Applied Differential Geometry by Burke

In summary, "Applied Differential Geometry" by William Burke is an undergraduate level textbook that covers the fundamentals of differential geometry. It covers topics such as linear and affine spaces, manifolds, transformations, the calculus of differential forms, and applications in classical electrodynamics, dynamics of particles and fields, calculus on fiber bundles, and gravitation. The book also emphasizes the use of twisted tensors in differential geometry.

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Table of Contents:
Code:
[LIST]
[*] Preface
[*] Glossary of notation
[*] Introduction
[*] Tensor in linear spaces
[LIST]
[*] Linear and affine spaces
[*] Differential calculus
[*] Tensor algebra
[*] Alternating products
[*] Special relativity
[*] The uses of covariance
[/LIST]
[*] Manifolds
[LIST]
[*] Manifolds
[*] Tangent vectors and 1-forms
[*] Lie bracket
[*] Tensors on manifolds
[*] Mappings
[*] Cotangent bundle
[*] Tangent bundle
[*] Vector fields and dynamical systems
[*] Contact bundles
[*] The geometry of thermodynamics
[/LIST]
[*] Transformations
[LIST]
[*] Lie groups
[*] Lie derivative
[*] Holonomy
[*] Contact transformations
[*] Symmetries
[/LIST]
[*] The calculus of differential forms
[LIST]
[*] Differential forms
[*] Exterior calculus
[*] The * Operator
[*] Metric Symmetries
[*] Normal forms
[*] Index notation
[*] Twisted differential forms
[*] Integration
[*] Cohomology
[/LIST]
[*] Applications of the exterior calculus
[LIST]
[*] Diffusion equations
[*] First-order partial differential equations
[*] Conservation laws
[*] Calculus of variations
[*] Constrained variations
[*] Variations of multiple integrals
[*] Holonomy and thermodynamics
[*] Exterior differential systems
[*] Symmetries and similarity solutions
[*] Variational principles and conservation laws
[*] When not to use forms
[/LIST]
[*] Classical electrodynamics
[LIST]
[*] Electrodynamics and differential forms
[*] Electrodynamics in spacetime
[*] Laws of conservation and balance
[*] Maccroscopic electrodynamics
[*] Electrodynamics of moving bodies
[/LIST]
[*] Dynamics of particles and fields
[LIST]
[*] Lagrangian mechanics of conservative systems
[*] Lagrange's equations for general systems
[*] Lagrangian field theory
[*] Hamiltonian systems
[*] Symplectic geometry
[*] Hamiltonian optics
[*] Dynamics of wave packets
[/LIST]
[*] Calculus on fiber bundles
[LIST]
[*] Connections
[*] Parallel transport
[*] Curvature and torsion
[*] Covariant differentiation
[*] Metric connections
[/LIST]
[*] Gravitations
[LIST]
[*] General relativity
[*] Geodesics
[*] Geodesic deviation
[*] Symmetries and conserved quantities
[*] Schwarzschild orbit problem
[*] Light deflection
[*] Gravitational lenses
[*] Moving frames
[/LIST]
[*] Bibliography
[*] Index
[/LIST]
 
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One of the few differential geometry books that emphasize the importance of twisted tensors.
 

FAQ: Applied Differential Geometry by Burke

What is Applied Differential Geometry?

Applied Differential Geometry is the application of differential geometry, a branch of mathematics that deals with the study of curves and surfaces, to various fields such as engineering, physics, and computer science.

Who is Burke and why is his book important?

Burke is the author of "Applied Differential Geometry", a book that has become a widely used reference in the field. His book provides a comprehensive and accessible introduction to the subject, making it an important resource for students and researchers alike.

What are some real-world applications of Applied Differential Geometry?

Applied Differential Geometry has numerous applications in various fields such as computer graphics, robotics, fluid mechanics, and relativity. It is used to model and analyze complex systems, develop algorithms, and solve problems in these areas.

What background knowledge is required to understand "Applied Differential Geometry by Burke"?

A basic understanding of calculus, linear algebra, and differential equations is necessary to understand "Applied Differential Geometry by Burke". Some familiarity with programming languages and mathematical software may also be helpful for practical applications.

Are there any resources available for further learning about Applied Differential Geometry?

Yes, there are many online resources such as lectures, tutorials, and textbooks available for further learning about Applied Differential Geometry. Additionally, attending conferences and workshops related to the subject can also provide valuable insights and opportunities for networking with other researchers in the field.

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