Differential Geometry in Physics
By Gabriel Lugo
372 pp., 6.14 x 9.21, 80 figs

Paperback ISBN: 9781469669250
Published: October 2021 
Hardcover ISBN: 9781469669243
Published: October 2021
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Distributed for the University of North Carolina Wilmington William Madison Randall Library
The approach is to carve an optimal path to learning this challenging field by appealing to the much more accessible theory of curves and surfaces. The transition from classical differential geometry as developed by Gauss, Riemann and other giants, to the modern approach, is facilitated by a very intuitive approach that sacrifices some mathematical rigor for the sake of understanding the physics. The book features numerous examples of beautiful curves and surfaces often reflected in nature, plus more advanced computations of trajectory of particles in black holes. Also embedded in the later chapters is a detailed description of the famous Dirac monopole and instantons.
Features of this book:
* Chapters 14 and chapter 5 comprise the content of a onesemester course taught by the author for many years.
* The material in the other chapters has served as the foundation for many master’s thesis at University of North Carolina Wilmington for students seeking doctoral degrees.
* An open access ebook edition is available at Open UNC (https://openunc.org)
* The book contains over 80 illustrations, including a large array of surfaces related to the theory of soliton waves that does not commonly appear in standard mathematical texts on differential geometry.