--- product_id: 2595695 title: "The Geometry of Physics: An Introduction" price: "528 zΕ‚" currency: PLN in_stock: true reviews_count: 13 url: https://www.desertcart.pl/products/2595695-the-geometry-of-physics-an-introduction store_origin: PL region: Poland --- # 750 pages of advanced physics geometry Bridges physics, engineering & geometry Fully worked calculations & examples The Geometry of Physics: An Introduction **Price:** 528 zΕ‚ **Availability:** βœ… In Stock ## Summary > πŸ“ Unlock the geometry behind the universe β€” don’t just study physics, experience it! ## Quick Answers - **What is this?** The Geometry of Physics: An Introduction - **How much does it cost?** 528 zΕ‚ with free shipping - **Is it available?** Yes, in stock and ready to ship - **Where can I buy it?** [www.desertcart.pl](https://www.desertcart.pl/products/2595695-the-geometry-of-physics-an-introduction) ## Best For - Customers looking for quality international products ## Why This Product - Free international shipping included - Worldwide delivery with tracking - 15-day hassle-free returns ## Key Features - β€’ **Advanced Yet Accessible:** Ideal for those with a solid foundation in analytic geometry and calculus seeking to elevate their grasp of modern physics applications. - β€’ **Interdisciplinary Approach:** Experience a unique blend of physics, engineering, and analytic geometry that no other text attempts, perfect for the ambitious professional. - β€’ **Comprehensive 750-Page Volume:** Dive deep into the geometry of physics with an extensive, best-in-class text that covers classical to quantum applications. - β€’ **Illustrations That Spark Insight:** Benefit from numerous diagrams and visual aids designed to trigger those essential 'aha' moments in understanding. - β€’ **Rich Worked Examples & Calculations:** Master complex concepts through detailed, step-by-step computations that make advanced topics accessible for the prepared reader. ## Overview The Geometry of Physics: An Introduction (3rd Edition) is a 750-page authoritative text by Frankel that uniquely integrates analytic geometry with physics and engineering applications. It offers fully worked examples, numerous illustrations, and advanced treatments of topics from classical mechanics to quantum gauge theories. Designed for readers with a strong math background, it serves as both a reference and a deep dive into the geometric foundations of modern physics. ## Description This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are helpful for a deeper understanding of both classical and modern physics and engineering. It is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. A main addition introduced in this Third Edition is the inclusion of an Overview, which can be read before starting the text. This appears at the beginning of the text, before Chapter 1. Many of the geometric concepts developed in the text are previewed here and these are illustrated by their applications to a single extended problem in engineering, namely the study of the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis. Review: Third Edition Best of Class & Only Modern Text in this Genre - Some texts are designed to increase understanding, others to aid in practical computation, making them as much references as pedagogic tools. The latter are especially suited for self study. In this new edition, Frankel does something amazing-- instead of completely reorganizing an already stellar text, he "ties it all together" with a new "example" introduction-- a 34 page (roman numeral numbered!) "preface" illustrating Cartan's exterior differential forms with a "metal torsion" example application to Cauchy's stress tensor. Don't mistakely think that this means Frankel limits this text to the differential geometry of engineering mechanics and materials-- he covers a vast field of physics all the way from classic to quantum, sans string but with numerous gauge applications, in 750 packed pages, most containing fully worked out calculations for the aforementioned reference value. It seems today that all publishers just parrot "for grad students or advanced undergrads with a year of calculus and some linear algebra." Is this to sell more books? Not sure, but I wouldn't tackle this for self study or even calculative reference without "advanced" calculus (in my definition, analysis) PLUS a good course in analytic geometry first. Although this is packed with AG, it does not start by teaching AG-- the geometry knowledge is assumed, and we're then treated to an astonishing adventure of detailed APPLICATIONS of geometry to nearly every aspect of physics, including numerous cutting edge and intractable problems. There also are NUMEROUS engineering applications examples, blending physics, engineering and geometry in a way no other text even attempts. I've long felt that some pundits who tease the Greeks for seeing everything as geometric would someday eat their words. Well.. wow. This volume clearly demonstrates how much what comes round goes round. OK, looking at physical spheres is not the same as spacetime curvature spheres, let alone "field" geometry that isn't even a physical geometry, but the geometry of a vector bundle! So, to be honest, if you see the word "introduction" in this text's title, and think you'll be guided through the UNDERSTANDING of Lie algebras, matrix calculus, Yang-Mills and other gauges via geometry-- be careful. "Introduction" as I read it after reading this text means intro to the APPLICATION and CALCULATION techniques available to someone already well grounded in analytic geometry. Don't get me wrong, the author is simply amazing, as were the very successful first two editions, in carefully explaining many neglected applications of AG to physics, but this book would be 3,000 pages if we actually expected it to "introduce" every notation. So, it does blast right off assuming a good base in analytic geometry, and a fair base in physics. One really cool dimension for self-study-- the author is obviously first a mathematician, and within that a geometer, so the pedagogic artifact from older days of showing NUMEROUS diagrams and illustrations made its way into this fine text. Even if I weigh the overall presentation as more computational that didactic, the illustrations themselves bely that evaluation-- each one gives one of those "aha" moments. The author also does take the time to explain the WHY of certain formula elements so you really "get" them. For example, if we're given an element where x^(exp polynomial) = b*(expression), the author WILL digress enough to remind us that b is acting as a proportionality constant. I find this really helpful as a way to generalize the lesson learned, otherwise we're just rote memorizing or referring back to a process we're not really getting! Highly recommended with the caveats mentioned about brushing up on your analytic/ differential geometry. Library Picks reviews only for the benefit of desertcart shoppers and has nothing to do with desertcart, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for desertcart shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases. Review: Highly recommended. Wish Kindle ebook was PDF instead of EPUB - Highly recommended. It's well written, covers a lot of material, and is suitable for self study . I wish that the Kindle ebook were a PDF ebook for which the equations are always properly sized in proportion to the text (available from ebooks and vitalsource at much greater cost). I also recommend the classic Differential Forms by Harley Flanders. It's much shorter but still covers some important material such as the converse to the Poincare Lemma, the Frobenius theorem, and an elegant concise derivation of the Riemann tensor-valued curvature two-forms, the Bianchi identity, and the Einstein tensor. But much that is discussed in Frankel's book is entirely missing from Flander's book, such as Frankel's elegant treatment of the Lie derivative, even though it is somewhat sloppy in its treatment of time-dependent "flows" on a manifold M, which can be made onto true flows by considering an extended manifold RxM. Usually when he says that the Lie derivative with respect to the flow vector field X on RxM of a particular time-dependent differential form with no dt^ terms is zero, what he really means is that it's zero after discarding any dt^ terms. ## Features - Used Book in Good Condition ## Technical Specifications | Specification | Value | |---------------|-------| | Best Sellers Rank | #249,553 in Books ( See Top 100 in Books ) #14 in Differential Geometry (Books) #29 in Topology (Books) #81 in Mathematical Physics (Books) | | Customer Reviews | 4.4 out of 5 stars 67 Reviews | ## Images ![The Geometry of Physics: An Introduction - Image 1](https://m.media-amazon.com/images/I/61vDd-1+soL.jpg) ## Customer Reviews ### ⭐⭐⭐⭐⭐ Third Edition Best of Class & Only Modern Text in this Genre *by P***Z on May 16, 2013* Some texts are designed to increase understanding, others to aid in practical computation, making them as much references as pedagogic tools. The latter are especially suited for self study. In this new edition, Frankel does something amazing-- instead of completely reorganizing an already stellar text, he "ties it all together" with a new "example" introduction-- a 34 page (roman numeral numbered!) "preface" illustrating Cartan's exterior differential forms with a "metal torsion" example application to Cauchy's stress tensor. Don't mistakely think that this means Frankel limits this text to the differential geometry of engineering mechanics and materials-- he covers a vast field of physics all the way from classic to quantum, sans string but with numerous gauge applications, in 750 packed pages, most containing fully worked out calculations for the aforementioned reference value. It seems today that all publishers just parrot "for grad students or advanced undergrads with a year of calculus and some linear algebra." Is this to sell more books? Not sure, but I wouldn't tackle this for self study or even calculative reference without "advanced" calculus (in my definition, analysis) PLUS a good course in analytic geometry first. Although this is packed with AG, it does not start by teaching AG-- the geometry knowledge is assumed, and we're then treated to an astonishing adventure of detailed APPLICATIONS of geometry to nearly every aspect of physics, including numerous cutting edge and intractable problems. There also are NUMEROUS engineering applications examples, blending physics, engineering and geometry in a way no other text even attempts. I've long felt that some pundits who tease the Greeks for seeing everything as geometric would someday eat their words. Well.. wow. This volume clearly demonstrates how much what comes round goes round. OK, looking at physical spheres is not the same as spacetime curvature spheres, let alone "field" geometry that isn't even a physical geometry, but the geometry of a vector bundle! So, to be honest, if you see the word "introduction" in this text's title, and think you'll be guided through the UNDERSTANDING of Lie algebras, matrix calculus, Yang-Mills and other gauges via geometry-- be careful. "Introduction" as I read it after reading this text means intro to the APPLICATION and CALCULATION techniques available to someone already well grounded in analytic geometry. Don't get me wrong, the author is simply amazing, as were the very successful first two editions, in carefully explaining many neglected applications of AG to physics, but this book would be 3,000 pages if we actually expected it to "introduce" every notation. So, it does blast right off assuming a good base in analytic geometry, and a fair base in physics. One really cool dimension for self-study-- the author is obviously first a mathematician, and within that a geometer, so the pedagogic artifact from older days of showing NUMEROUS diagrams and illustrations made its way into this fine text. Even if I weigh the overall presentation as more computational that didactic, the illustrations themselves bely that evaluation-- each one gives one of those "aha" moments. The author also does take the time to explain the WHY of certain formula elements so you really "get" them. For example, if we're given an element where x^(exp polynomial) = b*(expression), the author WILL digress enough to remind us that b is acting as a proportionality constant. I find this really helpful as a way to generalize the lesson learned, otherwise we're just rote memorizing or referring back to a process we're not really getting! Highly recommended with the caveats mentioned about brushing up on your analytic/ differential geometry. Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases. ### ⭐⭐⭐⭐⭐ Highly recommended. Wish Kindle ebook was PDF instead of EPUB *by D***P on January 30, 2017* Highly recommended. It's well written, covers a lot of material, and is suitable for self study . I wish that the Kindle ebook were a PDF ebook for which the equations are always properly sized in proportion to the text (available from ebooks and vitalsource at much greater cost). I also recommend the classic Differential Forms by Harley Flanders. It's much shorter but still covers some important material such as the converse to the Poincare Lemma, the Frobenius theorem, and an elegant concise derivation of the Riemann tensor-valued curvature two-forms, the Bianchi identity, and the Einstein tensor. But much that is discussed in Frankel's book is entirely missing from Flander's book, such as Frankel's elegant treatment of the Lie derivative, even though it is somewhat sloppy in its treatment of time-dependent "flows" on a manifold M, which can be made onto true flows by considering an extended manifold RxM. Usually when he says that the Lie derivative with respect to the flow vector field X on RxM of a particular time-dependent differential form with no dt^ terms is zero, what he really means is that it's zero after discarding any dt^ terms. ### ⭐⭐⭐⭐ Topics are great. Notation and typesetting could be improved *by G***E on November 30, 2015* Topics are great. Notation and typesetting could be improved, but since this is already the 3rd edition, I can only say I don't understand the author/publisher's decision of insisting on using unconventional notations every now and then and such ugly typesetting. ## Frequently Bought Together - The Geometry of Physics: An Introduction - Geometry, Topology and Physics (Graduate Student Series in Physics) - Topology and Geometry for Physicists (Dover Books on Mathematics) --- ## Why Shop on Desertcart? - πŸ›’ **Trusted by 1.3+ Million Shoppers** β€” Serving international shoppers since 2016 - 🌍 **Shop Globally** β€” Access 737+ million products across 21 categories - πŸ’° **No Hidden Fees** β€” All customs, duties, and taxes included in the price - πŸ”„ **15-Day Free Returns** β€” Hassle-free returns (30 days for PRO members) - πŸ”’ **Secure Payments** β€” Trusted payment options with buyer protection - ⭐ **TrustPilot Rated 4.5/5** β€” Based on 8,000+ happy customer reviews **Shop now:** [https://www.desertcart.pl/products/2595695-the-geometry-of-physics-an-introduction](https://www.desertcart.pl/products/2595695-the-geometry-of-physics-an-introduction) --- *Product available on Desertcart Poland* *Store origin: PL* *Last updated: 2026-05-24*