Product Description
This graduate-level, self-contained text addresses the basic and characteristic properties of linear differential operators, examining ideas and concepts and their interrelations rather than mere manipulation of formulae. Written at an advanced level, the text requires no specific knowledge beyond the usual introductory courses, and some 350 problems and their solutions are included. Preface. Bibliography. Appendix. Index.
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Customer Reviews (5)

Master Piece
As the other reviewers have said, this is a master piece for various reasons. Lanczos is famous for his work on linear operators (and efficient algorithms to find a subset of eigenvalues). Moreover,he has an "atomistic" (his words)view of differential equations, very close to the founding father's one (Euler, Lagrange,...).

A modern book on linear operators begins with the abstract concept of function space as a vector space, of scalar product asintegrals,... The approach is powerful but somehow we loose our good intuition about differential operators.

Lanczos begins with the simplest of differential equations and use a discretization scheme (very natural to anybody who has used a computer to solve differential equations) to show how a differential equation transforms into a system a linear algebraic equation. It is then obvious that this system is undetermined and has to be supplemented by enough boundary condition to be solvable. From here, during the third chapters, Lanczos develops the concept of linear systems and general (n x m) matrices, the case of over and under determination, the compatibility conditions, ...
It is only after these discussions that he returns (chapter 4) to the function space and develops the operator approach and the role of boundary conditions in over and under-determination of solutions and the place of the adjoint operators. The remaining of the book develops these concepts : chp5 is devoted to Green's function and hermitian problems, chap7 to Sturm-Liouville,... The last chapter is devoted to numerical techniques, amazing if one think that the book was written at the verybeginning of computers, which is a gem by itself.

Lanczos again
Somebody writen:
"Some mathematics and physics writers stand head and shoulders above the rest. Goldstein...Liboff...Morrison...Morse and Feshbach...and Lanczos. A joy to read, if you are both mathematically and verbally inclined."

I think some mathematics and physics writers stand head and shoulders above even Goldstein...Liboff...Morrison...Morse and Feshbach. It is the case of Lanczos and Dirac.

wonderful book, elegantly written
This book has material I've found in no other book. Lanczos is a pleasure to read -- his writing is clear, elegant, and entertainingly opinionated. I've liked every book of his that I've read.

A must!
A very intuitive (geometrical) exposition of matrix calculus, adjoint problems, bilinear identity and Green's function (and more). If you really want to understand these concepts, read this masterpiece!

A joy to read.
Some mathematics and physics writers stand head and shoulders above the rest.Goldstein...Liboff...Morrison...Morse and Feshbach...and Lanczos.A joy to read, if you are both mathematically and verbally inclined. ... Read more

Product Description
Philosophic, less formalistic approach to perennially important field of analytical mechanics. Model of clear scholarly exposition at graduate level with coverage of basic concepts, calculus of variations, principle of virtual work, equations of motion, relativistic mechanics, much more. First inexpensive paperbound edition. Index. Bibliography.
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Customer Reviews (15)

Clear and affordable introduction to variational principles
I am not a mathematician or physicist and my background on these subjects is rather basic, but I have an strong interest and since some years ago have been studying them from books like this. Although this book is probably very dated, I can only say that I learned a lot from it, that is clearly and pedagogically written and, last but not least, it is has the right price!

A pedagogical introduction into analytical mechanics
Before reading this book, I knew almost nothing about analytical mechanics. My first text books taught Physics from a Newtonian approach, using mostly vectors and potentials. So, the first time I encountered Lagrangians and Hamiltonians I could not understand what these concepts meant. Because of that many areas of Theoretical Physics were forbidden for me: Phase and configuration space, Noether's theorem, Hilbert relativistic equations, Feynman quantum-mechanical interpretation of the principle of least action, and so on.

So, two years ago, I decided to buy this book. And what I encountered? A systematical and pedagogical approach to analytical mechanics, which enabled me to acquire the fundamentals of the subject.

For me, the most interesting features of this book are the following:

1) It explains the differences between VARIATION and DIFFERENTIATION, something that most books in the subject, leave behind.
2) It explains clearly D'Alembert Principle and the Principle of Virtual Work.
3) From those principles he derives the Principle of Least Action, using just elemental calculus.
4) He introduces the reader in Legendre's transformation and the relations between the two fundamental quantities of Analytical mechanics: Lagrangian and Hamiltonian.
5) You get the equations of movement corresponding to those quantities: Euler-Lagrange (Lagrangian) and canonical (Hamiltonian) equations.
6) A powerful insight in Configuration and Phase Spaces is given, including the wonderful Liouville's theorem.
7) Lanczos shows the analogies between Optics and Mechanics when he explains the Hamilton-Jabobi equations.

So, why to learn Analytical Mechanics and why to buy this book?? These are my reasons:

1) From a historical point of view, Analytical Mechanics was developed by Continental Mathematicians like Maupertuis, Euler, D'Alembert and Lagrange as a rival system to the Newtonian one exposed in the Principia Mathematica. Newton used vectors and potentials. Euler and Lagrange employed the Principle of Least Action.
2) It was Analytical Mechanics the first to develop the principle of energy conservation. Even when this principle in its general form was developed by Wilhelm von Helmholtz in 1847, the conservation of the sum of kinetic and potential energy was well known to Euler a century earlier.
3) The concept of phase space is very important in Thermodynamics. In fact, the definition of entropy given by Ludwig Boltzmann refers to the logarithm of a volume in phase space. Liouville theorem, which states the conservation of such phase space volumes, is very usefull today in black hole thermodynamics.
4) The quantum-mechanical interpretation of the Principle of Least Action given by Richard Feynmann was a fundamental contribution in the development of Quantum Field Theory, so any student who desires to progress in this field, must have substantial knowledge of Analytical Mechanics.

So, to all of you that eventually decide to buy this book, I wish you a good reading.

Best book EVER!!!!
The most lucid and pedagogical presentation concerning the calculus of variations applied in mechanics. The developments are put in a historical context and the intrinsic connections with Riemannian geometry are explained. Simply, a must-have for everyone interested in really understanding the principles of mechanics.

a lot of unfamiliar variational tricks, sometimes lacks proofs or underexplains
I've read this gem and done most of the evercises in about 3 months. Before that legendary book I'd had the usual crappy course in Classical Mechanics based on Goldstein. The bottom line is the book will show you a lot of advanced material and unfamiliar manipulations. On the other hand there are sometimes statements lacking proof or more detailed lucid explanation. The book is appropriate for readers that already know what action is, totall beginners will be too shocked by the new concepts and won't be able to pick up the important nuances revealed by Lanczos.

Lanczos work clarified some of the concepts in which my CM course failed:
- the important difference in treating holonomic and nonholonomic constraints
- exact constraints are mathematical idealization of infinitely rigid constraint forces
- Lagrange multipliers for functionals (actions) not only functions
- the logical thread virtual work -> d'Alembert -> Hamilton's principle
- the connection between the action in configuration space andin phase space

The book introduced me to topics not covered by the course, which was my initial goal:
- elimination of ignorable variables in L or H formulation
- canonical transformations, definition and importance
- generating function of canonical transformation
- test for canonicity of transformation using Poisson brackets
- integral invariants of canonical transformations
- Hamilton's principal function
- Hamilton-Jackobi equation and analogy with optical wave surfaces
- separation of variables in H-J equation
- action-angle variables for separable periodic systems
- evolution of the system as a sequence of canonical transformation
- introducing geometry and geodesics in phase space

The reading definitely increased my freedom in manipulating the variational problem into equivalent variational problem. Examples of the two most weird for me manipulations are in the appendices. In the first appendix the Hamiltonian formulation is derived from the Lagrangian by introducing new variables, constraints and corresponding Lagrange multipliers, and then eliminating the variables. In appendix II, the most popular cases of Noether's theorem are derived by introducing new field variables in the action - I had no idea that was allowed. Very interesting was the idea that the world line of the system in configuration space can be parametrized with arbitrary parameter and the time becomes a function of that parameter that is varied together with the other generalized coordinates. Such variation is normal for GR but I've never seen it done in non-relativistic mechanics. EDIT: Sept 2008. Recently I've found a textbook that clearly explains some of the fuzzy examples in Lanczos like varying the time: "Analytical Mechanics for Relativity and Quantum Mechanics" by Oliver Johns.

Some of the other reviews described the book as 'lucid'. I find that eggagerated - although the book shows lots of unfamiliar manipulations, sometimes proofs of validity or the necessary more detailed conceptual or calculational explanations are lacking. An example is the inclusion, all of a sudden, of the time as variable to be varied - where is the proof one is allowed to do that? In another case, the book tells you that by nullifying the boundary term when varying the action, one gets 'natural' boundary conditions for the Euler-Lagrange diff. equations. I failed to see how the physics of the problem would demand exactly those boundary conditions. Where the analogy between mechanics and optics was discussed, the book creates the impression it derived the Fermat's principle but in reality it simply proved that the path following the gradient of of constant surfaces is shortest between two points. So there is a certain gegree of fuzziness on calculational level (lacking proofs of validity) or conceptual level (underexplained concepts and relations).

I liked the the abundance of historical notes. You will learn that there are several formulations of the least action principle - Euler and Lagrange version, Jackobi version and Hamilton version. Each subsection has a small summary and there are a few problems per section to illustrate the main ideas but not enough for exercises.

There are two chapters that I think appeared in later editions and are too sketchy compared to the book core:

Chapter 9 discusses special relativity where you can see that guessing the relativistic Lagrangian on general grounds of Lorentz invariance gives almost effortlessly the relativistic dynamics without the usual gedanken experiments. At the end, Lanczos dives a little into GR using the Schwartzchild metric to derive orbits, bending of light rays and gravitational redshift around spherical body.

Chapter 11 gives a short presentation of fluid mechanics (a little unclear derivation, in Lagrange and Euler coordinates), elasticity, and electromagnetism. Noether's principle is used to derive the canonical and the symmetric energy momentum tensor. I haven't seen a crystal clear derivation of Noether anywhere and Lancsoz is not an exception. The problem is as usual ommiting what exactly is being transformed and why is that allowed.

Timeless classic, masterful ...
If you ask 10 PhD scientists: "Why is Schrodinger's Equation complex?" (contains the square-root of minus one), 9 out of 10 won't be able to give you the correct answer.

It has little to do with taking the root of negative numbers. After reading Lanczos you will know it has do with "space" and what is a proper physical law. (Now you have to read the book to parse this sentence. Good.)

This is one of many wonderful insights Lanczos provides; with humor, wonder and crystal clarity. This is not a 'text book' on mechanics, you will get more out of it if you are familiar with the subject. He gives you understanding, not technique.

It is as if you can hum a few tunes. Reading Lanczos is experiencing the entire opera for the first time. Now you know the full story, how each aria is a part of the fabric; how each fits in the situation, the motivation behind it. The tunes you liked become richer, more profound, they are connected. The next time you sing you fancy you are a Caruso, a Puccini.

It is so rare to encounter a master who is also a gifted writer.

Some reviewers compare Lanczos to Feynman's Lectures, I agree partly.Lanczos is more literate and much more humble. Feynman is so busy being the genius from Brooklyn that his exposition is choppy and uneven.Lanczos is a better organizer and writer.




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Product Description
Basic text for graduate and advanced undergraduate deals with search for roots of algebraic equations encountered in vibration and flutter problems and in those of static and dynamic stability. Other topics devoted to matrices and eigenvalue problems, large-scale linear systems, harmonic analysis and data analysis, more.
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Customer Reviews (6)

An interesting if some what dated book
Applied Analysis, by Cornelius Lanczos is, in the author's words in the Preface, that branch of analysis devoted to the analysis of finite algorithms, or "workable mathematics". Today it would be called numerical analysis.

Written in 1956,foloowing assignments with then North american Aviation and the Boeing Airplane Company, the book is a compendium of compuational techniques for the solution of cubic, quartic and higher order algebraic equations, matrices and eigenvalue problems, large scale linear systems, harmonic analyis.An entire chapter of 65 pages is devoted to data analysis, the problems associates with processing large amounts of data, and some of the hidden dangers of straightforward(equidistant) interpolation. A chapter is devoted to quadrature methods, and the book concludes with a chapter on power expansions.

Most of the computational methods are devoted to hand calculation, or electro mechanical calculation. Today, algorithms developed specifically for high speed digital processors make most of these methods obsolete.

I bought the book because of an interest in Legendre polynomials, and their use in fitting to data. However, fascinating tidbits (at least to me) pop up unexpectedly. One tidbit that caught my eye was in the chapter on Data Analysis(Chapter V) in which the Sturm-Liouville equation suddenly appears, is solved by an application of Green's identity, and hence the result is a proof of the orthoganility of a class of equations (Legendre's being just one of several) in just two steps. Perhaps I missed something when I studied Series and Special Functions, but I've not seen this anywhere else.

A very pleasant characteristic of the book is the almost seamless movement back and forth between theory and computationl application. On the other hand, be prepared to spend time with a pencil and paper following not only the derivations and proofs, but the computational algorithms. For someone doing, or planning to do, a massive amount of number crunching of large collections of physical date, this is probably a good book to have.

Master of Exposition
It's an excellent book.The best parts for
we were the chapters on Matrices and on
Harmonic Analysis. An outstanding aspect
of the latter chapter is Lanczos's exposition
of the motivation behind the Fourier integral
(transform) and its basic theory.The quality
of the writing is superb, very classical
and lucid.

It cannot, of course, serve as a textbook.
But if you're taking a Fourier theory
course using Stein and Shakarchi's book, say,
as I am currently, then it's a very handy
book that can complement abstract theory
with physical intuition.

very fine but could be more advanced
Lanczos' work is a fine, thorough text that covers most areas of advanced analysis in a readable style. His derivations are clear, his tangential explorations are absorbing, and he cites practical examples. The one area in which I find the book weak is harmonic functions, potential theory, and the applications of these to the calculus of resides. Consequently, the book is not "one-shop stopping" for all the mathematical techniques that an electrical engineer or physicist might require in his bag of tricks....

If you don't want just recipes...
Then this is the best book. Well, Hamming's is also so good! For Fourier analysis, and the taming of the Gibbs phenomenon, go straight to Lanczos. He knew it all, and was one of the inventorsof the fast Fourier transform. This book is in the class of Sommerfeld's "Partial Differential Equations of Physics" and Lighthill's "Fourier Analysis and Generalizaed Functions". This is a very high compliment. Did you know hewas also a first rate physicist, and a pioneer of quantum mechanics?

Simply the best book on numerical analysis
My dissertation advisor introduced me to this book over thirty years ago.I have since read it in its entirety twice and it is still the first book I consult when confronted with a new mathematical problem.

Lanczos'sunderstanding of applied mathematics is very deep and he has a rare way ofexplaining things clearly yet concisely.I find his description of linearsystems in terms of multidimensional coordinate systems, both orthogonaland skewed, to be the best anywhere.Also, his understanding andexplanation of harmonic analysis (he invented the FFT after all) is worththe price of the book by itself.

Buy it, read it (at least once) then seeif really need any other book on applied mathematics. ... Read more

Product Description
Kapitel: Cornelius Lanczos, Gene H. Golub, Friedrich Ludwig Bauer, George Dantzig, Eduard Stiefel, Hans Georg Bock, Roland Bulirsch, Richard Von Mises, Peter Lax, Lewis Fry Richardson, Stanley Osher, James H. Wilkinson, Tassilo Küpper, Ulrich Trottenberg, James Sethian, Olgierd Cecil Zienkiewicz, Heinz Rutishauser, Karl Hessenberg, Volker Strassen, Ivo Babuška, Leonid Witaljewitsch Kantorowitsch, Peter Henrici, Wolfgang Hackbusch, Germund Dahlquist, Ingrid Daubechies, Leonid Gendrichowitsch Chatschijan, Martin Hermann, Arnold Schönhage, Peter Deuflhard, Alfred Louis, Alston Scott Householder, Peter Shor, Nikolai Mitrofanowitsch Krylow, Wolfgang Dahmen, Sergei Konstantinowitsch Godunow, Hermann Heine Goldstine, Götz Alefeld, Walter Gautschi, Ramon E. Moore, Carl Adam Petri, Martin Wilhelm Kutta, Narendra Karmarkar, Uwe Zimmermann, Rudolf Zurmühl, Karl Zeller, Franco Brezzi, Manil Suri, Klaus Glashoff, Wallace Givens, William Kahan, Boris Grigorjewitsch Galjorkin, André-Louis Cholesky, Theodore Hill, John C. Butcher, Douglas Rayner Hartree, Isaac Jacob Schoenberg, Lester Randolph Ford Junior, Werner Romberg, Rupert Klein. Aus Wikipedia. Nicht dargestellt. Auszug: Lewis Fry Richardson, FRS (11 October 1881 - 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work on fractals and a method for solving a system of linear equations known as modified Richardson iteration. Lewis Fry Richardson was the youngest of seven children born to Catherine Fry (1838-1919) and David Richardson (1835-1913). They were a prosperous Quaker family, David Richardson running a successful tanning and leather manufacturing business. At age 12 he was sent to a Quaker boarding school, Bootham in York, where h...http://booksllc.net/?l=de ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Edward Teller, Theodore Von Kármán, Dennis Gabor, Leó Szilárd, Cornelius Lanczos, Nicholas Kurti, Roland Eötvös, Tivadar Puskás, Zoltán Lajos Bay, David Gruby. Non illustré. Mises à jour gratuites en ligne. Extrait : Edward (Ede) Teller (né le 15 janvier 1908 à Budapest et décédé le 9 septembre 2003 à Stanford) est un physicien nucléaire hongro-américain. Il est connu proverbialement comme le père de la bombe à hydrogène et un fervent défenseur de cette arme, à l'encontre de plusieurs scientifiques ayant travaillé avec lui sur le Projet Manhattan (notamment Robert Oppenheimer). Cela entraîna une profonde rupture entre lui et le flanc gauche, "pacifiste", du monde scientifique, à tel point qu'Isidor Isaac Rabi déclare : . Edward Teller avant de quitter l'Autriche-Hongrie pour l'AllemagneEdward Teller nait dans une famille juive à Budapest, alors en Autriche-Hongrie. Il quitte en 1926 son pays pour l'Allemagne (en partie à cause du Numerus clausus institué par Miklós Horthy, limitant le nombre de juifs pouvant être admis à l'Université) et y suivre un cursus de chimie à l'Université de Karlsruhe, où il obtient un diplôme en ingénierie chimique. Il se prend d'intérêt pour la physique et entre à l'Université de Leipzig en 1928 pour suivre cette nouvelle voie. À Munich, il a un accident de voiture qui blesse gravement une de ses jambes et le voit contraint de se faire amputer de son pied, qui est remplacé par une prothèse (ce qui le fait boiter toute sa vie). Il obtient son doctorat en physique en 1930, sous la direction de Werner Heisenberg. Cette même année il se lie d'amitié avec deux jeunes scientifiques russes, George Gamow et Lev Landau, alors en visite en Europe de l'Ouest. Il passe deux ans à l'Université de Götting...http://booksllc.net/?l=fr ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : Krisztián Palkovics, Péter Czvitkovics, Viktor Orbán, Ignaz Goldziher, Cornelius Lanczos, Lajos Kü, Nándor Fa, Katarina Ivanović. Non illustré. Mises à jour gratuites en ligne. Extrait : Krisztián Palkovics (né le 10 juillet 1975 à Székesfehérvár en Hongrie) est un joueur professionnel de hockey sur glace hongrois. Depuis 1993, il joue dans le club d'Alba Volán Székesfehérvár, dans le Championnat de Hongrie de hockey sur glace. En 2007, son équipe intègre l'EBEL, l'élite autrichienne. Depuis le début de sa carrière, il formait un duo prolifique avec le centre Gábor Ocskay. Le 25 mars 2009, ce meilleur coéquipier décède d'une crise cardiaque. Quelques jours après avoir décroché un neuvième titre national avec Volan. Depuis 1993, il représente l'équipe de Hongrie de hockey sur glace. Il a participé à 15 championnats du monde. En 2008, il est l'un des artisans de la montée de la Hongrie en élite pour l'édition 2009. Quelques semaines avant l'échéance, son coéquipier en club et en sélection Gábor Ocskay décède d'une crise cardiaque. La Hongrie joue en sa mémoire mais elle termine seizième et dernière. Au cours de la compétition, l'entraîneur Pat Cortina associe Szélig à János Vas et Dániel Fekete. Elle est reléguée en division 1. Borsodi Liga EBEL Championnat du monde junior de hockey sur glace Championnat du monde de hockey sur glace Pour les significations des abréviations, voir Statistiques du hockey sur glace. ...http://booksllc.net/?l=fr ... Read more

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Les achats comprennent une adhésion à l'essai gratuite au club de livres de l'éditeur, dans lequel vous pouvez choisir parmi plus d'un million d'ouvrages, sans frais. Le livre consiste d'articles Wikipedia sur : John Von Neumann, János Bolyai, Paul Erdős, Abraham Wald, Béla Bollobás, András Sárközy, Cornelius Lanczos, Paul Halmos, George Pólya, Raoul Bott, Miklós Laczkovich, László Lovász, Marcel Grossmann, Frigyes Riesz, Lipót Fejér, Rózsa Péter, Peter Lax, Alfréd Rényi, Julius König, Endre Szemerédi, Farkas Bolyai, Dénes Kőnig, Éva Tardos, Sándor Csörgő, Alfréd Haar, Mario Szegedy. Non illustré. Mises à jour gratuites en ligne. Extrait : John von Neumann (né Neumann János, 1903-1957), mathématicien et physicien américain d'origine hongroise, a apporté d'importantes contributions tant en mécanique quantique, qu'en analyse fonctionnelle, en théorie des ensembles, en informatique, en sciences économiques ainsi que dans beaucoup d'autres domaines des mathématiques et de la physique. Il a de plus participé aux programmes militaires américains. Benjamin d'une fratrie de trois, il s'appelle tout d'abord Neumann János Lajos (les Hongrois placent les noms de famille en tête) à Budapest en Autriche-Hongrie. Il est le fils de Neumann Miksa (Max Neumann), un avocat-banquier, et de Kann Margit (Marguerite Kann). Il ne prête guère attention à ses origines juives, sinon pour son répertoire de blagues. János est un enfant prodige : à six ans, il converse avec son père en grec ancien et peut mentalement faire la division d'un nombre à huit chiffres. Une anecdote rapporte qu'à huit ans, il a déjà lu les quarante-quatre volumes de l'histoire universelle de la bibliothèque familiale et qu'il les a entièrement mémorisés : doté d'une mémoire eidétique, il sera capable de citer de mémoire des pages entières de livres lus des années auparavant. Il entre au lycée luthérien de Budapest (Budapesti Evangélikus Gimnázium) qui était germanophone en 1911. E...http://booksllc.net/?l=fr ... Read more

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Der Erwerb des Buches enthält gleichzeitig die kostenlose Mitgliedschaft im Buchklub des Verlags zum Ausprobieren - dort können Sie von über einer Million Bücher ohne weitere Kosten auswählen. Das Buch besteht aus Wikipedia-Artikeln: Don Zagier, Cornelius Lanczos, Shiing-Shen Chern, Barry Mazur, Mark Kac, Günter M. Ziegler, Andrew Granville, Heinz Bauer, Martin Davis, Shreeram Abhyankar, Joan Birman, Norman Levinson, Leon Henkin, Gilbert Ames Bliss, John Stillwell, Thomas W. Hawkins, Philip Davis, Neil Sloane, W. B. R. Lickorish, Jonathan Borwein, François Treves, Carl Pomerance, Guido Weiss, Michael Rosen, Gordon Thomas Whyburn, Dunham Jackson, Reuben Hersh, David Harold Bailey, Richard Bruck,. Online finden Sie die kostenlose Aktualisierung der Bücher. Nicht dargestellt. Auszug: Don Bernhard Zagier (* 29. Juni 1951 in Heidelberg) ist ein amerikanischer Mathematiker. Derzeit ist er einer der Direktoren des Max-Planck-Instituts für Mathematik in Bonn und Professor am französischen Collège de France in Paris. Seine Hauptarbeitsgebiete sind Zahlentheorie, Theorie der Modulformen und Verbindungen zur Topologie. Zagier ist 1951 in Heidelberg als Sohn amerikanischer Eltern geboren und in den USA aufgewachsen. Er bestand im Alter von 13 Jahren sein Abitur. Er studierte am MIT Mathematik und Physik und wurde 1967 - im Alter von 16 Jahren - Putnam Fellow (im Jahr zuvor gewann er den ersten Preis in der Mathematik-Olympiade). 1968 erhielt er den B.A., ging dann an die Oxford University und an die Universität Bonn, wo er bei Friedrich Hirzebruch mit 19 promovierte (offiziell in Oxford). Nach zweijährigem Aufenthalt an der ETH Zürich und am IHES in Bures-sur-Yvette bei Paris kam er 1974 nach Bonn, habilitierte sich 1975 und wurde 1976 Deutschlands jüngster Professor. 1984 wurde er als Wissenschaftliches Mitglied der Max-Planck-Gesellschaft an das Max-Planck-Institut für Mathematik in Bonn berufen, wo er 1995 zum Direktor ernannt wurde. ...http://booksllc.net/?l=de&id=1263139 ... Read more

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Chapters: Cornelius Lanczos, Péter Czvitkovics, Attila Kuttor, József Magasföldi, Lajos Nagy, Marcell Fodor, Dávid Mohl, Norbert Lattenstein, Dániel Köntös. Source: Wikipedia. Pages: 28. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Cornelius Lanczos (Hungarian: , Hungarian pronunciation: ), born (til 1906) Löwy (Lwy) Kornél (February 2, 1893 June 25, 1974) was a Hungarian mathematician and physicist. He was born at Székesfehérvár, as a son of Karl Löwy (Lwy Károly) and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory. In 1924 he discovered an exact solution of the Einstein field equation which represents a cylindrically symmetric rigidly rotating configuration of dust particles. This was later rediscovered by Willem Jacob van Stockum and is known today as the van Stockum dust. It is one of the simplest known exact solutions in general relativity and regarded as an important example, in part because it exhibits closed timelike curves. Lanczos served as assistant to Albert Einstein during the period 192829. He did pioneering work along with G.C. Danielson on what is now called the fast Fourier transform (1940), but the significance of his discovery was not appreciated at the time and today the FFT is credited to Cooley and Tukey (1965). (As a matter of fact, similar claims can be made for several other mathematicians; some even name Carl Friedrich Gauss as a progenitor of the FFT.) Working in Los Angeles at the U.S. National Bureau of Standards after 1949 Lanczos developed a number of techniques for mathematical calculations using digital computers, including: In 1962, Lanczos showed that the Weyl tensor, which plays a fundamental role in general relativity, can be obtained from a tensor potential which is now called the Lanczos potential. Lanczos resampling is based on a...More: http://booksllc.net/?id=1657748 ... Read more