Lectures on Differential Equations and Differential Geometry
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Publisher:
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ISBN-13: 9787040503029
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Differential Geometry, Differential Equations, and Mathematical Physics
Author: Maria Ulan
Publisher: Springer Nature
Published: 2021-02-12
Total Pages: 231
ISBN-13: 3030632539
DOWNLOAD EBOOKThis 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.
Lectures on Differential Geometry
Author: Shlomo Sternberg
Publisher: American Mathematical Society
Published: 2024-10-21
Total Pages: 462
ISBN-13: 1470478986
DOWNLOAD EBOOKThis book is based on lectures given at Harvard University during the academic year 1960?1961. The presentation assumes knowledge of the elements of modern algebra (groups, vector spaces, etc.) and point-set topology and some elementary analysis. Rather than giving all the basic information or touching upon every topic in the field, this work treats various selected topics in differential geometry. The author concisely addresses standard material and spreads exercises throughout the text. his reprint has two additions to the original volume: a paper written jointly with V. Guillemin at the beginning of a period of intense interest in the equivalence problem and a short description from the author on results in the field that occurred between the first and the second printings.
A Course in Differential Geometry
Author: W. Klingenberg
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 188
ISBN-13: 1461299233
DOWNLOAD EBOOKThis English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition. Suitable references for ordin ary differential equations are Hurewicz, W. Lectures on ordinary differential equations. MIT Press, Cambridge, Mass., 1958, and for the topology of surfaces: Massey, Algebraic Topology, Springer-Verlag, New York, 1977. Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some e1aborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour. 1 wish to thank David for his work and his enthusiasm during the whole period of our collaboration. At the same time I would like to commend the editors of Springer-Verlag for their patience and good advice. Bonn Wilhelm Klingenberg June,1977 vii From the Preface to the German Edition This book has its origins in a one-semester course in differential geometry which 1 have given many times at Gottingen, Mainz, and Bonn.
Lectures on Analytic Differential Equations
Author: I︠U︡. S. Ilʹi︠a︡shenko
Publisher: American Mathematical Soc.
Published: 2008
Total Pages: 641
ISBN-13: 0821836676
DOWNLOAD EBOOKThe book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the mor The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. on several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.
Lectures on Differential Geometry
Author: Richard M. Schoen
Publisher:
Published: 1994
Total Pages: 414
ISBN-13: 9781571461988
DOWNLOAD EBOOKLectures on Differential and Integral Equations
Author: K?saku Yoshida
Publisher: Courier Corporation
Published: 1991-01-01
Total Pages: 242
ISBN-13: 9780486666792
DOWNLOAD EBOOKLucid, self-contained exposition of theory of ordinary differential equations and integral equations. Boundary value problem of second order linear ordinary differential equations, Fredholm integral equations, many other topics. Bibliography. 1960 edition.
Lectures on Partial Differential Equations
Author: Vladimir I. Arnold
Publisher: Springer Science & Business Media
Published: 2013-06-29
Total Pages: 168
ISBN-13: 3662054418
DOWNLOAD EBOOKChoice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.
Lectures on Ordinary Differential Equations
Author: Witold Hurewicz
Publisher: Courier Corporation
Published: 1990-01-01
Total Pages: 146
ISBN-13: 0486664201
DOWNLOAD EBOOKIntroductory treatment explores existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. "A rigorous and lively introduction." — The American Mathematical Monthly. 1958 edition.
Lectures on Classical Differential Geometry
Author: Dirk J. Struik
Publisher: Courier Corporation
Published: 2012-04-26
Total Pages: 254
ISBN-13: 0486138186
DOWNLOAD EBOOKElementary, 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.
