Visual Complex Analysis

Author: Tristan Needham
Publisher: Oxford University Press
ISBN: 9780198534464
Category : Mathematics
Languages : en
Pages : 620

Book Description
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Visual Complex Functions

Author: Elias Wegert
Publisher: Springer Science & Business Media
ISBN: 3034801807
Category : Mathematics
Languages : en
Pages : 374

Book Description
This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.

Visual Differential Geometry and Forms

Author: Tristan Needham
Publisher: Princeton University Press
ISBN: 0691203709
Category : Mathematics
Languages : en
Pages : 530

Book Description
An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

Complex Analysis

Author: Eberhard Freitag
Publisher: Springer Science & Business Media
ISBN: 3540308237
Category : Mathematics
Languages : en
Pages : 553

Book Description
All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included

Complex Made Simple

Author: David C. Ullrich
Publisher: American Mathematical Soc.
ISBN: 0821844792
Category : Mathematics
Languages : en
Pages : 506

Book Description
Presents the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains. This book is suitable for a first-year course in complex analysis

Complex Analysis with MATHEMATICA®

Author: William T. Shaw
Publisher: Cambridge University Press
ISBN: 0521836263
Category : Computers
Languages : en
Pages : 6

Book Description
This book presents a way of learning complex analysis, using Mathematica. Includes CD with electronic version of the book.

Mathematics and Its History

Author: John Stillwell
Publisher: Springer Nature
ISBN: 3030551938
Category : Mathematics
Languages : en
Pages : 400

Book Description
This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition

Introduction to Complex Analysis

Author: H. A. Priestley
Publisher: OUP Oxford
ISBN: 0191037206
Category : Mathematics
Languages : en
Pages : 344

Book Description
Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics.

Interactive Visual Data Analysis

Author: Christian Tominski
Publisher: CRC Press
ISBN: 1351648748
Category : Computers
Languages : en
Pages : 313

Book Description
In the age of big data, being able to make sense of data is an important key to success. Interactive Visual Data Analysis advocates the synthesis of visualization, interaction, and automatic computation to facilitate insight generation and knowledge crystallization from large and complex data. The book provides a systematic and comprehensive overview of visual, interactive, and analytical methods. It introduces criteria for designing interactive visual data analysis solutions, discusses factors influencing the design, and examines the involved processes. The reader is made familiar with the basics of visual encoding and gets to know numerous visualization techniques for multivariate data, temporal data, geo-spatial data, and graph data. A dedicated chapter introduces general concepts for interacting with visualizations and illustrates how modern interaction technology can facilitate the visual data analysis in many ways. Addressing today’s large and complex data, the book covers relevant automatic analytical computations to support the visual data analysis. The book also sheds light on advanced concepts for visualization in multi-display environments, user guidance during the data analysis, and progressive visual data analysis. The authors present a top-down perspective on interactive visual data analysis with a focus on concise and clean terminology. Many real-world examples and rich illustrations make the book accessible to a broad interdisciplinary audience from students, to experts in the field, to practitioners in data-intensive application domains. Features: Dedicated to the synthesis of visual, interactive, and analysis methods Systematic top-down view on visualization, interaction, and automatic analysis Broad coverage of fundamental and advanced visualization techniques Comprehensive chapter on interacting with visual representations Extensive integration of automatic computational methods Accessible portrayal of cutting-edge visual analytics technology Foreword by Jack van Wijk For more information, you can also visit the author website, where the book's figures are made available under the CC BY Open Access license.

An Introduction to Complex Analysis

Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 146140195X
Category : Mathematics
Languages : en
Pages : 345

Book Description
This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.