## Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces

**Author**: R. Courant

**Publisher:**Springer Science & Business Media

**ISBN:**1461299179

**Category:**Mathematics

**Page:**332

**View:**1150

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## Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces

**Author**: Richard Courant

**Publisher:**Courier Corporation

**ISBN:**0486445526

**Category:**Mathematics

**Page:**330

**View:**4966

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Originally published: New York: Interscience Publishers, 1950, in series: Pure and applied mathematics (Interscience Publishers); v. 3.

## Conformal Mapping on Riemann Surfaces

**Author**: Harvey Cohn

**Publisher:**Courier Corporation

**ISBN:**0486153290

**Category:**Mathematics

**Page:**352

**View:**4764

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Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.

## Conformal Mapping

**Author**: Zeev Nehari

**Publisher:**Courier Corporation

**ISBN:**0486145034

**Category:**Mathematics

**Page:**396

**View:**527

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DIVTheoretical and practical approach covers functions of a complex variable and conformal mapping. Only prerequisite is advanced calculus. /div

## guide to the literature of mathematics and physics

**Author**: nathan grier parke III

**Publisher:**N.A

**ISBN:**N.A

**Category:**

**Page:**N.A

**View:**4304

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## Conformal Mapping on Riemann Surfaces

**Author**: Harvey Cohn

**Publisher:**Courier Corporation

**ISBN:**0486153290

**Category:**Mathematics

**Page:**352

**View:**520

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Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.

## Methods of Mathematical Physics, Volume 2

*Differential Equations*

**Author**: Richard Courant,D. Hilbert

**Publisher:**John Wiley & Sons

**ISBN:**3527617248

**Category:**Science

**Page:**852

**View:**6178

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Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.

## Selected Papers of Takeyuki Hida

**Author**: Takeyuki Hida,Luigi Accardi

**Publisher:**World Scientific

**ISBN:**9810243332

**Category:**Mathematics

**Page:**480

**View:**836

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The topics discussed in this book can be classified into three parts: (i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed.(ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called ?generalized white noise functionals?, and sometimes ?Hida distribution?.(iii) Variational calculus for random fields. This topic will certainly represent one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume

## Scientific and Technical Books in Print

**Author**: N.A

**Publisher:**N.A

**ISBN:**N.A

**Category:**Engineering

**Page:**N.A

**View:**9335

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## Lectures on Classical Differential Geometry

**Author**: Dirk Jan Struik

**Publisher:**Courier Corporation

**ISBN:**9780486656090

**Category:**Mathematics

**Page:**232

**View:**3143

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Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.

## A Course in Minimal Surfaces

**Author**: Tobias H. Colding,William P. Minicozzi

**Publisher:**American Mathematical Soc.

**ISBN:**0821853236

**Category:**Mathematics

**Page:**313

**View:**8064

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Minimal surfaces date back to Euler and Lagrange and the beginning of the calculus of variations. Many of the techniques developed have played key roles in geometry and partial differential equations. Examples include monotonicity and tangent cone analysis originating in the regularity theory for minimal surfaces, estimates for nonlinear equations based on the maximum principle arising in Bernstein's classical work, and even Lebesgue's definition of the integral that he developed in his thesis on the Plateau problem for minimal surfaces. This book starts with the classical theory of minimal surfaces and ends up with current research topics. Of the various ways of approaching minimal surfaces (from complex analysis, PDE, or geometric measure theory), the authors have chosen to focus on the PDE aspects of the theory. The book also contains some of the applications of minimal surfaces to other fields including low dimensional topology, general relativity, and materials science. The only prerequisites needed for this book are a basic knowledge of Riemannian geometry and some familiarity with the maximum principle.

## Practical Applied Mathematics

*Modelling, Analysis, Approximation*

**Author**: Sam Howison

**Publisher:**Cambridge University Press

**ISBN:**9780521842747

**Category:**Mathematics

**Page:**326

**View:**9722

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Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations. Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling. The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow. The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.

## Value Distribution Theory of the Gauss Map of Minimal Surfaces in Rm

**Author**: Hirotaka Fujimoto

**Publisher:**Springer Science & Business Media

**ISBN:**332280271X

**Category:**Mathematics

**Page:**208

**View:**9922

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This book presents in a systematic and almost self-contained way the striking analogy between classical function theory, in particular the value distribution theory of holomorphic curves in projective space, on the one hand, and important and beautiful properties of the Gauss map of minimal surfaces on the other hand. Both theories are developed in the text, including many results of recent research. The relations and analogies between them become completely clear. The book is written for interested graduate students and mathematicians, who want to become more familiar with this modern development in the two classical areas of mathematics, but also for those, who intend to do further research on minimal surfaces.

## Hydrodynamics in Theory and Application

**Author**: James Mueller Robertson

**Publisher:**N.A

**ISBN:**N.A

**Category:**Fluid dynamics

**Page:**652

**View:**5993

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## Introduction to Calculus and Analysis

**Author**: Richard Courant,Fritz John

**Publisher:**Springer Science & Business Media

**ISBN:**9783540665694

**Category:**Mathematics

**Page:**556

**View:**5014

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Biography of Richard Courant Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence. For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John. (P.D. Lax) Biography of Fritz John Fritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was half-Jewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994. John's research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMO-functions (bounded mean oscillations). Fritz John's work exemplifies the unity of mathematics as well as its elegance and its beauty. (J. Moser)

## Conformally Invariant Processes in the Plane

**Author**: Gregory F. Lawler

**Publisher:**American Mathematical Soc.

**ISBN:**0821846248

**Category:**Mathematics

**Page:**242

**View:**4703

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Theoretical physicists have predicted that the scaling limits of many two-dimensional lattice models in statistical physics are in some sense conformally invariant. This belief has allowed physicists to predict many quantities for these critical systems. The nature of these scaling limits has recently been described precisely by using one well-known tool, Brownian motion, and a new construction, the Schramm-Loewner evolution (SLE). This book is an introduction to the conformally invariant processes that appear as scaling limits. The following topics are covered: stochastic integration; complex Brownian motion and measures derived from Brownian motion; conformal mappings and univalent functions; the Loewner differential equation and Loewner chains; the Schramm-Loewner evolution (SLE), which is a Loewner chain with a Brownian motion input; and applications to intersection exponents for Brownian motion. The prerequisites are first-year graduate courses in real analysis, complex analysis, and probability. The book is suitable for graduate students and research mathematicians interested in random processes and their applications in theoretical physics.

## A Survey of Minimal Surfaces

**Author**: Robert Osserman

**Publisher:**Courier Corporation

**ISBN:**0486167690

**Category:**Mathematics

**Page:**224

**View:**1665

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Newly updated accessible study covers parametric and non-parametric surfaces, isothermal parameters, Bernstein’s theorem, much more, including such recent developments as new work on Plateau’s problem and on isoperimetric inequalities. Clear, comprehensive examination provides profound insights into crucial area of pure mathematics. 1986 edition. Index.

## An Imaginary Tale

*The Story of √-1*

**Author**: Paul J. Nahin

**Publisher:**Princeton University Press

**ISBN:**9781400833894

**Category:**Mathematics

**Page:**296

**View:**8341

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Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.

## Mathematical Thought From Ancient to Modern Times

**Author**: Morris Kline

**Publisher:**Oxford University Press

**ISBN:**0199770468

**Category:**Mathematics

**Page:**432

**View:**2351

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The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.