Differential Geometry, Differential Equations, and Special Functions PDF Download
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Author: Galina Filipuk
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311077464X
Category : Computers
Languages : en
Pages : 274
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Book Description
This book is devoted to applications: differential equations, elements of special functions and differential geometry of curves and surfaces with a specific focus on visualization in Mathematica®. Discusses how Mathematica® can be used as an aid in solving mathematical problems and discovering a solution. A complete tutorial provides the background needed for understanding the examples and how to compute in Mathematica®.
Author: Galina Filipuk
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311077464X
Category : Computers
Languages : en
Pages : 274
Get Book Here
Book Description
This book is devoted to applications: differential equations, elements of special functions and differential geometry of curves and surfaces with a specific focus on visualization in Mathematica®. Discusses how Mathematica® can be used as an aid in solving mathematical problems and discovering a solution. A complete tutorial provides the background needed for understanding the examples and how to compute in Mathematica®.
Author: Maria Ulan
Publisher: Springer Nature
ISBN: 3030632539
Category : Mathematics
Languages : en
Pages : 240
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Book Description
This volume presents lectures given at the Wisła 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.
Author: Marius van der Put
Publisher: Springer Science & Business Media
ISBN: 3642557503
Category : Mathematics
Languages : en
Pages : 446
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Book Description
From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews
Author: Serge Lang
Publisher: Springer Science & Business Media
ISBN: 1461205417
Category : Mathematics
Languages : en
Pages : 553
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Book Description
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Author: Francis J. Murray
Publisher: Courier Corporation
ISBN: 0486154955
Category : Mathematics
Languages : en
Pages : 178
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Book Description
This text examines fundamental and general existence theorems, along with uniqueness theorems and Picard iterants, and applies them to properties of solutions and linear differential equations. 1954 edition.
Author: Walter A. Strauss
Publisher: John Wiley & Sons
ISBN: 0470054565
Category : Mathematics
Languages : en
Pages : 467
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Book Description
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Author: D. E. Rutherford
Publisher: Courier Corporation
ISBN: 048615453X
Category : Mathematics
Languages : en
Pages : 148
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Book Description
This text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. 1957 edition.
Author: H. Blaine Lawson
Publisher: Princeton University Press
ISBN: 1400883911
Category : Mathematics
Languages : en
Pages : 442
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Book Description
This book offers a systematic and comprehensive presentation of the concepts of a spin manifold, spinor fields, Dirac operators, and A-genera, which, over the last two decades, have come to play a significant role in many areas of modern mathematics. Since the deeper applications of these ideas require various general forms of the Atiyah-Singer Index Theorem, the theorems and their proofs, together with all prerequisite material, are examined here in detail. The exposition is richly embroidered with examples and applications to a wide spectrum of problems in differential geometry, topology, and mathematical physics. The authors consistently use Clifford algebras and their representations in this exposition. Clifford multiplication and Dirac operator identities are even used in place of the standard tensor calculus. This unique approach unifies all the standard elliptic operators in geometry and brings fresh insights into curvature calculations. The fundamental relationships of Clifford modules to such topics as the theory of Lie groups, K-theory, KR-theory, and Bott Periodicity also receive careful consideration. A special feature of this book is the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry and has led to some of the most profound relations known between the curvature and topology of manifolds.
Author: Albert L. Rabenstein
Publisher: Academic Press
ISBN: 1483226220
Category : Mathematics
Languages : en
Pages : 444
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Book Description
Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutions, and that should be of interest to the mathematics major, such as the theorems about the existence and uniqueness of solutions. The final chapters discuss the stability of critical points of plane autonomous systems and the results about the existence of periodic solutions of nonlinear equations. This book is great use to mathematicians, physicists, and undergraduate students of engineering and the science who are interested in applications of differential equation.
Author: Shing-tung Yau
Publisher: Princeton University Press
ISBN: 1400881919
Category : Mathematics
Languages : en
Pages : 720
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Book Description
This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.
