Lectures On Complex Integration

Author: Alexander O. Gogolin
Publisher: Springer Science & Business Media
ISBN: 3319002120
Size: 54.51 MB
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The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.

Introduction To Methods Of Approximation In Physics And Astronomy

Author: Maurice H. P. M. van Putten
Publisher: Springer
ISBN: 9811029326
Size: 37.90 MB
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This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based on their usefulness and educational value, their applicability to a broad range of problems and their utility in highlighting key mathematical concepts. Modern astronomy reveals an evolving universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data-analysis. The book is organized to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal detection algorithms involving the Fourier transform and examples of numerical integration of ordinary differential equations and some illustrative aspects of modern computational implementation. Some of the topics highlighted introduce the reader to selected problems with comments on numerical methods and implementation on modern platforms including CPU-GPU computing. Developed from lectures on mathematical physics in astronomy to advanced undergraduate and beginning graduate students, this book will be a valuable guide for students and a useful reference for practicing researchers. To aid understanding, exercises are included at the end of each chapter. Furthermore, some of the exercises are tailored to introduce modern symbolic computation.

Classical Electrodynamics

Author: Francesco Lacava
Publisher: Springer
ISBN: 3319394746
Size: 12.48 MB
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This book proposes intriguing arguments that will enable students to achieve a deeper understanding of electromagnetism, while also presenting a number of classical methods for solving difficult problems. Two chapters are devoted to relativistic electrodynamics, covering all aspects needed for a full comprehension of the nature of electric and magnetic fields and, subsequently, electrodynamics. Each of the two final chapters examines a selected experimental issue, introducing students to the work involved in actually proving a law or theory. Classical books on electricity and magnetism are mentioned in many references, helping to familiarize students with books that they will encounter in their further studies. Various problems are presented, together with their worked-out solutions. The book is based on notes from special lectures delivered by the author to students during the second year of a BSc course in Physics, but the subject matter may also be of interest to senior physicists, as many of the themes covered are completely ignored or touched only briefly in standard textbooks.

Recollections Of A Scientist

Author: Norman N. Greenwood
Publisher: Xlibris Corporation
ISBN: 1469179377
Size: 69.89 MB
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Recollections of a Scientist 1: Boyhood and Youth in Australia (1925-1948) This illustrated book is the first volume of the Memoirs of a distinguished, internationally renowned scientist, Professor Norman N. Greenwood, FRS. It gives a lively and intimate account of his boyhood and youth in Australia during the nineteen thirties and forties and is divided into thirteen chapters. It is a personal account rather than a formal history and describes in refreshing detail his richly diverse experiences. Chapter 1 explains how he came to be born in Melbourne although both of his parents as well as his elder sister and younger brother were all born in Northern England---his father Professor John Neill Greenwood had just been appointed as the first Professor of Metallurgy in an Australian University. The scene is further set by a brief account of the extraordinary events that led up to the founding of the University of Melbourne following the Victorian Gold Rush of the mid nineteenth century and its subsequent development into one of the major Universities of the then British Empire. The young family settled in Mont Albert, one of the developing eastern suburbs of the expanding metropolis, but unfortunately his parents separated soon afterwards and subsequently divorced. The children moved with their mother to the neighbouring suburb of Surrey Hills and one of her sisters came out from England to help with the growing family. Norman goes on to describe the various schools he attended and has some perceptive comments on his teachers, the ethos of the schools and the gradual changes that have occurred in the approach to education in Victoria over the years since the nineteen thirties. Initially vacations were spent at a country cottage being built by his father at Kinglake in the densely wooded hills to the north of Melbourne, and Norman evokes a childhood view of the exotic plants and animals of the bush, the deep secluded tree-fern gullies and tumbling mountain streams. His father was one of the main protagonists for the development of the Kinglake National Park which he had helped to found. Tragically, much of the Park was engulfed by the enormous bush fires (the worst in Australia’s history) that wiped out the little township of Kinglake with great loss of life in February 2009. Other holidays were spent on the beaches of Port Phillip Bay or on the cooler slopes of the Dandenong Ranges to the east. Norman and his younger brother Eric (always known in his youth as Peter or ‘Nipper’) loved roaming in the Olinda State Forest and Sherwood Forest where the tall mountain ash (eucalyptus) trees towered above the dense undergrowth of tree ferns and other plants. Bush animals abounded as did the raucous cockatoos and multicoloured parrots. The great prize, however, was to sight a lyre bird performing his stately dance and singing his amazing repertoire of all the other birds’ songs and even the man-mad sounds of car horns, chain saws and steam engines. For the three years 1939-40-41 Norman attended University High School near the city centre and adjacent to the grounds of the University itself. It was a remarkable school with an excellent academic reputation but also known for fostering of musical talent and for its prowess in sport. Norman joined the School Orchestra (as second flute) and they gave concerts in the Melbourne Town Hall and occasionally on the State broadcasting station 3LO. He also edited the School Magazine, The Record, perhaps an early portent of his later prolific output of scientific research papers, reviews, monographs and textbooks. In the summer vacation of January 1940 (during which Norman had his fifteenth birthday) he went on and extended (1300 mile) concert-party tour of twenty eight country towns in Western Victoria and over the border into South Australia. The trip was organised by the Young Australia League (YAL) and took the form of a White Minstrels Review of thirty boys with songs, i

Lectures On Differential Geometry

Author: S S Chern
Publisher: World Scientific Publishing Company
ISBN: 9813102985
Size: 67.55 MB
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This book is a translation of an authoritative introductory text based on a lecture series delivered by the renowned differential geometer, Professor S S Chern in Beijing University in 1980. The original Chinese text, authored by Professor Chern and Professor Wei-Huan Chen, was a unique contribution to the mathematics literature, combining simplicity and economy of approach with depth of contents. The present translation is aimed at a wide audience, including (but not limited to) advanced undergraduate and graduate students in mathematics, as well as physicists interested in the diverse applications of differential geometry to physics. In addition to a thorough treatment of the fundamentals of manifold theory, exterior algebra, the exterior calculus, connections on fiber bundles, Riemannian geometry, Lie groups and moving frames, and complex manifolds (with a succinct introduction to the theory of Chern classes), and an appendix on the relationship between differential geometry and theoretical physics, this book includes a new chapter on Finsler geometry and a new appendix on the history and recent developments of differential geometry, the latter prepared specially for this edition by Professor Chern to bring the text into perspectives.

Complex Analysis With Applications To Flows And Fields

Author: Luis Manuel Braga da Costa Campos
Publisher: CRC Press
ISBN: 1420071203
Size: 77.40 MB
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Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady heat conduction, and other problems. It provides the mathematical results to sufficiently justify the solution of these problems, eliminating the need to consult external references. The book is conveniently divided into four parts. In each part, the mathematical theory appears in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. Each chapter begins with an introduction or summary and concludes with related topics. The last chapter in each section offers a collection of many detailed examples. This self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.