Overview
- Provides a concise and accessible introduction to a selection of topics at the intersection of differential geometry, differential equations, and mathematical physics
- Features lecture notes, surveys, and original research, ideal for pedagogical use either independently or in the classroom
- Covers a wide variety of topics, using both theoretical and applied approaches
Part of the book series: Tutorials, Schools, and Workshops in the Mathematical Sciences (TSWMS)
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About this book
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:
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.
- 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.
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Keywords
- Differential geometry math physics
- Differential geometry fluid dynamics
- Differential geometry thermodynamics
- Differential equations geometry
- Differential equations math physics
- Wisla summer school
- Poisson and symplectic structures
- Tractor calculus
- Finite dimensional dynamics
- Transformation groups
- Parabolic geometry
- Darcy Euler flows
- Differential invariants fluid flow
- Dirichlet filtration problem
- Finite dimensional dynamics
- Cartan geometries
- partial differential equations
- fluid- and aerodynamics
Table of contents (6 chapters)
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Front Matter
Editors and Affiliations
Bibliographic Information
Book Title: Differential Geometry, Differential Equations, and Mathematical Physics
Book Subtitle: The Wisła 19 Summer School
Editors: Maria Ulan, Eivind Schneider
Series Title: Tutorials, Schools, and Workshops in the Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-030-63253-3
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Baltic Institute of Mathematics 2021
Hardcover ISBN: 978-3-030-63252-6Published: 13 February 2021
Softcover ISBN: 978-3-030-63255-7Published: 13 February 2022
eBook ISBN: 978-3-030-63253-3Published: 12 February 2021
Series ISSN: 2522-0969
Series E-ISSN: 2522-0977
Edition Number: 1
Number of Pages: XIV, 231
Number of Illustrations: 9 b/w illustrations, 20 illustrations in colour
Topics: Partial Differential Equations, Differential Geometry, Classical Mechanics, Fluid- and Aerodynamics, Quantum Field Theories, String Theory