Complex Analysis


Book Description

This unusually lively textbook introduces the theory of analytic functions, explores its diverse applications and shows the reader how to harness its powerful techniques. The book offers new and interesting motivations for classical results and introduces related topics that do not appear in this form in other texts. For the second edition, the authors have revised some of the existing material and have provided new exercises and solutions.







The DFT


Book Description

This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.




Odd as F*ck


Book Description

In this collection, the author loses, finds and redefines herself, in poems that are sometimes visceral and often humorous. She ultimately shows how meaningful life can become after a period of darkness and how transformative those experiences can be. Anne Walsh Donnelly's debut chapbook with Fly on the Wall Press 'The Woman With An Owl Tattoo' came 2nd at the International Poetry Book Awards 2020. 'These are personal poems, where the reader shares with the poet a space as intimate as the conjugal bed. From the everyday idiom of housewives and farmers to the imagined voices of beasts and inanimate objects, Anne Walsh Donnelly captures the humour and pathos of real life with unique honesty.' - Audrey Molloy, poet and author of Satyress 'In Odd as F*ck, Anne Walsh Donnelly recounts one woman's journey through pain and growth. The poems are poignant, stark, and beautiful, heavy with unanswered questions, but buoyed up by levity. This is potent work.' -Nuala O'Connor, author of The Juno Charm Sample poem; 1957 - 1959 On the hottest Sunday in July, the same day Mam got her first period, she was sent to her father's room to wake him for tea. She cried when she touched his tepid skin and begged him to open his eyes. In the fields cattle lowed, udders heavy with milk. Two Christmases later, my grandmother pressed Mam's hand against her abdomen, told her of the operation in January. 'I'm afraid I might not wake up.' 'You mustn't cry, you have to be strong for your sisters, ' the nuns told Mam, the day before the funeral. She watched over her sisters as they stood shivering in the graveyard, under the shadow of a Great Oak. She became the roots of their saplings, chainsawed through her own pain. 'This is poetry; raw, untethered, honest poetry. It is poetry that doesn't hide, doesn't whisper but instead stands tall and roars. It allows us to get to know the author, to journey with her as she navigates through family, sexuality, ageing and motherhood. This is poetry that tells us that it's okay, that life is often not easy but there is always hope, poetry that gets straight to the point, that is pure, that is real. This is poetry.' -Steve Denehan, poet and author of Days of Falling Flesh and Rising Moons 'Anne Walsh Donnelly states that Death is not nothing, it is everything-this could be the manifesto for her fierce and delicate poetry. A disarming openness and honesty lights up in every poem while her voice never loses its humour or balance, ranging. from the visionary to a wonderfully universal everyday demotic.' - Martina Evans, poet and author of Now We Can Talk Openly About Men




Signals and Systems (Edition 5.0)


Book Description

This book is intended for use in teaching undergraduate courses on continuous-time and/or discrete-time signals and systems in engineering (and related) disciplines. It provides a detailed introduction to continuous-time and discrete-time signals and systems, with a focus on both theory and applications. The mathematics underlying signals and systems is presented, including topics such as: signal properties, elementary signals, system properties, continuous-time and discrete-time linear time-invariant systems, convolution, continuous-time and discrete-time Fourier series, the continuous-time and discrete-time Fourier transforms, frequency spectra, and the bilateral and unilateral Laplace and z transforms. Applications of the theory are also explored, including: filtering, equalization, amplitude modulation, sampling, feedback control systems, circuit analysis, Laplace-domain techniques for solving differential equations, and z-domain techniques for solving difference equations. Other supplemental material is also included, such as: a detailed introduction to MATLAB, a review of complex analysis, an introduction to partial fraction expansions, an exploration of time-domain techniques for solving differential equations, and information on online video-lecture content for material covered in the book. Throughout the book, many worked-through examples are provided. Problem sets are also provided for each major topic covered.




Handbook of Computational Methods for Integration


Book Description

During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-ended. The importance of numerical integration in so many areas of science and technology has made a practical, up-to-date reference on this subject long overdue. The Handbook of Computational Methods for Integration discusses quadrature rules for finite and infinite range integrals and their applications in differential and integral equations, Fourier integrals and transforms, Hartley transforms, fast Fourier and Hartley transforms, Laplace transforms and wavelets. The practical, applied perspective of this book makes it unique among the many theoretical books on numerical integration and quadrature. It will be a welcomed addition to the libraries of applied mathematicians, scientists, and engineers in virtually every discipline.




Singularity Theory and its Applications


Book Description

A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory, and applications in the sciences. The papers are orginal research, stimulated by the symposium and workshops: All have been refereed, and none will appear elsewhere. The main topic, deformation theory, is represented by several papers on descriptions of the bases of versal deformations, and several more on descriptions of the generic fibres. Other topics include stratifications, and applications to differential geometry.




Fourier Analysis with Applications


Book Description

A two-volume advanced text for graduate students. This first volume covers the theory of Fourier analysis.




Selected Papers of J. Robert Schrieffer


Book Description

Presents papers by theoretical physicist J. Robert Schrieffer on topics in superconductivity and condensed matter physics.




Geometry, Particles, and Fields


Book Description

Geometry, Particles and Fields is a direct reprint of the first edition. From a review of the first edition: "The present volume is a welcome edition to the growing number of books that develop geometrical language and use it to describe new developments in particle physics...It provides clear treatment that is accessible to graduate students with a knowledge of advanced calculus and of classical physics...The second half of the book deals with the principles of differential geometry and its applications, with a mathematical machinery of very wide range. Here clear line drawings and illustrations supplement the multitude of mathematical definitions. This section, in its clarity and pedagogy, is reminiscent of Gravitation by Charles Misner, Kip Thorne and John Wheeler...Felsager gives a very clear presentation of the use of geometric methods in particle physics...For those who have resisted learning this new language, his book provides a very good introduction as well as physical motivation. The inclusion of numerous exercises, worked out, renders the book useful for independent study also. I hope this book will be followed by others from authors with equal flair to provide a readable excursion into the next step." PHYSICS TODAY Bjoern Felsager is a high school teacher in Copenhagen. Educated at the Niels Bohr Institute, he has taught at the Universities of Copenhagen and Odense.