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\u503c\u6b642024\u5e743\u670814\u65e5\u7b2c\u516d\u5c46\u570b\u969b\u6578\u5b78\u65e5<\/strong>\u4f86\u81e8\u4e4b\u969b\uff0c\u6211\u5011\u7cbe\u907812<\/strong>\u672c\u7f8e\u570b\u6578\u5b78\u5b78\u6703\u51fa\u7248\u7684\u7d93\u5178\u5916\u6587\u6578\u5b78\u8457\u4f5c<\/strong>\u3002\u9019\u4e9b\u7d93\u5178\u4e4b\u4f5c\u5c07\u5f15\u9818\u60a8\u6df1\u5165\u6578\u5b78\u7684\u8c50\u5bcc\u4e16\u754c\uff0c\u63a2\u7d22\u5176\u6df1\u5967\u7684\u5967\u79d8\uff0c\u9ad4\u9a57\u6578\u5b78\u4e4b\u7f8e\u3002\u8b80\u8005\u73fe\u53ef\u901a\u904e Ebook Central <\/strong>\u5e73\u81fa<\/strong>\u63a2\u7d22\u9019\u4e9b\u73cd\u8cb4\u7684\u5b78\u8853\u8cc7\u6e90\uff0c\u8b93\u6211\u5011\u5171\u540c\u5728\u77e5\u8b58\u7684\u6d77\u6d0b\u4e2d\u9068\u904a\uff0c\u6176\u795d\u6578\u5b78\u7684\u7121\u9650\u9b45\u529b\u3002<\/p>\n <\/p>\n Lectures on Quasiconformal Mappings<\/strong><\/p>\n \u300a\u64ec\u5171\u5f62\u6620\u5c04\u8b1b\u7fa9\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong> Lars V. Ahlfors<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n Lars Ahlfors’s\u00a0Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichm\u00fcller spaces, including the Bers embedding and the Teichm\u00fcller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichm\u00fcller spaces from these lecture notes.<\/p>\n <\/p>\n A Course in Metric Geometry<\/strong><\/p>\n \u300a\u5ea6\u91cf\u5e7e\u4f55\u5b78\u6559\u7a0b\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>Dmitri Burago\uff0cYuri Burago\u7b49<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n Metric geometry is an approach to geometry based on the notion of length on a topological space. This approach experienced a very fast development in the last few decades and penetrated into many other mathematical disciplines, such as group theory, dynamical systems, and partial differential equations.<\/p>\n The objective of this graduate textbook is twofold: to give a detailed exposition of basic notions and techniques used in the theory of length spaces, and, more generally, to offer an elementary introduction into a broad variety of geometrical topics related to the notion of distance, including Riemannian and Carnot-Carath\u00e9odory metrics, the hyperbolic plane, distance-volume inequalities, asymptotic geometry (large scale, coarse), Gromov hyperbolic spaces, convergence of metric spaces, and Alexandrov spaces (non-positively and non-negatively curved spaces). The authors tend to work with \u201ceasy-to-touch\u201d mathematical objects using \u201ceasy-to-visualize\u201d methods.<\/p>\n <\/p>\n \u00a0<\/strong><\/p>\n A Course in Minimal Surfaces<\/strong><\/p>\n \u300a\u6975\u5c0f\u66f2\u9762\u6559\u7a0b\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>\u00a0Tobias Holck Colding\uff0cWilliam P. Minicozzi lI<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n 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.<\/p>\n 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.<\/p>\n <\/p>\n Fourier Analysis<\/strong><\/p>\n \u300a\u5085\u7acb\u8449\u5206\u6790\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>\u00a0Javier Duoandikoetxea<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n Fourier analysis encompasses a variety of perspectives and techniques. This volume presents the real variable methods of Fourier analysis introduced by Calder\u00f3n and Zygmund. The text was born from a graduate course taught at the Universidad Aut\u00f3noma de Madrid and incorporates lecture notes from a course taught by Jos\u00e9 Luis Rubio de Francia at the same university.<\/p>\n Motivated by the study of Fourier series and integrals, classical topics are introduced, such as the Hardy-Littlewood maximal function and the Hilbert transform. The remaining portions of the text are devoted to the study of singular integral operators and multipliers. Both classical aspects of the theory and more recent developments, such as weighted inequalities,\u00a0BMO spaces, and the\u00a0T1 theorem, are discussed.<\/p>\n <\/p>\n An Introduction to Complex Analysis and Geometry<\/strong><\/p>\n \u300a\u8907\u5206\u6790\u8207\u5e7e\u4f55\u5f15\u8ad6\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>John P. D\u2019Angelo<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n An Introduction to Complex Analysis and Geometry\u00a0provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics. The book developed from courses given in the Campus Honors Program at the University of Illinois Urbana-Champaign. These courses aimed to share with students the way many mathematics and physics problems magically simplify when viewed from the perspective of complex analysis. The book begins at an elementary level but also contains advanced material.<\/p>\n <\/p>\n Partial Differential Equations<\/strong><\/p>\n \u300a\u504f\u5fae\u5206\u65b9\u7a0b\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>\u00a0Lawrence C. Evans<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE.<\/p>\n <\/p>\n Function Theory of One Complex Variable<\/strong><\/p>\n \u300a\u55ae\u8907\u8b8a\u51fd\u6578\u8ad6\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>\u00a0\u00a0Robert E. Greene\uff0cStevenG. Krantz<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point.<\/p>\n The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat\u00a0H<\/em><\/strong>p<\/sup><\/em><\/strong> spaces and Painlev\u00e9’s theorem on smoothness to the boundary for conformal maps.<\/p>\n <\/p>\n \u00a0Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems<\/strong><\/p>\n \u300a\u5fae\u5206\u5e7e\u4f55\u4e2d\u5609\u7576\u7684\u6d3b\u52d5\u6a19\u67b6\u6cd5\u548c\u5916\u5fae\u5206\u7cfb\u7d71\u521d\u6b65\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>Thomas A. lvey\uff0cJ.M. Landsberg<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n This book is an introduction to Cartan’s approach to differential geometry. Two central methods in Cartan’s geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems.<\/p>\n It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs.<\/p>\n <\/p>\n Representations of Algebraic Groups<\/strong><\/p>\n \u300a\u4ee3\u6578\u7fa4\u8868\u793a\u8ad6\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>\u00a0Jens Carsten Jantzen<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n Back in print from the AMS, the first part of this book is an introduction to the general theory of representations of algebraic group schemes. Here, Janzten describes important basic notions: induction functors, cohomology, quotients, Frobenius kernels, and reduction mod\u00a0p<\/em><\/strong>, among others. The second part of the book is devoted to the representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, the Borel-Bott-Weil theorem and Weyl’s character formula, and Schubert schemes and line bundles on them.<\/p>\n <\/p>\n \u00a0Lectures on the Orbit Method<\/strong>\u300a\u8ecc\u9053\u6cd5\u8b1b\u7fa9\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>\u00a0\u00a0A. A. Kirillov<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for non-experts and gives the first systematic, detailed, and self-contained exposition of the method. It starts with a convenient “User’s Guide” and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for non-experts and a reference book for research mathematicians and mathematical physicists.<\/p>\n <\/p>\n \u00a01001 Problems in Classical Number Theory<\/strong><\/p>\n \u300a\u7d93\u5178\u6578\u8ad6\u4e2d\u76841001\u500b\u554f\u984c\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>\u00a0\u00a0Jean-Marie De Koninck\uff0cArmel Mercier<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n In the spirit of\u00a0The Book of the One Thousand and One Nights, the authors offer 1001 problems in number theory in a way that entices the reader to immediately attack the next problem. Whether a novice or an experienced mathematician, anyone fascinated by numbers will find a great variety of problems\u2014some simple, others more complex\u2014that will provide them with a wonderful mathematical experience.<\/p>\n <\/p>\n Complex Proofs of Real Theorems<\/strong><\/p>\n \u300a\u5be6\u5b9a\u7406\u7684\u8907\u8b49\u660e\u300b<\/p>\n \u4f5c\u8005\uff1a<\/strong>\u00a0\u00a0Peter D. Lax\uff0cLawrence Zalcman<\/p>\n \u5167\u5bb9\u7c21\u4ecb\uff1a<\/strong><\/p>\n Complex Proofs of Real Theorems\u00a0is an extended meditation on Hadamard’s famous dictum, \u201cThe shortest and best way between two truths of the real domain often passes through the imaginary one.\u201d Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics.<\/p>\n <\/p>\n <\/p>\n <\/p>\n \u7f8e\u570b\u6578\u5b78\u5b78\u6703\uff08<\/span>American Mathematical Society\uff0c<\/span>AMS\uff09\u662f\u7f8e\u570b\u6578\u5b78\u9818\u57df\u63a8\u52d5\u6578\u5b78\u7814\u7a76\u548c\u6578\u5b78\u6559\u80b2\u7684\u77e5\u540d\u7d44\u7e54\uff0c\u672c\u8eab\u70ba\u4e00\u975e\u71df\u5229\u6a5f\u69cb\uff0c\u65e8\u5728\u4fc3\u9032\u95dc\u65bc\u6578\u5b78\u4e4b\u7814\u7a76\uff0c\u4e26\u4e14\u5c0d\u6578\u5b78\u6559\u80b2\u63d0\u4f9b\u5354\u52a9\u8207\u5efa\u8b70\u4ee5\u53ca\u4fc3\u9032\u5404\u570b\u6578\u5b78\u5bb6\u4e4b\u4ea4\u6d41\u6d3b\u52d5\u7b49\u7b49\u3002<\/span><\/p>\n \u7f8e\u570b\u6578\u5b78\u5b78\u6703\u65bc<\/span>1888\u5e74\u6210\u7acb\u81f3\u4eca<\/span>130\u591a\u5e74\u4f86\uff0c\u5df2\u7d93\u51fa\u7248\u4e86\u975e\u5e38\u5927\u91cf\u9ad8\u54c1\u8cea\u4e4b\u9ad8\u7b49\u6578\u5b78\u9818\u57df\u7684\u66f8\u7c4d\uff0c\u5305\u62ec<\/span>19\u4e16\u7d00\u4ee5\u4f86\u6578\u5b78\u5c08\u696d\u9818\u57df\u7684\u5404\u7a2e\u6703\u8b70\u8ad6\u6587\u96c6<\/span>(Proceedings)\u3001\u5c08\u66f8<\/span>(Monograph)\u4ee5\u53ca\u5c08\u8ad6<\/span>(Memoirs)\u3002<\/span><\/p>\n <\/p>\n ProQuest Ebook Central \u5e73\u81fa\uff08\u7c21\u7a31EBC\uff09\uff0c\u662f\u4e00\u500b\u7d9c\u5408\u985e\u7684\u5916\u6587\u96fb\u5b50\u66f8\u5e73\u81fa\uff0c\u5171\u6536\u9304\u5168\u74032400\u591a\u5bb6\u8457\u540d\u5927\u5b78\u51fa\u7248\u793e\u3001\u5c08\u696d\u51fa\u7248\u5546\u3001\u5b78\u8853\u51fa\u7248\u6a5f\u69cb\u51fa\u7248\u7684\u8fd1200\u842c\u7a2e\u96fb\u5b50\u66f8\uff0c\u4ee5\u8fd1\u5e74\u4f86\u65b0\u51fa\u7248\u7684\u5716\u66f8\u70ba\u4e3b\uff0c\u4e26\u6703\u5b9a\u671f\u66f4\u65b0\u96fb\u5b50\u66f8\u8cc7\u6e90\u3002EBC \u4e3b\u8981\u5167\u5bb9\u8986\u84cb\u96fb\u8166\u79d1\u5b78\u3001\u7d93\u6fdf\u3001\u5546\u696d\u3001\u6587\u5b78\u3001\u8a9e\u8a00\u3001\u6b77\u53f2\u3001\u85dd\u8853\u3001\u54f2\u5b78\u8207\u6559\u80b2\u5b78\u7b49\u5168\u5b78\u79d1\u9818\u57df\u3002\u6d89\u53ca50\u591a\u7a2e\u8a9e\u8a00\uff0c\u8986\u84cb\u82f1\u8a9e\u3001\u5fb7\u8a9e\u3001\u6cd5\u8a9e\u3001\u897f\u73ed\u7259\u8a9e\u3001\u8461\u8404\u7259\u8a9e\u3001\u963f\u62c9\u4f2f\u8a9e\u7b49\u3002<\/p>\n <\/p>\n<\/h3>\n
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