Introduction to Tensor Calculus, Relativity and Cosmology (Dover Books on Physics) by D. F. Lawden (PDF)

Description

This elementary introduction pays special attention to aspects of tensor calculus and relativity that students tend to find most difficult. Its use of relatively unsophisticated mathematics in the early chapters allows readers to develop their confidence within the framework of Cartesian coordinates before undertaking the theory of tensors in curved spaces and its application to general relativity theory.Topics include the special principle of relativity and Lorentz transformations; orthogonal transformations and Cartesian tensors; special relativity mechanics and electrodynamics; general tensor calculus and Riemannian space; and the general theory of relativity, including a focus on black holes and gravitational waves. The text concludes with a chapter offering a sound background in applying the principles of general relativity to cosmology. Numerous exercises advance the theoretical developments of the main text, thus enhancing this volume’s appeal to students of applied mathematics and physics at both undergraduate and postgraduate levels. Preface. List of Constants. References. Bibliography.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐If you have background in Maxwell’s equations and vector calculus, you are able to follow this book. It is a decent book to learn general relativity for the first time. The mathematics involved is very much self contained.The book prints are of high quality, dover standard.

⭐As a writer and philosopher I have tried to get a genuine scientific understanding of topics like quantum physics and relativity. Treatments tend to be either over-simplified (no math) or presume you are very competent at graduate-level math. My past efforts have raised my math competence to the point where this book, for me, is at a near-perfect level. I found the explanation and use of tensors tied to physics in a way that helped me with both subjects.I was also pleased with the treatment of general relativity. Many books give good accounts of special relativity, but this is the best presentation of general relativity that includes the mathematics involved.I would recommend this to anyone who is willing to do the math. But without at least a basic understanding of vectors and partial derivatives, you will not be able to follow the text.

⭐This book provides a good introduction to the basics of both the special and the general Theory of Relativity. I do not, however, like its style entirely. It is a little dated, too. For example, for the special part of the theory, the author sticks to Cartesian tensors only, which is advantageous only from the vantage of a student interested in… Special Relativity! This wastes time; moreover, I regard the choice of x_4 = ict unfortunate. Finally, despite the book being only 205 pages long and covering a reasonable amount of basic stuff, the style is wordy.Study elsewhere (the book by D’Inverno is OK, the ones by Schutz and Wald rock), and if you feel the need for practice with some elementary point, go for the exercises in this book.

⭐If you’re serious about learning (general & special) relativity, this is probably one of the most pedagogical books out there. Very few (and small) steps or explanations missing. Concise and to the point. It covers the basics so you’ll be able to pick other GR books later on to learn what you need. I really like teaching one-semester courses with it.

⭐Really need a very strong mathematical background in order to keep up.

⭐Although the book is requiring me to do an extensive review of vector calculus, I’m learning things I did not catch when I took the course. The book answers many of the questions that I have asked over the years; I am sure after reviewing vector fields I will continue to the book and have a much better understanding of how to apply tensors in various fields of Physics!!!

⭐I’m really impressed with the clarity of the material.I’ve worked through 21 problems in chapter 2, and the answers to the exercies do not have a single mistake in them yet.The publisher will also email you a .pdf file of all of the chapter problems worked out in detail. I’ve found the solutions to the problems to be a good supplement to the text itself.I would buy other titles from this author and publisher.

⭐Good

⭐This is a great book about relativity, starting with SR, working through tensors all the way to GR. I wanted a small paperback to take on holiday (believe it or not!) and this guy the bill perfectly. The author works through the mathematics without using coordinate bases, but does that they are not needed in order to get to the result. You will need to know calculus up to partial differentiation and some linear algebra such as matrix multiplication, and it would help if you already knew about vectors; but if you want a full analysis then I recommend Bernard Schultz (but that was a little too heavy a book to take on holiday), but believe me when I say that Lawden takes no short cuts, and thankfully has very few places where he says “it can be shown that…”, which I hate. Plenty of exercises too, but the answers have to be found via a search on the internet.

⭐Definitely not for the beginner. You will want to understand, quantitatively, what General Relativity is about. You will need to understand and use Matrix Algebra to A level standard. You will need to understand and use Vector Spaces and Vector Fields to undergraduate level. You will need to understand and use Partial Differentiation and Integration. You will need to understand Differential Equations and methods of solution. If you have these skills then you have some chance of effectively using this book.It is hard going and requires effort but at the end you will be able to interpret and explain what Einstein’s General Relativity is and why it has many solutions.

⭐This book covers the main ideas of Relativity. It gives a clear, and traditional, account of the main concepts.

⭐Fantastic book. Clearly presented

⭐Excellent text book … clearly written with examples to test oneself on … Thanks

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