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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.

Partial differential equations. --- Differential geometry. --- Mechanics. --- Fluids. --- Quantum field theory. --- String theory. --- Partial Differential Equations. --- Differential Geometry. --- Classical Mechanics. --- Fluid- and Aerodynamics. --- Quantum Field Theories, String Theory. --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Hydraulics --- Mechanics --- Physics --- Hydrostatics --- Permeability --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Differential geometry --- Partial differential equations --- Geometry, Differential --- Differential equations --- 517.91 Differential equations

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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.

Differential equations, Partial --- Differential equations, partial. --- Global differential geometry. --- Partial Differential Equations. --- Differential Geometry. --- Geometry, Differential --- Partial differential equations --- Partial differential equations. --- Differential geometry. --- Differential geometry

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