Download or read book The Implicit Function Theorem written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2012-11-26 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non- smooth functions, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash--Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve. "The Implicit Function Theorem" is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas.

Download or read book Giuseppe Peano between Mathematics and Logic written by Fulvia Skof and published by Springer Science & Business Media. This book was released on 2011-04-30 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the papers developing out the presentations given at the International Conference organized by the Torino Academy of Sciences and the Department of Mathematics Giuseppe Peano of the Torino University to celebrate the 150th anniversary of G. Peano's birth - one of the greatest figures in modern mathematics and logic and the most important mathematical logician in Italy - a century after the publication of Formulario Mathematico, a great attempt to systematise Mathematics in symbolic form.

Download or read book The Foundations of Differential Geometry written by Oswald Veblen and published by . This book was released on 1960 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Analytic Art written by François Viète and published by Courier Corporation. This book was released on 2006-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This historic work consists of several treatises that developed the first consistent, coherent, and systematic conception of algebraic equations. Originally published in 1591, it pioneered the notion of using symbols of one kind (vowels) for unknowns and of another kind (consonants) for known quantities, thus streamlining the solution of equations. Francois Viète (1540-1603), a lawyer at the court of King Henry II in Tours and Paris, wrote several treatises that are known collectively as The Analytic Art. His novel approach to the study of algebra developed the earliest articulated theory of equations, allowing not only flexibility and generality in solving linear and quadratic equations, but also something completely new—a clear analysis of the relationship between the forms of the solutions and the values of the coefficients of the original equation. Viète regarded his contribution as developing a "systematic way of thinking" leading to general solutions, rather than just a "bag of tricks" to solve specific problems. These essays demonstrate his method of applying his own ideas to existing usage in ways that led to clear formulation and solution of equations.

Download or read book The System Of The World written by Neal Stephenson and published by Random House. This book was released on 2012-06-30 with total page 917 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neal Stephenson follows his highly-praised historical novels, Quicksilver and The Confusion, with the extraordinary third and final volume of the Baroque Cycle. The year is 1714. Daniel Waterhouse has returned to England, where he joins forces with his friend Isaac Newton to hunt down a shadowy group attempting to blow up Natural Philosophers with 'Infernal Devices' - time bombs. As Daniel and Newton conspire, an increasingly vicious struggle is waged for England's Crown: who will take control when the ailing queen dies? Tories and Whigs clash as one faction jockeys to replace Queen Anne with 'The Pretender' James Stuart, and the other promotes the Hanoverian dynasty of Princess Caroline. Meanwhile, a long-simmering dispute between Newton and Gottfried Wilhelm Leibniz comes to a head, with potentially cataclysmic consequences. Wildly inventive, brilliantly conceived, The System of the World is the final volume in Neal Stephenson's hugely ambitious and compelling saga. Filled with a remarkable cast of characters in a time of genius, discovery and change, the Baroque Cycle is a magnificent and unique achievement.

Download or read book The First Three Sections of Newton s Principia written by Isaac Newton and published by . This book was released on 1871 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Peano written by H. Kennedy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: All students of mathematics know of Peano's postulates for the natural numbers and his famous space-filling curve, yet their knowledge often stops there. Part of the reason is that there has not until now been a full-scale study of his life and works. This must surely be surprising, when one realizes the length of his academic career (over 50 years) and the extent of his publica tions (over 200) in a wide variety of fields, many of which had immediate and long-term effects on the development of modern mathematics. A study of his life seems long overdue. It appeared to me that the most likely person to write a biography of Peano would be his devoted disciple Ugo Cassina, with whom I studied at the University of Milan in 1957-58. I wrote to Professor Cassina on 29 October, 1963, inquiring if he planned to write the biography, and I offered him my assistance, since I hoped to return to Italy for a year. He replied on 28 November, 1963, suggesting that we collaborate, meaning by this that I would write the biography, in English, using his material and advice. I gladly agreed to this suggestion, but work on the project had hardly begun when Professor Cassina died unexpectedly on 5 October, 1964. I then decided to continue the project on my own. I spent the academic year 1966-67 in Turin; completion of the book took ten years.

Download or read book Model Theory written by and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Two Valued Iterative Systems of Mathematical Logic written by Emil L. Post and published by Princeton University Press. This book was released on 1942-01-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, The Two-Valued Iterative Systems of Mathematical Logic. (AM-5), Volume 5, will be forthcoming.

Download or read book Orders of Infinity written by Godfrey Harold Hardy and published by . This book was released on 1910 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Joseph Fourier 1768 1830 written by Ivor Grattan-Guinness and published by . This book was released on 2003-02-01 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beyond being the first substantial publication on Fourier, this work contains the text of Fourier's seminal paper of 1807 on the propagation of heat, marking the first time it has ever appeared in print. This paper incorporates many of the mathematical creations on which Fourier's fame rests, including derivation of the diffusion equation, the separation of the treatment of surface phenomena from internal phenomena, the use of boundary values and initial conditions, and the development of "Fourier series" and the so-called "Bessel functions."When submitted to the examiners of the Institut de France, the originality of the paper and the surprising nature of some of its mathematical revelations caused great controversy, and it was denied publication both in 1807 and in later years. Fourier had the support, among the examiners, of Laplace and Monge, but Lagrange was adamantly in opposition, so that Fourier's work did not appear in print until 1822, reworked into book form.Fourier's mathematical discoveries are intimately related to his interest in the solution of physical problems and their experimental verification. The mathematical methods he developed in connection with heat diffusion apply to physical situations far beyond the boundaries of this area. Generally, Fourier may be credited with one of the first major extensions of mathematical physics beyond the applications of Newton's laws of motion and universal gravitation.The opening biographical chapter of this book follows Fourier's career up to the submission of the 1807 paper, and the two closing chapters take up his life and work from that point on. Fourier had strong political motivations and spent much of his life in the public service. These chapters trace his political difficulties, both before and after 1807, when he was the prefect of a department of France and was subjected to the dislocations of Napoleon's ups and downs. These chapters also describe aspects of the turbulent but productive development of French science from the Revolution to 1830.The core of the book presents the paper of 1807 in its original French and with the original notation. Grattan-Guinness has divided the paper into sections by the sequence of the problems taken up, and he introduces and, where necessary, closes each section with commentary relevant to Fourier's later work in these areas. The paper itself (cllows the chronology of Fourier's discoveries, and among the topics treated are, in this order: heat diffusion between disjoint bodies and in continuous bodies; the appearance of partial differential equations; the special solution for the lamina; sine and cosine series for an arbitrary function; reflections on the vibrating string problem; solution for the annulus; the full Fourier series for an arbitrary function; reflections on n-body analysis; solution for the sphere; solution for the cylinder; steady-state diffusion in the rectangular prism; time-dependent diffusion in the cube; and Fourier's experimental work.

Download or read book The Astronomical Tables of Giovanni Bianchini written by José Chabás and published by BRILL. This book was released on 2009 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes and analyses, for the first time, the astronomical tables of Giovanni Bianchini of Ferrara (d. after 1469), explains their context, inserts them into an astronomical tradition that began in Toledo, and addresses their diffusion.

Download or read book Selected Works of Giuseppe Peano written by Hubert C. Kennedy and published by University of Toronto Press. This book was released on 1973-12 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the decade before 1900, the Italian mathematician Giuseppe Peano was one of the most original and influential pioneers of modern mathematical logic. He made significant contributions to the development of the foundations of mathematics and the axiomatic method (for example, his postulates for the natural numbers), dimension theory (including the space-filling curve), measure theory, vector analysis, differential equations, and the rigorization of analysis. Several of Peano's works have been translated into other languages; here for the first time is a generous selection of works translated into English. Fifteen articles, one booklet, and parts of two books and one monograph, published between 1883 and 1921, chosen with the interests of mathematicians and logicians in mind, are included. Each selection is preceded by an introductory note. The volume also contains a biographical sketch, a chronological list of Peano's publications (larger by one fifth than any previously published list), and a bibliography on the life and work of Peano. This selection will appeal especially to historians of mathematics and logic, but also to those mathematicians and logicians who wish to know more about how their subject came to be.

Download or read book A Comprehensive Course in Analysis written by Barry Simon and published by . This book was released on 2015 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Comprehensive Course in Analysis by Poincar Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis

Download or read book An Elementary Treatise on Coordinate Geometry of Three Dimensions written by Robert J T Bell and published by Legare Street Press. This book was released on 2022-10-26 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Download or read book Soundings and Crossings written by Katharine Anderson and published by Science History Publications/USA. This book was released on 2016-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: