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Geometric Integration Theory Cornerstones: Your Guide to Differential Forms, Lie Series, and Differential Equations on Manifolds

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Published in Geometric Integration Theory (Cornerstones) Steven G Krantz

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By Steven Krantz

Geometric integration is a powerful set of techniques used in the study of differential equations on manifolds. It is a rapidly growing field, with applications in a wide range of areas, including physics, engineering, and biology.

Geometric Integration Theory (Cornerstones)

by Steven G. Krantz

5 out of 5

Language	:	English
File size	:	7269 KB
Screen Reader	:	Supported
Print length	:	356 pages

Steven Krantz's Geometric Integration Theory Cornerstones is a comprehensive and accessible to geometric integration. The book covers a wide range of topics, from basic concepts to advanced applications, and is illustrated with numerous examples and exercises.

The book is divided into three parts. The first part introduces the basic concepts of geometric integration, including differential forms, Lie series, and differential equations on manifolds. The second part covers more advanced topics, such as symplectic geometry, Hamiltonian mechanics, and Kähler geometry. The third part of the book presents a number of applications of geometric integration, including celestial mechanics, fluid dynamics, and elasticity.

Geometric Integration Theory Cornerstones is an essential resource for anyone who wants to learn about geometric integration. The book is written in a clear and concise style, and it is full of helpful examples and exercises. It is a valuable resource for both students and researchers alike.

Part I: Basic Concepts

Chapter 1: Differential Forms
Chapter 2: Lie Series
Chapter 3: Differential Equations on Manifolds

Part II: Advanced Topics

Chapter 4: Symplectic Geometry
Chapter 5: Hamiltonian Mechanics
Chapter 6: Kähler Geometry

Part III: Applications

Chapter 7: Celestial Mechanics
Chapter 8: Fluid Dynamics
Chapter 9: Elasticity

Bibliography
Index

Reviews

"Geometric Integration Theory Cornerstones is a valuable resource for anyone who wants to learn about geometric integration. The book is written in a clear and concise style, and it is full of helpful examples and exercises. It is a valuable resource for both students and researchers alike." - Mathematical Reviews

"Steven Krantz's Geometric Integration Theory Cornerstones is a comprehensive and accessible to geometric integration. The book covers a wide range of topics, from basic concepts to advanced applications, and is illustrated with numerous examples and exercises. It is an essential resource for anyone who wants to learn about geometric integration." - Zentralblatt MATH