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Emmy Noether's Wonderful Theorem [Englisch] [Taschenbuch]

Dwight E. Neuenschwander
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Kurzbeschreibung

7. Januar 2011
A beautiful piece of mathematics, Noether's Theorem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space, or rotation will obey the laws of conservation of energy, linear momentum, or angular momentum, respectively. This exciting result offers a rich unifying principle for all of physics. Dwight E. Neuenschwander's introduction to the theorem's genesis, applications, and consequences artfully unpacks its universal importance and unsurpassed elegance. Drawing from over thirty years of teaching the subject, Neuenschwander uses mechanics, optics,geometry, and field theory to point the way to a deep understanding of Noether's Theorem. The three sections provide a step-by-step, simple approach to the less-complex concepts surrounding the theorem, in turn instilling the knowledge and confidence needed to grasp the full wonder it encompasses. Illustrations and worked examples throughout each chapter serve as signposts on the way to this apex of physics. Noether's Theorem is an essential principle of post-introductory physics. This handy guide includes end-of-chapter questions for review and appendixes detailing key related physics concepts for further study.

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Emmy Noether's Wonderful Theorem + Elliptic Tales: Curves, Counting, and Number Theory + Riemann's Zeta Function (Dover Books on Mathematics)
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Produktinformation

  • Taschenbuch: 243 Seiten
  • Verlag: Johns Hopkins Univ Pr (7. Januar 2011)
  • Sprache: Englisch
  • ISBN-10: 0801896940
  • ISBN-13: 978-0801896941
  • Vom Hersteller empfohlenes Alter: Ab 18 Jahren
  • Größe und/oder Gewicht: 2,3 x 13,5 x 21 cm
  • Durchschnittliche Kundenbewertung: 3.0 von 5 Sternen  Alle Rezensionen anzeigen (2 Kundenrezensionen)
  • Amazon Bestseller-Rang: Nr. 57.400 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)

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Produktbeschreibungen

Pressestimmen

Neuenschwander writes well and gives thorough explanations. Choice 2011

Über den Autor und weitere Mitwirkende

Dwight E. Neuenschwander is a professor of physics at Southern Nazarene University and editor of the Society of Physics Students Publications of the American Institute of Physics. He won the Excellence in Undergraduate Physics Teaching Award from the American Association of Physics Teachers.

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Buchdeckel | Copyright | Inhaltsverzeichnis | Auszug | Stichwortverzeichnis
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8 von 8 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Wonderful introduction 10. Juni 2012
Von HaraldK
Format:Taschenbuch|Verifizierter Kauf
For some time already I was looking for a good introduction into the topic of Lagrangians, the Euler-Lagrange equations, the action integral and how they relate to symmetries and invariance. With a background more in mathematics than in physics, I found a few derivations that used too much physicist's math shortcuts that made it hard for me to follow.

This book has just the right mathematical rigor and detail to understand the derivations.
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0 von 8 Kunden fanden die folgende Rezension hilfreich
Von Aki
Format:Taschenbuch
This book would be good for some one who isn't serious about theoretical physics, and just want to see how Noether's theory is like. Otherwise, it is better to study other things that are far more important such as Lie algebra.
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Amazon.com: 4.0 von 5 Sternen  15 Rezensionen
136 von 140 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen A work of Art 27. Januar 2011
Von Charles W. Glover - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
I am a lifelong student of Physics. I have been a student long beforeI got my PhD in Physics. I am currently a Distinguished Scientist at a Government Lab. This is first review (and possibly the last) I've written for an Amazon book, but I felt compelled to write this after reading this book. It is an excellent example of a 'true' teacher at work who understands how to relate information. This is an art form.

In this book you will learn about Emmy Noether and her work in relating a huge class of conservation laws to nature's symmetries. The book explores how symmetry, invariance and conserved quantities are related, quantitatively. The first half of the book is written for self-study by an undergrad Physics student. It deals predominately with functionals (what are they), functional extremals, and when they are invariant. These chapters are the prelude to Noether's Theorem and Rund-Trautman's version of the theorem. This work first inquires whether a functional is invariant under a given transformation, and if it is, it uses Noether's theorem to get the associated conservation law. Next, it examines the inverse problem; given the transformation can you seek the Lagrangian whose functionals are invariant. In each section the author works examples in some detail and carries these examples with further detail in each of the following chapters. It's like a novel for physicists.

In the last half of the book, the author teaches you how Noether's theorem is used in quantum field theory. He describes the concept of a field through simple examples and introduces Lagrangian densities. Then Noether's theorem is developed for fields and, in particular, quantum fields. Armed with the machinery from the first half of the book and the knowledge of what fields are, the author addresses the question of given gauge invariance what does Noether's theorem tell us about the properties of the Lagrangian.

Like most first addition books, there a few typos in the book but they are easy to spot and do not detract from the beautiful presentation of these subjects.

I hope you enjoy this as much as I did.
45 von 48 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen long-needed celebration of the world's most important uncelebrated scientist delivers 26. Februar 2011
Von Gary - Veröffentlicht auf Amazon.com
Format:Gebundene Ausgabe
About half-way through, but I already appreciate the biographical information about Noether, and the overview and applications of her results to a variety of problems. The mathematical level is appropriate for upper level undergraduate physics majors and the discussion really helps place the results in context. Nice problems and thought-provoking comments at the end of each chapter. Could use more graphics, and perhaps a little more prose to address the formal mathematical subtleties, but overall, this book admirably fills the largest hole in that small bookshelf containing useful celebrations of deeply significant science and the scientists who created it.
34 von 36 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen Would like to like it better 5. Dezember 2011
Von Henning Dekant - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
This book addresses an important gap in the landscape of textbooks on theoretical mechanics. I strongly feel this is the way the subject should be approached as Noether's theorem has such far reaching implications beyond just classical mechanics.

Yet, there are annoying glitches. E.g. the oversight on p.28 with regards to the fundamental lemma of the calculus of variations as has been pointed out in a previous review.

On page 99 the equation (6.3.1) for the Hamiltonian density is incorrect. The way it is written the first term sums over all coordinate indexes. Correct would be to only have time i.e. index zero appear in the first term and sum over all field components if we deal with more than a simple scalar field.

Other times the authors just presents an equation without a modicum of information of how we got there. I.e. the alternative form of the Rund-Trautman identity (RTI II) is given on p.68. It's easy enough to see how the right side follows from RTI I when substituting the canonical variables and using the product rule, but how does the left side of RTI II come about? How does the Euler-Lagrange identity reappear there? (I attached a comment to this review if you are looking for the answer).

Still, I enjoy the book but I would have liked to like it even better.
7 von 7 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Very clear. 4. Dezember 2012
Von Alvaro Pastor - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
Neuenschwander's superb explanation of Lagrangian and Hamiltonian mechanics will lead you to the best introduction to Noether's theorem I have read.
This well written book is graspable by anyone with multivariate calculus knowledge.
75 von 103 Kunden fanden die folgende Rezension hilfreich
2.0 von 5 Sternen Neuenschwander's Wonderful Lemma 4. Juli 2011
Von A techno geek - Veröffentlicht auf Amazon.com
Format:Taschenbuch
O.k. help me with this. On p. 28 the author writes (sorry if the math code is hard to read here):

"Lemma (Fundamental Lemma of the Calculus of Variations):
If n(t) is not identically zero in \int_a^b A(t) n(t) dt = 0,
where n(a)=n(b)=0, and
if on the closed interval [a,b] both A(t) and n(t) are twice differentiable,
then A(t) = 0 throughout [a,b]."

This is obviously not true, as seen in the following counterexample:
Let n(t) = sin( 2 pi (t-a)/(b-a) ), and A(t) = 1.
So, n(t) satisfies the stated constraints, and \int_a^b A(t) n(t) dt = \int_a^b sin( 2 pi (t-a)/(b-a) ) dt = 0, yet A(t)=1 is most certainly not 0.

What in the world? Consultation of other author's expositions (e.g. Weinstock's Calculus of Variations or Gelfand and Fomin's Calculus of Variations) reveals that Neuenschwander left out the most crucial phrase in his version of the lemma: "If for EVERY choice of the continuously differentiable function n(t) ..."

How could he be so sloppy in something as fundamental as the Fundamental Lemma of the Calculus of Variations? (I am tempted to make a physicist joke here but I won't).

Once one encounters an error this egregious --- and only on p. 28 --- how can one trust that the author is a faithful guide to this new territory?

And now my mind starts to wonder about other things in the book. I recall the discomfort I felt back on p. 20:

"2.2 Formal Definition of a Functional. Definition: A functional J is a mapping from a set of functions to the real numbers. ... The mapping is given by J= \int_a^b L(t,x^\mu, x*^\mu) dt ."

Here again we find a sloppiness in scope. He gives a particular example of a functional but calls this the definition of a functional. Without reading other books, you would not realize that this is Neuenschwander's idiosyncratic usage, and might go away thinking that all functionals have this form.

Now I am going to wonder at every moment if the reason I don't understand something is because it is not true. Am I going to have to check the literature to verify everything he writes? That is not why I bought this book. Tell me why I shouldn't send it back. (I did send it back).
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