Differential Geometry, Differential Equations, and Mathematical Physics: The Wisla 19 Summer School

This volume includes lectures from the Wisła 19 Summer School on Differential Geometry,Differential Equations,and Mathematical Physics,dedicated to symplectic and Poisson geometry,tractor calculus,and the integration of ordinary differential equations. It covers topics such as parabolic geometry,geometric methods for solving PDEs,Darcy and Euler flows,and differential invariants for fluid and gas flow. It is ideal for graduate students and researchers in these areas.

Format: Paperback / softback
Length: 231 pages
Publication date: 13 February 2022
Publisher: Springer Nature Switzerland AG

This volume presents a collection of lectures delivered during the Wisła 19 Summer School, which took place from August 19 to 29, 2019, in Wisła, Poland. The summer school was organized by the Baltic Institute of Mathematics and focused on three main topics: Differential Geometry, Differential Equations, and Mathematical Physics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations.

The first three chapters of this volume serve as lecture notes, covering these topics in detail. After that, the chapters combine theoretical and applied perspectives to explore various intersections between differential geometry, differential equations, and mathematical physics. Some of the specific topics covered include:

Parabolic Geometry: This topic explores the geometric aspects of partial differential equations (PDEs) and their applications in physics, mathematical biology, and mathematical finance. It discusses methods such as the method of characteristics, the theory of parabolic equations, and the study of hyperbolic surfaces.

Geometric Methods for Solving PDEs in Physics, Mathematical Biology, and Mathematical Finance: This chapter discusses the use of geometric methods to solve PDEs in these fields. It covers topics such as the heat equation, the Navier-Stokes equations, the wave equation, and the Schrödinger equation. Geometric methods offer advantages over traditional numerical methods in terms of accuracy, efficiency, and interpretability.

Darcy and Euler Flows of Real Gases: This chapter focuses on the study of fluid and gas flow using the Darcy and Euler equations. It discusses the principles of fluid mechanics, the concept of flow resistance, and the analysis of flow patterns in pipes, channels, and other geometries. The chapter also covers the application of these equations to real-world problems in the fields of petroleum engineering, chemical engineering, and aerospace.

Differential Invariants for Fluid and Gas Flow: This chapter explores the use of differential invariants to study the behavior of fluid and gas flow. It discusses the concept of invariants, their definition, and their applications in analyzing the flow of fluids and gases. Differential invariants provide a way to characterize the structure and dynamics of the flow and can be used to identify different flow regimes, predict flow behavior, and optimize flow systems.

Differential Geometry, Differential Equations, and Mathematical Physics is an excellent resource for graduate students and researchers working in these fields. A basic understanding of differential geometry is assumed, although the book provides a comprehensive introduction to the topics covered.

Overall, this volume offers a comprehensive and up-to-date overview of the latest developments in differential geometry, differential equations, and mathematical physics. It provides valuable insights into the theoretical and applied aspects of these fields and is sure to be of interest to scholars and researchers alike.

Weight: 385g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030632557
Edition number: 1st ed. 2021