Annali Di Matematica Pura Ed Applicata 2Nd 3Rd Series
Total Page:16
File Type:pdf, Size:1020Kb

Load more
Recommended publications
-
HOMOTECIA Nº 6-15 Junio 2017
HOMOTECIA Nº 6 – Año 15 Martes, 1º de Junio de 2017 1 Entre las expectativas futuras que se tienen sobre un docente en formación, está el considerar como indicativo de que logrará realizarse como tal, cuando evidencia confianza en lo que hace, cuando cree en sí mismo y no deja que su tiempo transcurra sin pro pósitos y sin significado. Estos son los principios que deberán pautar el ejercicio de su magisterio si aspira tener éxito en su labor, lo cual mostrará mediante su afán por dar lo bueno dentro de sí, por hacer lo mejor posible, por comprometerse con el porvenir de quienes confiadamente pondrán en sus manos la misión de enseñarles. Pero la responsabilidad implícita en este proceso lo debería llevar a considerar seriamente algunos GIACINTO MORERA (1856 – 1907 ) aspectos. Obtener una acreditación para enseñar no es un pergamino para exhib ir con petulancia ante familiares y Nació el 18 de julio de 1856 en Novara, y murió el 8 de febrero de 1907, en Turín; amistades. En otras palabras, viviendo en el mundo educativo, es ambas localidades en Italia. asumir que se produjo un cambio significativo en la manera de Matemático que hizo contribuciones a la dinámica. participar en este: pasó de ser guiado para ahora guiar. No es que no necesite que se le orie nte como profesional de la docencia, esto es algo que sucederá obligatoriamente a nivel organizacional, Giacinto Morera , hijo de un acaudalado hombre de pero el hecho es que adquirirá una responsabilidad mucho mayor negocios, se graduó en ingeniería y matemáticas en la porque así como sus preceptores universitarios tuvieron el compromiso de formarlo y const ruirlo cultural y Universidad de Turín, Italia, habiendo asistido a los académicamente, él tendrá el mismo compromiso de hacerlo con cursos por Enrico D'Ovidio, Angelo Genocchi y sus discípulos, sea cual sea el nivel docente donde se desempeñe. -
Real Proofs of Complex Theorems (And Vice Versa)
REAL PROOFS OF COMPLEX THEOREMS (AND VICE VERSA) LAWRENCE ZALCMAN Introduction. It has become fashionable recently to argue that real and complex variables should be taught together as a unified curriculum in analysis. Now this is hardly a novel idea, as a quick perusal of Whittaker and Watson's Course of Modern Analysis or either Littlewood's or Titchmarsh's Theory of Functions (not to mention any number of cours d'analyse of the nineteenth or twentieth century) will indicate. And, while some persuasive arguments can be advanced in favor of this approach, it is by no means obvious that the advantages outweigh the disadvantages or, for that matter, that a unified treatment offers any substantial benefit to the student. What is obvious is that the two subjects do interact, and interact substantially, often in a surprising fashion. These points of tangency present an instructor the opportunity to pose (and answer) natural and important questions on basic material by applying real analysis to complex function theory, and vice versa. This article is devoted to several such applications. My own experience in teaching suggests that the subject matter discussed below is particularly well-suited for presentation in a year-long first graduate course in complex analysis. While most of this material is (perhaps by definition) well known to the experts, it is not, unfortunately, a part of the common culture of professional mathematicians. In fact, several of the examples arose in response to questions from friends and colleagues. The mathematics involved is too pretty to be the private preserve of specialists. -
Complex Analysis
8 Complex Representations of Functions “He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical.” Henry David Thoreau (1817-1862) 8.1 Complex Representations of Waves We have seen that we can determine the frequency content of a function f (t) defined on an interval [0, T] by looking for the Fourier coefficients in the Fourier series expansion ¥ a0 2pnt 2pnt f (t) = + ∑ an cos + bn sin . 2 n=1 T T The coefficients take forms like 2 Z T 2pnt an = f (t) cos dt. T 0 T However, trigonometric functions can be written in a complex exponen- tial form. Using Euler’s formula, which was obtained using the Maclaurin expansion of ex in Example A.36, eiq = cos q + i sin q, the complex conjugate is found by replacing i with −i to obtain e−iq = cos q − i sin q. Adding these expressions, we have 2 cos q = eiq + e−iq. Subtracting the exponentials leads to an expression for the sine function. Thus, we have the important result that sines and cosines can be written as complex exponentials: 286 partial differential equations eiq + e−iq cos q = , 2 eiq − e−iq sin q = .( 8.1) 2i So, we can write 2pnt 1 2pint − 2pint cos = (e T + e T ). -
4 Complex Analysis
4 Complex Analysis “He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. The fact which interests us most is the life of the naturalist. The purest science is still biographical.” Henry David Thoreau (1817 - 1862) We have seen that we can seek the frequency content of a signal f (t) defined on an interval [0, T] by looking for the the Fourier coefficients in the Fourier series expansion In this chapter we introduce complex numbers and complex functions. We a ¥ 2pnt 2pnt will later see that the rich structure of f (t) = 0 + a cos + b sin . 2 ∑ n T n T complex functions will lead to a deeper n=1 understanding of analysis, interesting techniques for computing integrals, and The coefficients can be written as integrals such as a natural way to express analog and dis- crete signals. 2 Z T 2pnt an = f (t) cos dt. T 0 T However, we have also seen that, using Euler’s Formula, trigonometric func- tions can be written in a complex exponential form, 2pnt e2pint/T + e−2pint/T cos = . T 2 We can use these ideas to rewrite the trigonometric Fourier series as a sum over complex exponentials in the form ¥ 2pint/T f (t) = ∑ cne , n=−¥ where the Fourier coefficients now take the form Z T −2pint/T cn = f (t)e dt. -
Sunti Delle Conferenze
Sunti delle Conferenze Analisi complessa a Pisa, 1860-1900 UMBERTO BOTTAZZINI (Università di Milano) Nel 1859 Enrico Betti inaugura gli studi di analisi complessa a Pisa (e di fatto in Italia) pubblicando la traduzione italiana della Inauguraldissertation (1851) di Riemann. L’incontro con il grande matematico conosciuto l’anno prima a Göttingen segna una svolta nella carriera scientifica di Betti, che fa dell’analisi complessa l’oggetto delle sue lezioni e delle sue pubblicazioni (1860/61 e 1862) che incontrano l’approvazione di Riemann, durante il suo soggiorno in Italia. Nella conferenza saranno discussi i contributi all’analisi complessa di Betti, Dini e Bianchi. Ulisse Dini raccolse l’eredità del maestro dapprima in articoli (1870/71, 1871/73, 1881) che suscitano l’interesse della comunità internazionale, e poi in lezioni litografate (1890) che hanno offerto a Luigi Bianchi il modello e il riferimento iniziale per le sue celebri lezioni sulla teoria delle funzioni di variabile complessa in due volumi, apparse prima in versione litografata (1898/99) e poi a stampa in diverse edizioni. Il periodo romano di Luigi Cremona: tra Statica Grafica e Geometria Algebrica, la Biblioteca Nazionale, i Lincei, il Senato ALDO BRIGAGLIA (Università di Palermo) Il periodo romano (1873 – 1903) è considerato il meno produttivo, dal punto di vista scientifico, della vita di Luigi Cremona. Un periodo quasi unicamente dedicato agli aspetti politico – istituzionali della sua attività. Senza voler capovolgere questo giudizio consolidato, anzi sottolineando -
Science and Fascism
Science and Fascism Scientific Research Under a Totalitarian Regime Michele Benzi Department of Mathematics and Computer Science Emory University Outline 1. Timeline 2. The ascent of Italian mathematics (1860-1920) 3. The Italian Jewish community 4. The other sciences (mostly Physics) 5. Enter Mussolini 6. The Oath 7. The Godfathers of Italian science in the Thirties 8. Day of infamy 9. Fascist rethoric in science: some samples 10. The effect of Nazism on German science 11. The aftermath: amnesty or amnesia? 12. Concluding remarks Timeline • 1861 Italy achieves independence and is unified under the Savoy monarchy. Venice joins the new Kingdom in 1866, Rome in 1870. • 1863 The Politecnico di Milano is founded by a mathe- matician, Francesco Brioschi. • 1871 The capital is moved from Florence to Rome. • 1880s Colonial period begins (Somalia, Eritrea, Lybia and Dodecanese). • 1908 IV International Congress of Mathematicians held in Rome, presided by Vito Volterra. Timeline (cont.) • 1913 Emigration reaches highest point (more than 872,000 leave Italy). About 75% of the Italian popu- lation is illiterate and employed in agriculture. • 1914 Benito Mussolini is expelled from Socialist Party. • 1915 May: Italy enters WWI on the side of the Entente against the Central Powers. More than 650,000 Italian soldiers are killed (1915-1918). Economy is devastated, peace treaty disappointing. • 1921 January: Italian Communist Party founded in Livorno by Antonio Gramsci and other former Socialists. November: National Fascist Party founded in Rome by Mussolini. Strikes and social unrest lead to political in- stability. Timeline (cont.) • 1922 October: March on Rome. Mussolini named Prime Minister by the King. -
Considerations Based on His Correspondence Rossana Tazzioli
New Perspectives on Beltrami’s Life and Work - Considerations Based on his Correspondence Rossana Tazzioli To cite this version: Rossana Tazzioli. New Perspectives on Beltrami’s Life and Work - Considerations Based on his Correspondence. Mathematicians in Bologna, 1861-1960, 2012, 10.1007/978-3-0348-0227-7_21. hal- 01436965 HAL Id: hal-01436965 https://hal.archives-ouvertes.fr/hal-01436965 Submitted on 22 Jan 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. New Perspectives on Beltrami’s Life and Work – Considerations based on his Correspondence Rossana Tazzioli U.F.R. de Math´ematiques, Laboratoire Paul Painlev´eU.M.R. CNRS 8524 Universit´ede Sciences et Technologie Lille 1 e-mail:rossana.tazzioliatuniv–lille1.fr Abstract Eugenio Beltrami was a prominent figure of 19th century Italian mathematics. He was also involved in the social, cultural and political events of his country. This paper aims at throwing fresh light on some aspects of Beltrami’s life and work by using his personal correspondence. Unfortunately, Beltrami’s Archive has never been found, and only letters by Beltrami - or in a few cases some drafts addressed to him - are available. -
Mathematik Für Physiker
Mathematik f¨urPhysiker III Michael Dreher Fachbereich f¨urMathematik und Statistik Universit¨atKonstanz Studienjahr 2012/13 2 Acknowledgements: These are the lecture notes to a third semester course on Mathematics for Physicists, and the author is indebted to Nicola Wurz, Maria Lindauer, Florian Franz, Philip Lindner, Simon Sch¨uz,Samuel Greiner, Christian Schoder, Pascal Gumbsheimer for remarks which helped to improve the presentation, and to the audience for appropriating this huge amount of knowledge. Some Legalese: This work is licensed under the Creative Commons Attribution { Noncommercial { No Derivative Works 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea{shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. Sir Isaac Newton (1642 { 1727) 1 1As quoted in [3]. 4 Contents I Ordinary Differential Equations7 1 Existence and Uniqueness Results9 1.1 An Introductory Example....................................9 1.2 General Considerations...................................... 12 1.3 The Theorem of Picard and Lindelof¨ ............................ 19 1.4 Comparison Principles...................................... 23 2 Special Solution Methods 25 2.1 Equations with Separable Variables............................... 25 2.2 Substitution and Homogeneous Differential Equations.................... 27 2.3 Power Series Expansions (Or How to Determine the Sound of a Drum).......... -
The First Period: 1888 - 1904
The first period: 1888 - 1904 The members of the editorial board: 1891: Henri Poincaré entered to belong to “direttivo” of Circolo. (In that way the Rendiconti is the first mathematical journal with an international editorial board: the Acta’s one was only inter scandinavian) 1894: Gösta Mittag-Leffler entered to belong to “direttivo” of Circolo . 1888: New Constitution Art. 2: [Il Circolo] potrà istituire concorsi a premi e farsi promotore di congress scientifici nelle varie città del regno. [Il Circolo] may establish prize competitions and become a promoter of scientific congress in different cities of the kingdom. Art 17: Editorial Board 20 members (five residents and 15 non residents) Art. 18: elections with a system that guarantees the secrety of the vote. 1888: New Editorial Board 5 from Palermo: Giuseppe and Michele Albeggiani; Francesco Caldarera; Michele Gebbia; Giovan Battista Guccia 3 from Pavia: Eugenio Beltrami; Eugenio Bertini; Felice Casorati; 3 from Pisa: Enrico Betti; Riccardo De Paolis; Vito Volterra 2 from Napoli: Giuseppe Battaglini; Pasquale Del Pezzo 2 from Milano: Francesco Brioschi; Giuseppe Jung 2 from Roma: Valentino Cerruti; Luigi Cremona 2 from Torino: Enrico D’Ovidio; Corrado Segre 1 from Bologna: Salvatore Pincherle A very well distributed arrangement of the best Italian mathematicians! The most important absence is that of the university of Padova: Giuseppe Veronese had joined the Circolo in 1888, Gregorio Ricci will never be a member of it Ulisse Dini and Luigi Bianchi in Pisa will join the Circolo respectively in 1900 and in 1893. The first and the second issue of the Rendiconti Some papers by Palermitan scholars and papers by Eugène Charles Catalan, Thomas Archer Hirst, Pieter Hendrik Schoute, Corrado Segre (first issue, 1887) and Enrico Betti, George Henri Halphen, Ernest de Jonquières, Camille Jordan, Giuseppe Peano, Henri Poincaré, Corrado Segre, Alexis Starkov, Vito Volterra (second issue, 1888). -
Testo Completo
Università degli Studi di Ferrara DOTTORATO DI RICERCA IN "MATEMATICA E INFORMATICA" CICLO XXVI COORDINATORE Prof. Mella Massimiliano L’INTERNAZIONALIZZAZIONE DEGLI STUDI MATEMATICI IN ITALIA A METÀ OTTOCENTO Settore Scientifico Disciplinare MAT / 04 Dottorando Tutore Dott. Nagliati Iolanda Prof. Borgato Maria Teresa ________________________ ___________________________ (firma) (firma) Anni 2011/2013 1 1 L’internazionalizzazione degli studi matematici in Italia a metà Ottocento Introduction p. 3 Introduzione 17 L’internazionalizzazione degli studi 21 I rapporti di Betti con studiosi stranieri: temi delle lettere Corrispondenti stranieri di Brioschi Corrispondenti stranieri di Tardy La situazione degli esuli: Mossotti da Corfù a Pisa 43 Il ritorno dall’esilio I primi anni dell’attività a Pisa e i rapporti con Betti Vicende politiche, organizzazione degli studi e della ricerca nella corrispondenza tra Brioschi e Tardy 59 L’organizzazione degli studi superiori Gli “Annali” Le equazioni algebriche di quinto grado 73 La teoria degli invarianti 81 Ricerche sui differenziali ad indice fratto 99 Le riviste scientifiche toscane nell’Ottocento 109 Documenti: Lettere di Giorgini a Mossotti 127 Lettere di Mossotti a Tardy 135 Lettere di Mossotti a Betti 139 Carteggio Brioschi-Tardy 191 Lettere a Betti di studiosi stranieri 285 Lettere a Tardy di studiosi stranieri 342 Lettere a Brioschi di studiosi stranieri 369 Bibliografia 371 1 2 Introduction The past few decades have seen several studies carried out by historians of mathematics on mathematics in the post unification period in Italy, further interest being recently stimulated by the celebration of 150 years since the Unification of Italy; this moment brought about a period of renewal of structures and infrastructures suitable for the new state, a sort of modernisation of the economy, which, at the same time, required a new institutional organisation on a national level for the scientific community, to carry on the work already started in the previous decades by single states, like Piedmont and the Grand Duchy of Tuscany. -
Writing the History of the Exact Sciences in Nineteenth-Century Rome
ORE Open Research Exeter TITLE For science and for the Pope-king: writing the history of the exact sciences in nineteenth-century Rome AUTHORS Mazzotti, Massimo JOURNAL The British Journal for the History of Science DEPOSITED IN ORE 01 August 2008 This version available at http://hdl.handle.net/10036/33812 COPYRIGHT AND REUSE Open Research Exeter makes this work available in accordance with publisher policies. A NOTE ON VERSIONS The version presented here may differ from the published version. If citing, you are advised to consult the published version for pagination, volume/issue and date of publication BJHS, 2000, 33, 257–282 For science and for the Pope-king: writing the history of the exact sciences in nineteenth-century Rome MASSIMO MAZZOTTI* Abstract. This paper analyses the contents and the style of the Bullettino di bibliografia e di storia delle scienze matematiche e fisiche (1868–1887), the first journal entirely devoted to the history of mathematics. It is argued that its innovative and controversial methodological approach cannot be properly understood without considering the cultural conditions in which the journal was conceived and realized. The style of the Bullettino was far from being the mere outcome of the eccentric personality of its editor, Prince Baldassarre Boncompagni. Rather, it reflected in many ways, at the level of historiography of science, the struggle of the official Roman Catholic culture against the growing secularization of knowledge and society. While history of mathematics was a well-established discipline by the mid-nineteenth century, no periodical which was entirely devoted to such a discipline existed until 1868. -
Maurizio Cornalba Attualit`Adi Eugenio Beltrami
Maurizio Cornalba Attualit`adi Eugenio Beltrami Cremona, 20 maggio 2000 M. Cornalba, Attualit`adi Eugenio Beltrami Cronologia essenziale - Nasce a Cremona il 16-11-1835 - 1853-1856: studia matematica presso l’Universit`adiPavia - 1856-59: interrotti gli studi universitari per ristrettezze eco- nomiche, `e segretario del direttore delle ferrovie del Lombardo-Veneto, a Verona - 1860: trasferitosi a Milano, riprende gli studi matematici - 1862: `e nominato professore straordinario a Bologna - 1864: si trasferisce presso l’Universit`a di Pisa - 1866: ritorna a Bologna - 1873: si trasferisce presso l’Universit`a di Roma - 1876: si trasferisce presso l’Universit`adiPavia - 1891: ritorna a Roma - 1898: diviene presidente dell’Accademia dei Lincei - 1899: `e nominato senatore - Muore a Roma il 18-2-1900 M. Cornalba, Attualit`a di Eugenio Beltrami Prima e dopo Beltrami Ebbero forte influenza sulla formazione matematica di Beltrami i matematici: - Francesco Brioschi (1824-1897, fondatore del Politecnico di Milano), suo professore a Pavia, ritrovato poi a Milano - Luigi Cremona (1830-1903), conosciuto a Pavia durante gli anni dell’universit`ae poi ritrovato a Milano e in seguito a Bologna - Enrico Betti (1823-1892), conosciuto a Pisa - Felice Casorati (1835-1890), suo coetaneo e compagno di studi a Pavia, e in seguito per lunghi anni suo collega presso l’Universit`adiPavia M. Cornalba, Attualit`adi Eugenio Beltrami Una forte influenza indiretta, sia attraverso Betti che attraverso gli scritti, ebbe anche Bernhard Riemann (1826-1866), cui princi- palmente si deve la svolta rivoluzionaria che ha portato al modo moderno di concepire la geometria. Beltrami fu uno dei primi continuatori, sia in Italia che fuori d’Ita- lia, dell’opera di Riemann nell’ambito della geometria differenziale.