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Differential Geometry of Manifolds: Textbooks in Mathematics

Autor Stephen Lovett
en Limba Engleză Paperback – 21 ian 2023
Differential Geometry of Manifolds, Second Edition presents the extension of differential geometry from curves and surfaces to manifolds in general. The book provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. It introduces manifolds in a both streamlined and mathematically rigorous way while keeping a view toward applications, particularly in physics.


The author takes a practical approach, containing extensive exercises and focusing on applications, including the Hamiltonian formulations of mechanics, electromagnetism, string theory.


The Second Edition of this successful textbook offers several notable points of revision.


New to the Second Edition:







  • New problems have been added and the level of challenge has been changed to the exercises







  • Each section corresponds to a 60-minute lecture period, making it more user-friendly for lecturers







  • Includes new sections which provide more comprehensive coverage of topics







  • Features a new chapter on Multilinear Algebra


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Specificații

ISBN-13: 9781032474908
ISBN-10: 1032474904
Pagini: 450
Ilustrații: 73
Dimensiuni: 191 x 235 x 29 mm
Greutate: 0.83 kg
Ediția:2
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Textbooks in Mathematics


Notă biografică

Stephen Lovett is a Professor of Mathematics at Wheaton College in Illinois. He has also taught at Eastern Nazerene College. He holds a PhD from Northeastern University. He also authored three well-received texts with CRC Press, including the companion volume, Differential Geometry of Curves and Surfaces, Second Edition, with Tom Banchoff and Abstract Algebra: Structures and Applications.

Cuprins

Analysis of Multivariable Functions


Variable Frames


Differentiable Manifolds


Multilinear Algebra


Analysis of Manifolds


Introduction to Riemannian Geometry


Applications of Manifolds to Physics


A: Point Set Topology


B: Calculus of Variations


C: Further Topics in Multilinear Algebra

Descriere

The author presents the extension of differential geometry from curves and surfaces to manifolds in general. It provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together classical and modern formulations. The goal is to introduce manifolds in a both streamlined and mathematically rigorous way.