Nonlinear PDEs, their geometry, and applications : proceedings of the Wisła 18 Summer School /
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| Imprint: | Cham : Birkhäuser, [2019] ©2019 |
|---|---|
| Description: | 1 online resource |
| Language: | English |
| Series: | Tutorials, schools, and workshops in the mathematical sciences Tutorials, schools, and workshops in the mathematical sciences. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11895532 |
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| 245 | 0 | 0 | |a Nonlinear PDEs, their geometry, and applications : |b proceedings of the Wisła 18 Summer School / |c editors, Radosław A. Kycia, Maria Ułan and Eivind Schneider. |
| 264 | 1 | |a Cham : |b Birkhäuser, |c [2019] | |
| 264 | 4 | |c ©2019 | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Tutorials, schools, and workshops in the mathematical sciences | |
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed May 22, 2019). | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Intro; Foreword; Preface; Acknowledgements; Contents; Contributors; Acronyms; Part I Lectures; 1 Contact Geometry, Measurement, and Thermodynamics; 1.1 Preface; 1.2 A Crash Course in Probability Theory; 1.2.1 Measure Spaces and Measurable Maps; 1.2.2 Operations Over Measures, Measure Spaces, and Measurable Maps; 1.2.3 The Lebesgue Integral; 1.2.4 The Radon-Nikodym Theorem; 1.2.5 The Fubini Theorem; 1.2.6 Random Vectors; 1.2.7 Conditional Expectation; 1.2.8 Dependency, Coherence Conditions, and Tensor Product of Random Vectors; 1.3 Measurement of Random Vectors | |
| 505 | 8 | |a 1.3.1 Entropy and the Shannon Formula1.3.2 Gain of Information; 1.3.3 Principle of Minimal Information Gain; 1.3.4 The Gaussian Distribution; 1.3.5 Central Moments; 1.3.6 Change of Information Gain; 1.3.7 Constraints and Constitutive Relations; 1.3.8 Application to Classical Mechanics and Classical Field Theory; 1.4 Thermodynamics; 1.4.1 Laws of Thermodynamics; 1.4.2 Thermodynamics and Measurement; 1.4.3 Gases; 1.4.4 Thermodynamic Processes and Contact Transformations; References; 2 Lectures on Geometry of Monge-Ampère Equations with Maple; 2.1 Introduction | |
| 505 | 8 | |a 2.2 Lecture 1. Introduction to Contact Geometry2.2.1 Bundle of 1-Jets; 2.2.2 Contact Transformations; 2.3 Lecture 2. Geometrical Approach to Monge-Ampère Equations; 2.3.1 Non-linear Second-Order Differential Operators; 2.3.2 Multivalued Solutions of Monge-Ampère Equations; 2.3.3 Effective Forms; 2.4 Lecture 3. Contact Transformations of Monge-Ampère Equations; 2.5 Lecture 4. Geometrical Structures; 2.5.1 Pfaffians; 2.5.2 Fields of Endomorphisms; 2.5.3 Characteristic Distributions; 2.5.4 Symplectic Monge-Ampère Equations; 2.5.5 Splitting of Tangent Spaces | |
| 505 | 8 | |a 2.6 Lecture 5. Tensor Invariants of Monge-Ampère Equations2.6.1 Decomposition of de Rham Complex; 2.6.2 Tensor Invariants; 2.6.3 The Laplace Forms; 2.6.4 Contact Linearization of the Monge-Ampère Equations; References; 3 Geometry of Monge-Ampère Structures; 3.1 About These Lectures; 3.2 Lecture One: What Is It All About?; 3.2.1 Basic Geometric Structures; 3.2.2 Kähler, Special and Other Related Structures; 3.2.3 Holomorphic Symplectic Structures; 3.2.4 Lagrangian, Special Lagrangian and Complex Lagrangian Submanifolds; 3.2.5 Hyperkähler Manifolds; 3.2.6 Generalised Complex Structure | |
| 505 | 8 | |a 3.2.7 Notes and Further Reading3.3 Lecture Two: Recursion (Nijenuijs) Operators and Some Related Algebraic Constructions; 3.3.1 Recursion Operators and Its Properties; 3.3.2 Triples of Symplectic Forms; 3.3.3 Notes and Further Reading; 3.4 Lecture Three: Symplectic Monge-Ampère Operators and Equations; 3.4.1 Monge-Ampère Equations; 3.4.2 Geometry of Differential Forms; 3.4.3 Notes and Further Reading; 3.5 Lecture Four: Monge-Ampère Structures; 3.5.1 General Properties; 3.5.2 (4m+2)-Dimensional MA Geometry | |
| 520 | |a This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge-Ampère equations. Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.-- |c Provided by publisher. | ||
| 650 | 0 | |a Differential equations, Partial |v Congresses. | |
| 650 | 0 | |a Differential equations, Nonlinear |v Congresses. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Differential equations, Nonlinear. |2 fast |0 (OCoLC)fst00893474 | |
| 650 | 7 | |a Differential equations, Partial. |2 fast |0 (OCoLC)fst00893484 | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 655 | 7 | |a Conference papers and proceedings. |2 fast |0 (OCoLC)fst01423772 | |
| 655 | 7 | |a Conference papers and proceedings. |2 lcgft |0 http://id.loc.gov/authorities/genreForms/gf2014026068 | |
| 700 | 1 | |a Kycia, Radosław A., |e editor. | |
| 700 | 1 | |a Ułan, Maria, |e editor. | |
| 700 | 1 | |a Schneider, Eivind, |e editor. | |
| 830 | 0 | |a Tutorials, schools, and workshops in the mathematical sciences. |0 http://id.loc.gov/authorities/names/no2019044013 | |
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