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CultureMATH
ENSup. et Minist. EN

OE
I S

Encyclopédie des suites d'entiers

Séminaire MaMuX
Mathématiques, musique et relations avec d'autres disciplines

IHÉS

Institut des Hautes Études Scientifiques

L'INVERSEUR
de Plouffe

DÃ©rivÃ©es DiffÃ©rentielles Ãquations - Derivatives

PAGES WEB

La dÃ©rivation d'ordre non entier

Les DiffÃ©rentielles mÃ©taphysiques. StÃ©phane Dugowson.

Histoire et philosophie de la gÃ©nÃ©ralisation de l'ordre de dÃ©rivation

Principe (Diverses dÃ©finitions). Histoire. Applications. RÃ©fÃ©rences bibliographiques.

<http://s.dugowson.free.fr/recherche/dones/index.html>

SystÃ¨mes Ã dÃ©rivÃ©es non entiÃ¨res

LAP : Laboratoire d'Automatique, Productique, Signal et Image.

<http://www.lap.u-bordeaux.fr/OS/automatique/crone/crone2.html>

MATHÉMATIQUES - MATHEMATICS

Ordinary Differential Equations

The computer exercises in this section are based on MAPLE and are for a one semester course in differential equations at the sophomore level. For this course, we use the book: Elementary Differential Equations and Boundary Value Problems by Boyce and DiPrima (fifth edition).

html version

<http://www.math.udel.edu:80/teaching/course_materials/M302/monk/index.html>

DEMOS

Ordinary Differential Equations

Visual differential equation solver.

<http://www.falstad.com/diffeq/>

EXEMPLES - EXAMPLES

The Antikythera Mechanism II

With Java animations by Bill Casselman

<http://www.ams.org/new-in-math/cover/diff4.html>

The Antikythera Mechanism

One of the most important and interesting pieces of ancient technology, used possibly as an astronomical and calendar calculator. Mechanically, it is a most complex mechanism incorporating 32 gear-wheels as well as inscriptions related to the zodiac and the months. Discovered in 1900-1901 by sponge-divers from Syme in an ancient shipwreck near the island of Antikythera. Dated to ca 80 A.D. Inv. X 15087.

<http://www.culture.gr/2/21/214/21405m/00/lm05m04c.jpg>

The Differential Geometry of the Sphericon

<http://www.ams.org/new-in-math/cover/sphericon1.html>

The Antikythera Mechanism I

With Java animations by Bill Casselman

<http://www.ams.org/new-in-math/cover/kyth1.html>

APPLICATIONS

Commande robuste d'ordre non entier

(dÃ©rivation d'ordre non entier)

La commande CRONE a Ã©tÃ© implantÃ©e sur de nombreux systÃ¨mes rÃ©els. L'application la plus spectaculaire concerne les suspensions actives de vÃ©hicules automobiles.

<http://serv.spi.cnrs-dir.fr/100/technolo/crone.htm>

LOGICIELS - SOFTWARES

Netlib Ode

<http://www.netlib.org/ode/index.html>

Netlib Search

<http://www.netlib.org/cgi-bin/search.pl>

Software

This is a list of public domain and commercial mesh generators (click here for other sources of interest). I have listened only programs for which online information exists. There is also a section on papers that review mesh generators.

<http://www-users.informatik.rwth-aachen.de/~roberts/software.html#public_domain>

SOURCES

Free C/C++ Sources for Numerical Computation

a collection of pointers

<http://cliodhna.cop.uop.edu/~hetrick/c-sources.html>

C C++ code

ADOL-C: A Package for the Automatic Differentiation

of Algorithms Written in C/C++.

PAPERS - contains the ADOL-C documentation and short reference and some older ADOL-C related publications

<ftp://info.mcs.anl.gov/pub/ADOLC/>

DOCUMENTS - PAPERS

How to Differentiate a Number

Victor Ufnarovski and Bo Ãhlander

We define the derivative of an integer to be the map sending every prime to 1 and satisfying the Leibnitz rule. The aim of the article is to consider the basic properties of this map and to show how to generalize the notion to the case of rational and arbitrary real numbers. We make some conjectures and find some connections with Goldbach's Conjecture and the Twin Prime Conjecture. Finally, we solve the easiest associated differential equations and calculate the generating function.

the home page for the electronic Journal of Integer Sequences

<http://www.math.uwaterloo.ca/JIS/VOL6/Ufnarovski/ufnarovski.pdf>

JOURNAUX - LETTERS

E J D E

Electronic journal of differential equations

Since its foundation in 1993, this e-journal has been dedicated to the rapid dissemination of high quality research in mathematics. All topics related to differential equations and their applications (ODE's, PDE's, integral equations, functional differential equations, etc.) can be submitted for publication.

Monographs, Problems, Proceedings of Conferences

<http://ejde.math.txstate.edu/index.html>

COURS - COURSES

MÃ©thodes NumÃ©riques pour les Ãquations aux DÃ©rivÃ©es Partielles___Olivier Pironneau

<ftp://ftp.ann.jussieu.fr/pub/soft/pironneau/coursWebFR.pdf>

<http://www.math.unicaen.fr/~cougnard/polys/Geodif.pdf>

Georges Koepfler U. Paris V

<http://www.math-info.univ-paris5.fr/~gk/papers/cours_edp.pdf>

<http://www.univ-bpclermont.fr/formations/formations_en_ligne/Cours/orloff/cours03/cours03.html>

Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations

Lloyd N. Trefethen

Now available online - This 325-page textbook was written during 1985-1994 and used in graduate courses at MIT and Cornell on the numerical solution of partial differential equations.

Spectral Methods in Matlab built around forty short Matlab programs, or "M-files", which do everything from demonstrating spectral accuracy on functions of varying smoothness to solving the Poisson, biharmonic, Orr-Sommerfeld, KdV, and Allen-Cahn equations.

<http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html>

<http://www.gymnase-morges.info/math/javmath/polycopie/equadiff.pdf>

TUTORIELS - TUTORIALS - TUTORS

Fractional Calculus

differentiation and integration of arbitrary order, ...

Fractional Order Control, Chaos Theory, Solving of Industrial Problems, Information Technology, Microcontroller Devices

Ivo Petras

<http://www.steveselectronics.com/petras/research.html>

FIRMES - FIRMS

ModelMaker

Whether you are a research scientist, consultant or a teacher, ModelMaker is your ideal modeling environment. Its no nonsense approach to modeling and in-depth functionality brings modeling to novices and experts alike.

<http://www.modelkinetix.com/modelmaker/index.htm>

LIENS - LINKS

<liens_math.html>

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Copyright © 1999-2012 Jean-Paul Davalan - Reproduction interdite.

DÃ©rivÃ©es DiffÃ©rentielles Ãquations - Derivatives