Formalization Of Complex Analysis And Matrix Theory

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Formalization of Complex Analysis and Matrix Theory

Author : Zhiping Shi
Publisher : Springer Nature
ISBN 13 : 9811572615
Total Pages : 172 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Formalization of Complex Analysis and Matrix Theory by : Zhiping Shi

Download or read book Formalization of Complex Analysis and Matrix Theory written by Zhiping Shi and published by Springer Nature. This book was released on 2020-08-10 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.

Formal Methods for Industrial Critical Systems

Author : Frédéric Lang
Publisher : Springer
ISBN 13 : 331910702X
Total Pages : 213 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Formal Methods for Industrial Critical Systems by : Frédéric Lang

Download or read book Formal Methods for Industrial Critical Systems written by Frédéric Lang and published by Springer. This book was released on 2014-09-01 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 19th International Conference on Formal Methods for Industrial Critical Systems, FMICS 2014, held in Florence, Italy, in September 2014. The 13 papers presented in this volume were carefully reviewed and selected from 26 submissions. They are organized in topical sections named: cyber-physical systems; computer networks; railway control systems; verification methods; and hardware and software testing.

Applied and Computational Complex Analysis: Power series

Author : Peter Henrici
Publisher : Wiley-Interscience
ISBN 13 :
Total Pages : 708 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Applied and Computational Complex Analysis: Power series by : Peter Henrici

Download or read book Applied and Computational Complex Analysis: Power series written by Peter Henrici and published by Wiley-Interscience. This book was released on 1974 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Analysis

Author : Jane P. Gilman
Publisher : Springer Science & Business Media
ISBN 13 : 038774715X
Total Pages : 230 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Complex Analysis by : Jane P. Gilman

Download or read book Complex Analysis written by Jane P. Gilman and published by Springer Science & Business Media. This book was released on 2007-11-25 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.

Fundamentals of Complex Analysis

Author : K. K. Dube
Publisher : I. K. International Pvt Ltd
ISBN 13 : 9380026021
Total Pages : 293 pages
Book Rating : 4.3/5 (8 download)

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Book Synopsis Fundamentals of Complex Analysis by : K. K. Dube

Download or read book Fundamentals of Complex Analysis written by K. K. Dube and published by I. K. International Pvt Ltd. This book was released on 2013-12-30 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book divided in ten chapters deals with: " Algebra of complex numbers and its various geometrical properties, properties of polar form of complex numbers and regions in the complex plane. " Limit, continuity, differentiability. " Different kinds of complex valued functions. " Different types of transformations. " Conformal mappings of different functions. " Properties of bilinear and special bilinear transformation. " Line integrals, their properties and different theorems. " Sequences and series, Power series, Zero s of functions, residues and residue theorem, meromorphic functions, different kinds of singularities. " Evaluation of real integrals. " Analytic continuation, construction of harmonic functions, infinite product, their properties and Gamma function. " Schwarz-Christoffel transformations, mapping by multi valued functions, entire functions. " Jenson s theorem and Poisson-Jenson theorem. The book is designed as a textbook for UG and PG students of science as well as engineering

Complex Analysis

Author : Andrei Bourchtein
Publisher : Springer Nature
ISBN 13 : 9811592195
Total Pages : 357 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Complex Analysis by : Andrei Bourchtein

Download or read book Complex Analysis written by Andrei Bourchtein and published by Springer Nature. This book was released on 2021-02-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses all the major topics of complex analysis, beginning with the properties of complex numbers and ending with the proofs of the fundamental principles of conformal mappings. Topics covered in the book include the study of holomorphic and analytic functions, classification of singular points and the Laurent series expansion, theory of residues and their application to evaluation of integrals, systematic study of elementary functions, analysis of conformal mappings and their applications—making this book self-sufficient and the reader independent of any other texts on complex variables. The book is aimed at the advanced undergraduate students of mathematics and engineering, as well as those interested in studying complex analysis with a good working knowledge of advanced calculus. The mathematical level of the exposition corresponds to advanced undergraduate courses of mathematical analysis and first graduate introduction to the discipline. The book contains a large number of problems and exercises, making it suitable for both classroom use and self-study. Many standard exercises are included in each section to develop basic skills and test the understanding of concepts. Other problems are more theoretically oriented and illustrate intricate points of the theory. Many additional problems are proposed as homework tasks whose level ranges from straightforward, but not overly simple, exercises to problems of considerable difficulty but of comparable interest.

Nine Introductions in Complex Analysis

Author : Sanford L. Segal
Publisher : Elsevier
ISBN 13 : 008087164X
Total Pages : 733 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Nine Introductions in Complex Analysis by : Sanford L. Segal

Download or read book Nine Introductions in Complex Analysis written by Sanford L. Segal and published by Elsevier. This book was released on 2011-08-18 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nine Introductions in Complex Analysis

Complex Analysis

Author : Man-wah Wong
Publisher : World Scientific Publishing Company
ISBN 13 : 9813107162
Total Pages : 159 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Complex Analysis by : Man-wah Wong

Download or read book Complex Analysis written by Man-wah Wong and published by World Scientific Publishing Company. This book was released on 2008-03-14 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is ideal for a one-semester course for advanced undergraduate students and first-year graduate students in mathematics. It is a straightforward and coherent account of a body of knowledge in complex analysis, from complex numbers to Cauchy's integral theorems and formulas to more advanced topics such as automorphism groups, the Schwarz problem in partial differential equations, and boundary behavior of harmonic functions.The book covers a wide range of topics, from the most basic complex numbers to those that underpin current research on some aspects of analysis and partial differential equations. The novelty of this book lies in its choice of topics, genesis of presentation, and lucidity of exposition.

Theorem Proving in Higher Order Logics

Author : Joe Hurd
Publisher : Springer Science & Business Media
ISBN 13 : 3540283722
Total Pages : 418 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Theorem Proving in Higher Order Logics by : Joe Hurd

Download or read book Theorem Proving in Higher Order Logics written by Joe Hurd and published by Springer Science & Business Media. This book was released on 2005-08-08 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2005, held in Oxford, UK, in August 2005. The 20 revised full papers presented together with 2 invited papers and 4 proof pearls (concise and elegant presentations of interesting examples) were carefully reviewed and selected from 49 submissions. All current issues in HOL theorem proving and formal verification of software and hardware systems are addressed. Among the topics of this volume are theorem proving, verification, recursion and induction, mechanized proofs, mathematical logic, proof theory, type systems, program verification, and proving systems like HOL, Coq, ACL2, Isabelle/HOL and Isabelle/HOLCF.

Advances in Complex Analysis and Applications

Author : Francisco Bulnes
Publisher : BoD – Books on Demand
ISBN 13 : 1839683600
Total Pages : 172 pages
Book Rating : 4.8/5 (396 download)

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Book Synopsis Advances in Complex Analysis and Applications by : Francisco Bulnes

Download or read book Advances in Complex Analysis and Applications written by Francisco Bulnes and published by BoD – Books on Demand. This book was released on 2020-11-04 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The complex analysis, also known as theory of analytic functions or complex variable function theory, is the part of mathematical analysis that investigates the functions of complex numbers, their analyticity, holomorphicity, and integration of these functions on complex domains that can be complex manifolds or submanifolds. Also the extensions of these domains to the complex projective spaces and complex topological groups are study themes. The analytic continuing of complex domains where complex series representations are used and the exploring of singularities whose integration invariants obtain values as zeros of certain polynomials of the complex rings of certain vector bundles are important in the exploring of new function classes in the meromorphic context and also arithmetic context. Also important are established correspondences with complex vector spaces, or even in their real parts, using several techniques of complex geometrical analysis, Nevanlinna methods, and other techniques as the modular forms. All this is just some examples of great abundance of the problems in mathematics research that require the complex analysis application. This book covers some interesting and original research of certain topics of complex analysis. Also included are some applications for inverse and ill posed problems developed in engineering and applied research.

Theorizing Teaching and Learning in Asia and Europe

Author : John Chi-Kin Lee
Publisher : Taylor & Francis
ISBN 13 : 1317616553
Total Pages : 344 pages
Book Rating : 4.3/5 (176 download)

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Book Synopsis Theorizing Teaching and Learning in Asia and Europe by : John Chi-Kin Lee

Download or read book Theorizing Teaching and Learning in Asia and Europe written by John Chi-Kin Lee and published by Taylor & Francis. This book was released on 2017-03-27 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been much debate in recent times between the Anglo American tradition of curriculum studies and the Continental and North European tradition of didactics (Didaktik). As important as such debate has been, this book seeks to add new voices to the debate representing ideas and traditions from a different part of the world. The focus is on Chinese curriculum thinking that has passed through a number of stages and currently represents a blend of some aspects of the American tradition and Chinese cultural traditions. How does Chinese thinking about curriculum, teaching and learning resonate with European didactic traditions and what are the implications for theorizing an expanded field of curriculum studies? This book deliberately transcends borders and cultures to explore new territory, to provide a platform for open dialogue and to open up new areas of investigation Chapters include, Curriculum Reform and Research in China: A Social-Historical Perspective What Mathematics Did Teachers Learn? Comparison of the School and the Pre-Service Teacher Mathematics Curricula in Germany and Taiwan Living in Parallel Worlds: A Transatlantic Dialogue between General Didactics and Instructional Design

NASA Formal Methods

Author : Guillaume Brat
Publisher : Springer
ISBN 13 : 3642380883
Total Pages : 504 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis NASA Formal Methods by : Guillaume Brat

Download or read book NASA Formal Methods written by Guillaume Brat and published by Springer. This book was released on 2013-05-09 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Symposium on NASA Formal Methods, NFM 2013, held in Moffett Field, CA, USA, in May 2013. The 28 revised regular papers presented together with 9 short papers talks were carefully reviewed and selected from 99 submissions. The topics are organized in topical sections on model checking; applications of formal methods; complex systems; static analysis; symbolic execution; requirements and specifications; probabilistic and statistical analysis; and theorem proving.

An Introduction to Complex Analysis

Author : Wolfgang Tutschke
Publisher : CRC Press
ISBN 13 : 1584884789
Total Pages : 480 pages
Book Rating : 4.5/5 (848 download)

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Book Synopsis An Introduction to Complex Analysis by : Wolfgang Tutschke

Download or read book An Introduction to Complex Analysis written by Wolfgang Tutschke and published by CRC Press. This book was released on 2004-06-25 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork and mitigate the difficulties newcomers often experience, An Introduction to Complex Analysis begins with a complete review of concepts and methods from real analysis, such as metric spaces and the Green-Gauss Integral Formula. The approach leads to brief, clear proofs of basic statements - a distinct advantage for those mainly interested in applications. Alternate approaches, such as Fichera's proof of the Goursat Theorem and Estermann's proof of the Cauchy's Integral Theorem, are also presented for comparison. Discussions include holomorphic functions, the Weierstrass Convergence Theorem, analytic continuation, isolated singularities, homotopy, Residue theory, conformal mappings, special functions and boundary value problems. More than 200 examples and 150 exercises illustrate the subject matter and make this book an ideal text for university courses on complex analysis, while the comprehensive compilation of theories and succinct proofs make this an excellent volume for reference.

Fundamentals and Applications of Complex Analysis

Author : Harold Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 9780306477485
Total Pages : 442 pages
Book Rating : 4.4/5 (774 download)

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Book Synopsis Fundamentals and Applications of Complex Analysis by : Harold Cohen

Download or read book Fundamentals and Applications of Complex Analysis written by Harold Cohen and published by Springer Science & Business Media. This book was released on 2003-07-31 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as a text for first and second year courses in single variable complex analysis. The material that is appropriate for more advanced study is developed from elementary material. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter in other courses. For example, students who have taken an introductory physics course will have encountered analysis of simple AC circuits. This text revisits such analysis using complex numbers. Cauchy's residue theorem is used to evaluate many types of definite integrals that students are introduced to in the beginning calculus sequence. Methods of conformal mapping are used to solve problems in electrostatics. The book contains material that is not considered in other popular complex analysis texts.

Matrix Theory: A Second Course

Author : James M. Ortega
Publisher : Springer Science & Business Media
ISBN 13 : 9780306424335
Total Pages : 278 pages
Book Rating : 4.4/5 (243 download)

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Book Synopsis Matrix Theory: A Second Course by : James M. Ortega

Download or read book Matrix Theory: A Second Course written by James M. Ortega and published by Springer Science & Business Media. This book was released on 1987-02-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are essentially synonymous terms for an area of mathematics that has become one of the most useful and pervasive tools in a wide range of disciplines. It is also a subject of great mathematical beauty. In consequence of both of these facts, linear algebra has increasingly been brought into lower levels of the curriculum, either in conjunction with the calculus or separate from it but at the same level. A large and still growing number of textbooks has been written to satisfy this need, aimed at students at the junior, sophomore, or even freshman levels. Thus, most students now obtaining a bachelor's degree in the sciences or engineering have had some exposure to linear algebra. But rarely, even when solid courses are taken at the junior or senior levels, do these students have an adequate working knowledge of the subject to be useful in graduate work or in research and development activities in government and industry. In particular, most elementary courses stop at the point of canonical forms, so that while the student may have "seen" the Jordan and other canonical forms, there is usually little appreciation of their usefulness. And there is almost never time in the elementary courses to deal with more specialized topics like nonnegative matrices, inertia theorems, and so on. In consequence, many graduate courses in mathematics, applied mathe matics, or applications develop certain parts of matrix theory as needed.

Fundamentals of Matrix Analysis with Applications

Author : Edward Barry Saff
Publisher : John Wiley & Sons
ISBN 13 : 111895369X
Total Pages : 407 pages
Book Rating : 4.1/5 (189 download)

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Book Synopsis Fundamentals of Matrix Analysis with Applications by : Edward Barry Saff

Download or read book Fundamentals of Matrix Analysis with Applications written by Edward Barry Saff and published by John Wiley & Sons. This book was released on 2015-10-12 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible and clear introduction to linear algebra with a focus on matrices and engineering applications Providing comprehensive coverage of matrix theory from a geometric and physical perspective, Fundamentals of Matrix Analysis with Applications describes the functionality of matrices and their ability to quantify and analyze many practical applications. Written by a highly qualified author team, the book presents tools for matrix analysis and is illustrated with extensive examples and software implementations. Beginning with a detailed exposition and review of the Gauss elimination method, the authors maintain readers’ interest with refreshing discussions regarding the issues of operation counts, computer speed and precision, complex arithmetic formulations, parameterization of solutions, and the logical traps that dictate strict adherence to Gauss’s instructions. The book heralds matrix formulation both as notational shorthand and as a quantifier of physical operations such as rotations, projections, reflections, and the Gauss reductions. Inverses and eigenvectors are visualized first in an operator context before being addressed computationally. Least squares theory is expounded in all its manifestations including optimization, orthogonality, computational accuracy, and even function theory. Fundamentals of Matrix Analysis with Applications also features: Novel approaches employed to explicate the QR, singular value, Schur, and Jordan decompositions and their applications Coverage of the role of the matrix exponential in the solution of linear systems of differential equations with constant coefficients Chapter-by-chapter summaries, review problems, technical writing exercises, select solutions, and group projects to aid comprehension of the presented concepts Fundamentals of Matrix Analysis with Applications is an excellent textbook for undergraduate courses in linear algebra and matrix theory for students majoring in mathematics, engineering, and science. The book is also an accessible go-to reference for readers seeking clarification of the fine points of kinematics, circuit theory, control theory, computational statistics, and numerical algorithms.

Concise Complex Analysis (Revised Edition)

Author : Sheng Gong
Publisher : World Scientific Publishing Company
ISBN 13 : 9813106980
Total Pages : 258 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Concise Complex Analysis (Revised Edition) by : Sheng Gong

Download or read book Concise Complex Analysis (Revised Edition) written by Sheng Gong and published by World Scientific Publishing Company. This book was released on 2007-04-26 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise textbook on complex analysis for undergraduate and graduate students, this book is written from the viewpoint of modern mathematics: the Bar {Partial}-equation, differential geometry, Lie groups, all the traditional material on complex analysis is included. Setting it apart from others, the book makes many statements and proofs of classical theorems in complex analysis simpler, shorter and more elegant: for example, the Mittag-Leffer theorem is proved using the Bar {Partial}-equation, and the Picard theorem is proved using the methods of differential geometry.