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Python Programming for Mathematics
This book focuses on the practical use of the Python language in a range of different areas of mathematics. Through fifty-five exercises of increasing difficulty, the book provides an expansive overview of the power of using programming to solve complex mathematical problems.
Python Programming for Mathematics
Python Programming for Mathematics focuses on the practical use of the Python language in a range of different areas of mathematics. Through fifty-five exercises of increasing difficulty, the book provides an expansive overview of the power of using programming to solve complex mathematical problems. This book is intended for undergraduate and graduate students who already have learned the basics of Python programming and would like to learn how to apply that programming skill in mathematics. Features Innovative style that teaches programming skills via mathematical exercises. Ideal as a main textbook for Python for Mathematics courses, or as a supplementary resource for Numerical Analysis and Scientific Computing courses.
Lectures on Navier-Stokes Equations
This book is a graduate text on the incompressible Navier-Stokes system, which is of fundamental importance in mathematical fluid mechanics as well as in engineering applications. The goal is to give a rapid exposition on the existence, uniqueness, and regularity of its solutions, with a focus on the regularity problem. To fit into a one-year course for students who have already mastered the basics of PDE theory, many auxiliary results have been described with references but without proofs, and several topics were omitted. Most chapters end with a selection of problems for the reader. After an introduction and a careful study of weak, strong, and mild solutions, the reader is introduced to p...
The Mathematical Analysis of the Incompressible Euler and Navier-Stokes Equations
The aim of this book is to provide beginning graduate students who completed the first two semesters of graduate-level analysis and PDE courses with a first exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces. Chapters 1 and 2 cover the fundamentals of the Euler theory: derivation, Eulerian and Lagrangian perspectives, vorticity, special solutions, existence theory for smooth solutions, and blowup criteria. Chapters 3, 4, and 5 cover ...
On Singular Vortex Patches, I: Well-Posedness Issues
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Programmation Python par la pratique - 2e éd.
Python est un langage de programmation phare dans le monde scientifique. Il est parfaitement adapté pour programmer des problèmes mathématiques. Cet ouvrage est consacré à l’utilisation pratique du langage Python dans différents domaines des mathématiques : les suites, l’algèbre linéaire, l’intégration, la théorie des graphes, la recherche de zéros de fonctions, les probabilités, les statistiques, les équations différentielles, le calcul symbolique et la théorie des nombres. Dans cette deuxième édition enrichie, à travers 45 exercices de difficulté croissante et corrigés en détail, il dresse un panorama des applications de la programmation en Python dans les mathématiques permettant d’acquérir les compétences nécessaires pour résoudre des problèmes complexes. Les codes sources de l’ouvrage sont disponibles en ligne.
15 énigmes ludiques pour s'initier à la programmation Python
L’objectif proposé par cet ouvrage est de s’initier à la programmation avec Python en écrivant un petit programme informatique pour résoudre des énigmes amusantes. Les thèmes de ces énigmes ont été choisis pour découvrir à chaque fois un nouveau concept-clé en informatique. Les commandes Python qui seront utiles à la résolution des énigmes sont intégrées dans le livre pour qu’il soit auto-suffisant. Pour chaque énigme trois niveaux d’indice sont fournis pour ceux qui auront besoin d’un peu d'aide pour démarrer. La difficulté des énigmes est repérée par un système d’étoiles. La solution complète de toutes les énigmes est bien sûr détaillée en fin d’ouvrage. Elle comporte non seulement le programme Python qui permet de trouver la solution mais aussi des explications détaillées sur la conception de l’algorithme correspondant. Enfin de nombreux encadrés historiques, biographiques, culturels ou techniques viennent agrémenter la lecture.
Instability and Non-uniqueness for the 2D Euler Equations, After M. Vishik
An essential companion to M. Vishik’s groundbreaking work in fluid mechanics The incompressible Euler equations are a system of partial differential equations introduced by Leonhard Euler more than 250 years ago to describe the motion of an inviscid incompressible fluid. These equations can be derived from the classical conservations laws of mass and momentum under some very idealized assumptions. While they look simple compared to many other equations of mathematical physics, several fundamental mathematical questions about them are still unanswered. One is under which assumptions it can be rigorously proved that they determine the evolution of the fluid once we know its initial state and the forces acting on it. This book addresses a well-known case of this question in two space dimensions. Following the pioneering ideas of M. Vishik, the authors explain in detail the optimality of a celebrated theorem of V. Yudovich in the sixties, which states that, in the vorticity formulation, the solution is unique if the initial vorticity and the acting force are bounded. In particular, the authors show that Yudovich’s theorem cannot be generalized to the L^p setting.
