Nonlinear PDEs, their geometry, and applications : proceedings of the Wisła 18 Summer School /: proceedings of the Wisła 18 Summer School. ([2019])
- Record Type:
- Book
- Title:
- Nonlinear PDEs, their geometry, and applications : proceedings of the Wisła 18 Summer School /: proceedings of the Wisła 18 Summer School. ([2019])
- Main Title:
- Nonlinear PDEs, their geometry, and applications : proceedings of the Wisła 18 Summer School
- Further Information:
- Note: Editors, Radosław A. Kycia, Maria Ułan and Eivind Schneider.
- Editors:
- Kycia, Radosław A
Ułan, Maria
Schneider, Eivind - Contents:
- 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 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 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; 2.5Intro; 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 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 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 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 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 … (more)
- Publisher Details:
- Cham : Birkhäuser
- Publication Date:
- 2019
- Copyright Date:
- 2019
- Extent:
- 1 online resource
- Subjects:
- 515/.353
Differential equations, Partial -- Congresses
Differential equations, Nonlinear -- Congresses
MATHEMATICS / Calculus
MATHEMATICS / Mathematical Analysis
Conference papers and proceedings
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9783030170318
3030170314 - Related ISBNs:
- 9783030170301
- Notes:
- Note: Includes bibliographical references and index.
Note: Online resource ; title from PDF title page (EBSCO, viewed May 22, 2019). - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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- British Library HMNTS - ELD.DS.425976
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