Analyse Mathematique II/ Mathematical Analysis II : Calcul Différentiel Et Intégral, Séries De Fourier, Fonctions Holomorphes/ Differential and Integral Calculus, Fourier Series, Holomorphic Functions -Language: french
Language: French
Published by Springer, 2003
- Softcover
- Used

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- Title
- Analyse Mathematique II/ Mathematical Analysis II : Calcul Différentiel Et Intégral, Séries De Fourier, Fonctions Holomorphes/ Differential and Integral Calculus, Fourier Series, Holomorphic Functions -Language: french
- Author
- Godement, Roger
- Publisher
- Springer
- Publication year
- 2003
- Condition
- As New
- Binding
- Soft cover
- Language
- French
- ISBN 10
- 3540006559
- ISBN 13
- 9783540006558
"Synopsis" may belong to another edition of this title.
Review
Ce livre soumettra certains esprits rigides à la torture. Il est mathématiquement excellent, comme peuvent s’y attendre tous ceux qui savent quelque chose de l’auteur, grand mathématicien et merveilleux enseignant. On a là une des meilleurs façon d’apprendre l’analyse. Mais on a beaucoup plus, de l’histoire des concepts et des mathématiciens. Et encore davantage : une réflexion engagée sur notre époque, le tout enchainé de la manière la plus naturelle. Un exemple, page 84 nous examinons la convergence des séries, et en particulier la divergence de la série harmonique. L’auteur montre que certains procédés peuvent être utilisés abusivement, si l’on considère comme s’étendant aux sommes infinies les procédés justifiés quand il s’agit de sommes finies. Il montre (page 85&86) un grand nombre de tels «dérapages» réalisés par différents membres de la famille Bernoulli, et par Euler. De là, il passe à une petite présentation de la glorieuse famille Bernoulli et commence à expliquer les raisons des exigences de rigueur en mathématiques (page 87).
Enfin, s’addressant au citoyen, il l’invite à réfléchir sur les conséquences de telles exigences de rigueur (tout ce qui n’est pas intégralement démontré est potentiellement faux, etc.) si elles devaient avoir droit de cité en politique ! Il développe son propos en prenant l’exemple de la course aux armement (pages 88, 89, 90&91) puis il revient à Euler et aux opérations algébriques sur les limites (pages 94) après uns assez brève allusion au problème de la fraude scientifique. En dehors du fait que l’engagement de Roger Godement est au minimum très respectable, cette façon d’écrire possède un grand avantage pour tout un chacun : l’ouvrage y gagne en lisibilité. Les considérations didactiques, historiques et politiques reposent le lecteur des équations, et, sans doute, réciproquement.
J.-P. Boudine dans Quadrature no. 34, 1998
____________________
[...]Comment distinguer, dans la période la plus récente, les évolutions profondes des phénomènes de mode ? Comment analyser les articulations entre le savant, le téchnicien, l’industriel et le politique ? C’est à ce travail complexe que s’est consacré depuis vingt ans Roger Godement ; venu de la science «pure» (il a été membre du groupe Bourbaki), il a mis sa plume de polémiste et sa rigueur au service d’une analyse des développements des mathématiques appliquées, depuis les travaux de Von Neumann aux Etats-Unis, qui ont eu comme conséquences indirectes Hiroshima et Nagasaki, jusqu’á la création du CEA et du CNES en France et aux calculs scientifiques nécessaires à la mise au point de la bombe H française et aux divers projects spatiaux.
Ce postface historique à un cours d’Analyse mathématique classique, fruit d’une longue expérience d’enseignant d’université, constitue un document unique qui stimule la réflexion sur les rapports entre les scientifique et le politique, mais fait déjà œuvre d’histoire des sciences, car l’époque actuellle – depuis la fin de la guerre froide est marquée à la fois par la fusion de la «Big Science» et l’industrie (Génome), et la disparition des projets à caractère militaire (guerre des étoiles). Ce seront sans doute de plus en plus des banquier qui remplaceront les militaires pour tirer les ficelles de la politique de la science. Un progrès ?
Jean-Michel Kantor 1998
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