Topics In Mathematical Analysis And Differential Geometry
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Topics In Mathematical Analysis And Differential Geometry
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Author : Nicolas K. Laos
language : en
Publisher: World Scientific
Release Date : 1998
Topics In Mathematical Analysis And Differential Geometry written by Nicolas K. Laos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.
Lectures On Differential Geometry
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Author : Bennett Chow
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-23
Lectures On Differential Geometry written by Bennett Chow and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Mathematics categories.
Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics. The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern?Gauss?Bonnet formula, harmonic functions, eigenfunctions, and eigenvalues on Riemannian manifolds, minimal surfaces, the curve shortening flow, and the Ricci flow on surfaces. This will provide a pathway to further topics in geometric analysis such as Ricci flow, used by Hamilton and Perelman to solve the Poincar‚ and Thurston geometrization conjectures, mean curvature flow, and minimal submanifolds. The book is primarily aimed at graduate students in geometric analysis, but it will also be of interest to postdoctoral researchers and established mathematicians looking for a refresher or deeper exploration of the topic.
Topics In Contemporary Differential Geometry Complex Analysis And Mathematical Physics
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Author : Stancho Dimiev
language : en
Publisher: World Scientific
Release Date : 2007
Topics In Contemporary Differential Geometry Complex Analysis And Mathematical Physics written by Stancho Dimiev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas. Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.
Mathematical Analysis
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Author : Bernd S. W. Schröder
language : en
Publisher: John Wiley & Sons
Release Date : 2008-01-28
Mathematical Analysis written by Bernd S. W. Schröder and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-28 with Mathematics categories.
A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.
Introduction To Mathematical Analysis
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Author : Igor Kriz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-25
Introduction To Mathematical Analysis written by Igor Kriz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-25 with Mathematics categories.
The book begins at the level of an undergraduate student assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, Lebesgue integral, vector calculus and differential equations. After having built on a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis, as understood by a mathematician today.
Extended Abstracts 2021 2022
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Author : Duván Cardona
language : en
Publisher: Springer Nature
Release Date : 2024-02-28
Extended Abstracts 2021 2022 written by Duván Cardona and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-28 with Mathematics categories.
This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022. The contributions are from the speakers of the Methusalem Colloquium, Methusalem Junior Seminar and Geometric Analysis Seminar. The volume has two main topics: 1. Analysis and PDEs. The volume presents recent results in fundamental problems for solving partial integro-differential equations in different settings such as Euclidean spaces, manifolds, Banach spaces, and many others. Discussions about the global and local solvability using micro-local and harmonic analysis methods, studies of new techniques and approaches arising from a physical perspective or the mathematical point of view have also been included. Several connected branches arising in this regard are shown. 2. Geometric analysis. The volume presents studies of modern techniques for elliptic and subelliptic PDEs that in recent times have been used to establish new results in differential geometry and differential topology. These topics involve the intrinsic research in microlocal analysis, geometric analysis, and harmonic analysis abroad. Different problems having relevant geometric information for different applications in mathematical physics and other problems of classification have been considered.
Short Courses In Mathematics
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Author : S. Kumaresan
language : en
Publisher: Universities Press
Release Date : 2004
Short Courses In Mathematics written by S. Kumaresan and has been published by Universities Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematical analysis categories.
This book is a collection of lectures delivered by the author at mathematics instrutional workshop and refresher courses. Topics covered include the spectral theorem for operators in the finite dimensional case, Lebesgue integration theory via the Daniell method, Fourier transform on R, solution of the Dirichlet problem for the potential equation in the plane by Perron's method...
Global Analysis
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Author : Ilka Agricola
language : en
Publisher:
Release Date : 2002
Global Analysis written by Ilka Agricola and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with MATHEMATICS categories.
This book introduces the reader to the world of differential forms and their uses in geometry, analysis, and mathematical physics. It begins with a few basic topics, partly as review, then moves on to vector analysis on manifolds and the study of curves and surfaces in $3$-space. Lie groups and homogeneous spaces are discussed, providing the appropriate framework for introducing symmetry in both mathematical and physical contexts. The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics. There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics.
Differential Geometry Differential Equations And Mathematical Physics
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Author : Maria Ulan
language : en
Publisher: Birkhäuser
Release Date : 2021-02-13
Differential Geometry Differential Equations And Mathematical Physics written by Maria Ulan and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-13 with Mathematics categories.
This 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.
Wavelet Methods In Mathematical Analysis And Engineering
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Author : Alain Damlamian
language : en
Publisher: World Scientific
Release Date : 2010-09-21
Wavelet Methods In Mathematical Analysis And Engineering written by Alain Damlamian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-21 with Mathematics categories.
This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state-of-the-art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective.The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented. Applications range for the reconstruction of noisy or blurred images, pattern and face recognition, to nonlinear approximation in strongly anisotropic contexts, and to the classification tools based on multifractal analysis.