamental results. The others contain a number of theorems on Riesz summability, ordinary in the second, absolute in the third and strong in the fourth. The substance of chapter II has appeared in the Proceedings of the Glasgow Mathermatical Association.

The purpose of this thesis is to determine the spectrum of a type of integral operator called "Convolution Operator" acting on LP(0, °°) . In the special case p = 2 , we have a tool called the Mellin transform, this enables us to analyze the spectrum in more detail. A number of papers have dealt with special cases of our result, the reader is referred to the bibliography of a paper by D. W. Boyd; (to appear). Spectra of Convolution Operators. / Science, Faculty of / Mathematics, Department of / Graduate

No description available.