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Covariant Physics: From Classical Mechanics to General Relativity and Beyond
Covariant From Classical Mechanics to General Relativity and Beyond endeavours to provide undergraduate students as well as self-learners with training in the fundamentals of the modern theories of spacetime, most notably the general theory of relativity as well as physics in curved spacetime backgrounds in general. This text does so with the barest of mathematical preparation. In fact, very little beyond multivariable calculus and a bit of linear algebra is assumed.
Throughout this textbook, the main theme tying the various topics is the so-called principle of covariance - a fundamental symmetry of physics that one rarely encounters in undergraduate texts. The material is introduced very gradually, starting with the simplest of high school mathematics, and moving through the more intense notions of tensor calculus, geometry, and differential forms with ease. Familiar notions from classical mechanics and electrodynamics are used to increase familiarity with the advanced mathematical ideas, and to emphasize the unity of all of physics under the single principle of covariance.
The mathematical and physical techniques developed in this book should allow students to perform research in various fields of theoretical physics as early as their sophomore year in college. The language the reader will learn in this book is the foundational mathematical language of many modern branches of physics, and as such should allow them to read and generally understand many modern physics papers.
Throughout this textbook, the main theme tying the various topics is the so-called principle of covariance - a fundamental symmetry of physics that one rarely encounters in undergraduate texts. The material is introduced very gradually, starting with the simplest of high school mathematics, and moving through the more intense notions of tensor calculus, geometry, and differential forms with ease. Familiar notions from classical mechanics and electrodynamics are used to increase familiarity with the advanced mathematical ideas, and to emphasize the unity of all of physics under the single principle of covariance.
The mathematical and physical techniques developed in this book should allow students to perform research in various fields of theoretical physics as early as their sophomore year in college. The language the reader will learn in this book is the foundational mathematical language of many modern branches of physics, and as such should allow them to read and generally understand many modern physics papers.
- GenresPhysicsMathematics
416 pages, Hardcover
Published May 2, 2021
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Displaying 1 - 2 of 2 reviews
July 19, 2022
Despite not having read the entire textbook at the moment of which this was written, I felt the need to write a short little review here for anyone who happens to stumble by this book and is interested in learning the proposed topics. As I've noticed that there weren't any reviews for it unfortunately.
I've tried looking into various sources to learn Einstein's theories of special and general relativity. Including books like Hartle (which is a bit more physically motivated, but lacking on some of the more mathematical side of things) and Sean Carroll's book (which is good, but a bit more rigorous for someone just starting out and with little to no knowledge of tensor calculus and differential geometry). As I was a mere undergraduate student (by the time of this review) with some basic background in linear algebra, calculus and classical mechanics (though really, calculus & linear algebra are the bare minimum that you need. Some multivariable calculus knowledge is useful, but you can teach yourself the things that you need to know). So I needed something in the middle. And this book is most definitely it.
The textbook gorgeously introduces undergraduate students to the very abstract world of tensors and index notations. Which becomes very useful when describing the laws of physics in a way that is coordinate invariant. Symbols such as the anti-symmetric symbol, Christoffel symbols and many more are introduced at a very gradual pace throughout the book. After going through just the first 2 chapters alone, you will be able to recognize a lot of the mathematical notations used in a lot of modern theoretical physics research. Of course there's more to those papers, but that former sentence is a testament as to how clear the math is introduced throughout the book.
So for anyone hoping to learn the basic maths of general relativity and differential geometry (from a physicist's point of view) at an undergraduate level, I'd highly suggest you getting this book.
I've tried looking into various sources to learn Einstein's theories of special and general relativity. Including books like Hartle (which is a bit more physically motivated, but lacking on some of the more mathematical side of things) and Sean Carroll's book (which is good, but a bit more rigorous for someone just starting out and with little to no knowledge of tensor calculus and differential geometry). As I was a mere undergraduate student (by the time of this review) with some basic background in linear algebra, calculus and classical mechanics (though really, calculus & linear algebra are the bare minimum that you need. Some multivariable calculus knowledge is useful, but you can teach yourself the things that you need to know). So I needed something in the middle. And this book is most definitely it.
The textbook gorgeously introduces undergraduate students to the very abstract world of tensors and index notations. Which becomes very useful when describing the laws of physics in a way that is coordinate invariant. Symbols such as the anti-symmetric symbol, Christoffel symbols and many more are introduced at a very gradual pace throughout the book. After going through just the first 2 chapters alone, you will be able to recognize a lot of the mathematical notations used in a lot of modern theoretical physics research. Of course there's more to those papers, but that former sentence is a testament as to how clear the math is introduced throughout the book.
So for anyone hoping to learn the basic maths of general relativity and differential geometry (from a physicist's point of view) at an undergraduate level, I'd highly suggest you getting this book.
December 26, 2023
Very good for understanding undergraduate physics that leads to graduate level cosmology
Displaying 1 - 2 of 2 reviews