General Investigations of Curved Surfaces

Edited with an Introduction and Notes by Peter Pesic

Author: Karl Friedrich Gauss

Publisher: Courier Corporation

ISBN: 0486154815

Category: Mathematics

Page: 144

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This influential work defines the concept of surface curvature and presents the important theorem stating that the "Gauss curvature" is invariant under arbitrary isometric deformation of a curved surface. 1902 edition.
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Lectures on General Relativity

- paperbound edition -

Author: Bengt Månsson

Publisher: BoD - Books on Demand

ISBN: 9177856910

Category: Science

Page: 540

View: 6909

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Do you know the basics of general relativity? Do you want to know something of what more there is? Do you wonder how the theory of relativity came into being? Then this book is for you! Partial contents: - Black holes and gravitational collapse - Cosmological solutions of Einstein's field equations - Gravitational waves - Space-time singularities - The problem of motion for massive particles - A collection of exact solutions of Einstein's field equations - A history of Einstein's creation of the theory of relativity in the years 1905-1915 - A short course for repetition of the basics of general relativity - Bibliography, references, and index The book, although not very advanced, covers a number of topics not often seen in text books. The selection, of course, refelects my own interests. The different chapters may to a large extent, though not completely, be read in any desired order. The author has a PhD in theoretical physics and is lecturer of mathematics. He has for many years taught physics and mathematics at senior high school as well as university level.
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Worlds Out of Nothing

A Course in the History of Geometry in the 19th Century

Author: Jeremy Gray

Publisher: Springer Science & Business Media

ISBN: 9780857290601

Category: Mathematics

Page: 384

View: 5030

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Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.
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The Mechanics of Ribbons and Möbius Bands

Author: Roger Fosdick,Eliot Fried

Publisher: Springer

ISBN: 9401773009

Category: Technology & Engineering

Page: 352

View: 1948

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Recent developments in biology and nanotechnology have stimulated a rapidly growing interest in the mechanics of thin, flexible ribbons and Mobius bands. This edited volume contains English translations of four seminal papers on this topic, all originally written in German; of these, Michael A. Sadowsky published the first in 1929, followed by two others in 1930, and Walter Wunderlich published the last in 1962. The volume also contains invited, peer-reviewed, original research articles on related topics. Previously published in the Journal of Elasticity, Volume 119, Issue 1-2, 2015.
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Differential Equations with Applications and Historical Notes, Third Edition

Author: George F. Simmons

Publisher: CRC Press

ISBN: 1498702627

Category: Mathematics

Page: 764

View: 9021

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Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations—among others—as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author—a highly respected educator—advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter. With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity—i.e., identifying why and how mathematics is used—the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout. Provides an ideal text for a one- or two-semester introductory course on differential equations Emphasizes modeling and applications Presents a substantial new section on Gauss’s bell curve Improves coverage of Fourier analysis, numerical methods, and linear algebra Relates the development of mathematics to human activity—i.e., identifying why and how mathematics is used Includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout Uses explicit explanation to ensure students fully comprehend the subject matter Outstanding Academic Title of the Year, Choice magazine, American Library Association.
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A First Course in Geometric Topology and Differential Geometry

Author: Ethan D. Bloch

Publisher: Springer Science & Business Media

ISBN: 0817681221

Category: Mathematics

Page: 421

View: 1492

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The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.
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Mathematics

Its Content, Methods and Meaning

Author: A. D. Aleksandrov,A. N. Kolmogorov,M. A. Lavrent’ev

Publisher: Courier Corporation

ISBN: 0486157873

Category: Mathematics

Page: 1120

View: 5154

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Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.
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History of mathematics

Author: Arthur Gittleman

Publisher: Merrill Publishing Company

ISBN: N.A

Category: Mathematics

Page: 291

View: 9505

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Traces the origins and development of arithmetic, geometry, trigonometry, analytic geometry, and calculus from the ancient civilizations to the present
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