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General Relativity: A Geometric Approach
General Relativity: A Geometric Approach
by Malcolm Ludvigsen
Edition: Paperback
Price: $83.77
53 used & new from $6.97

4.0 out of 5 stars Sergei Winitzki's comment on this book, August 14, 2012
In his (really great) book/lectures notes "Advanced General Relativity" Winitzki dedicates a few paragraphs solely commenting on this book.
You can find Winitzki's book online for free as it was released under GNU FDL, and he also keeps it on his website. Try it here [...] , it should be the file "GR_course.pdf"

What he wrote (page 175, you should read it from the file to understand the equations and symbols):

"The book is M. Ludvigsen, General relativity: a geometric aproach (Cambridge University Press, 1999). Many explanations in that book are outstandingly clear, and I benefited greatly by reading it. Nevertheless, there are some minor gaffes:

1) On p. 91, eq. 9.27 is supposedly the same as eq. 9.20 when
"written in full." However, these equations actually differ by
the choice of the permuted indices. The relation 9.27 can be
obtained from 9.20 only if one assumes the identity R abcd =
R cdab , which Ludvigsen actually never mentions in the book.
This well-known standard identity is a consequence of 9.19
and 9.20.

2) On p. 103, eq. 10.14 contains ∇ a ∇ a φ = R..., while
the preceding (unnumbered) equation on p.102 contains
−∇ e ∇ a φ = R.... A minus sign has materialized from
nowhere! The answer (10.17) is correct, and the extra minus
sign is actually needed to compensate for an error made ear-
lier. In the last paragraph on p. 101, Ludvigsen writes (in
3-dimensional notation) a = ∇ φ whereas in fact a = −∇ φ
in Newtonian gravity. (The acceleration points down, the po-
tential grows upwards.) So the correct calculation starts by
introducing a a = ∇ a φ and not −∇ a φ.

3) On p. 108, top line, "Using the fact that l a n a = 1 and
∇ a l b = ∇ b l a , we have..." -- actually, the same result follows
with merely the assumption that l a is a null geodesic. It is not
necessary to assume that l a is integrable.

4) On p. 109, top line, -- one cannot actually derive Eq.
(11.10) as claimed. By contracting the top equation with
l a m b m c and using Eq. (11.8), which already assumes that l is
integrable, one gets
Dσ = R(l, m, l, m) + 2la¯m b ( ∇ a mb).
Now it is unclear how to show that the last term is equal to
2ρσ. There is a significant freedom in ∇ m since m is chosen
simply to be orthogonal to n, l and this is not sufficient
to fix ∇ m. In fact, the null tetrad can be changed by the
transformation m → e iλ m. Then σ → e 2iλ σ, as shown at top
of page 110. If λ is a function of position then the equation
Dσ = ... will be changed after the transformation! Thus this
equation really depends on the choice of the tetrad, and some
choices are better than others. The equation (11.10) is perhaps
obtained with a suitable choice of the tetrad, but this is not
discussed in the book."

[I rated Ludvigsen's 4 stars, because I haven't read the book myself.]
Comment Comment (1) | Permalink | Most recent comment: Aug 6, 2014 8:48 AM PDT

Selected Sonnets: A Bilingual Edition (English and Portuguese Edition)
Selected Sonnets: A Bilingual Edition (English and Portuguese Edition)
by Luís de Camões
Edition: Hardcover
Price: $26.42
30 used & new from $4.99

4 of 5 people found the following review helpful
3.0 out of 5 stars I didn't read, but..., April 22, 2010
[Edit: I must be clear. The only reason I'm not giving this 1 star only is because I have only read this sonnet, and nothing else from the book. In this translation the meaning of the text is altered and plus I don't even think the verses are that good in English. Besides altering the meaning, they convey nothing of the tone.

Maybe you should look at Landeg White's book, which I also haven't read. In hindsight I realize these verses given as example are really tough for a non native speaker. I know Richard Zenith [see Mark Baxter's comment below] and I was really surprised to see that he completely missed the meaning of the verses. I guarantee you: although a non native might be really confused, for a literate native there is no ambiguity in the meaning of these last 3 verses. Only beauty and sheer poetry, in one of the ultimate portuguese poems.]


I didn't read it, but I'm portuguese and I was looking for an English translation the other day of one of his sonnets so I stumbled upon this book.
Here's what I found [page 70, "Mudam-se os tempos, mudam-se as vontades..."]:

"E, afora este mudar-se cada dia,
outra mudança faz de mór espanto:
que não se muda já como soía."

This books translation:
"Yet even more
astonishing is yet another unseen
change within all these endless changes:
that for me, nothing ever changes anymore."


This is wrong, really wrong. It's without a doubt one of his top5 sonnets, one that every portuguese knows, and this translation completely misses it. I was in such shock I'm writing this review!
A quite accurate translation would be:

"But besides this daily vicissitude,
One further change is the greater woe
That it changes no longer as was its wont."

See the difference?


Now, I haven't read anything else on this book besides this sonnet, but even considering translating poetry is really tough, this translation is definitely poor. Again, judgind by this poem alone, one much better translation was the latter above, by Landeg White.
Comment Comments (2) | Permalink | Most recent comment: May 27, 2012 2:17 PM PDT

The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities (MAA Problem Books)
The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities (MAA Problem Books)
by J. Michael Steele
Edition: Paperback
Price: $37.34
39 used & new from $21.36

4 of 4 people found the following review helpful
5.0 out of 5 stars Amazing, June 26, 2008
Really, you should own it.
It's such a beautiful book. The text, the content, the structure, the exercises, the solutions, the tricks and insight, and it's soft and handy.
What a book. It's modern, rigorous, gives you references to more advanced texts, and teaches you a lot! A pleasure.
If you're interested in inequalities you should really buy it, but even you if don't want to, it's available on the internet (try [..]
Have a very very nice reading.

Basic Engineering Circuit Analysis
Basic Engineering Circuit Analysis
by J. David Irwin
Edition: Hardcover
Price: $159.44
50 used & new from $20.81

10 of 11 people found the following review helpful
3.0 out of 5 stars An okay book, that becomes very good with a little trick.., June 1, 2008
The book is quite okay concerning the explaining and teaching, and considering it's an introduction. (If you want diodes, transistors, etc search elsewhere! (Sedra/Smith?))

But the thing is: each of the fifteen chapters has about 70 exercises. And if you began learning this stuff, you know it: you'll always forget a term in the equations or switch a minus for a plus sign, etc.. The solutions are not on the book, but they do exist, and if your an instructor you may log in the site and ask for a copy.

If you're a student . . . it's actually even easier! Just get it on isoHunt or eMule and start working the problems.

Believe me, do half of each chapter's exercises and you'll breeze through your exam. Check or learn the correct answer on the Instructor's Manual.

P.S. - I really understand all the one-star ratings, but it's just because this is a subject where you need lots of practice, lots of exercises. And of course if you're trying to study and you're stuck on one exercise, you probably won't go further, and exasperate.. But go get the answers, and good work! You'll see the book will give you all the theory and explaining necessary.

The Feynman Lectures on Physics including Feynman's Tips on Physics: The Definitive and Extended Edition
The Feynman Lectures on Physics including Feynman's Tips on Physics: The Definitive and Extended Edition
by Robert B. Leighton
Edition: Hardcover
15 used & new from $184.58

1 of 6 people found the following review helpful
5.0 out of 5 stars Feynman once said..., February 27, 2008
Physics is like sex - it may lead to practical results, but that's not why we do it.

Numerical Analysis (Available Titles CengageNOW)
Numerical Analysis (Available Titles CengageNOW)
by Richard L. Burden
Edition: Hardcover
55 used & new from $16.64

2 of 2 people found the following review helpful
4.0 out of 5 stars is there much better already written?, January 24, 2008
Well, I must start by saying I wasn't sure between the 3 and 4 stars.
Definitely not 5, definitely not 2.

The thing is, it's an introduction! Some say it's written from a mathematical viewpoint, but I didn't find it so much. I mean, considering it's numerical analysis! You have to understand where the approximations come from.

Each chapter begins with a quite useful motivation, and each section has a set of about 20 exercises, of which the odds ones are answered. I guess you have to do the basic exercises, like 2 or 3, to really grasp what's going on, but in general every topic is explained quite well.

Another 2 features, which I find excellent. The layout is very nice, does not tire you, and the text is filled with references to other books. Something like 100 other numerical analysis books and papers. This is what an introduction book is supposed to be. Gives the basics of each topic, well explained, and if you want to learn some more, or read some more proofs check the other, more specialized, references.

Finally: Yes, the price is an outrage! Do not spend these dollars or euros. I worked with the seventh edition and compared it with the new one, and there's really nothing essentially better. Basically just some historical margin notes.

In short. An introduction, of course, but easy to follow but still quite rigorous. You understand where things come from, oh, and there's the algorithms (not bad). But don't buy it for more than 70 dollars. Get an used one, or maybe the seventh edition. Just as good.

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