Author | Dautray, Robert. author |
---|---|

Title | Mathematical Analysis and Numerical Methods for Science and Technology [electronic resource] : Volume 1 Physical Origins and Classical Methods / by Robert Dautray, Jacques-Louis Lions |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 2000 |

Connect to | http://dx.doi.org/10.1007/978-3-642-61527-6 |

Descript | XVIII, 720 p. online resource |

SUMMARY

In the first years of the 1970's Robert Dautray engaged in conversations with Jacques Yvon, High-Commissioner of Atomic energy, of the necessity of publishยญ ing mathematical works of the highest level to put at the disposal of the scientific community a synthesis of the modern methods of calculating physical pheยญ nomena. It is necessary to get away from the habit of treating mathematical concepts as elegant abstract entities little used in practice. We must develop a technique, but without falling into an impoverishing utilitarianism. The competence of the Commissariat a I'Energie Atomique in this matter can provide a support of exceptional value for such an enterprise. The work which I have the pleasure to present realises the synthesis ofmathematยญ ical methods, seen from the angle of their applications, and of use in designing computer programs. It should be seen as complete as possible for the present moment, with the present degree of development of each of the subjects. It is this specific approach which creates the richness of this work, at the same time a considerable achievement and a harbinger of the future. The encounter to which it gives rise among the originators of mathematical thought, the users of these concepts and computer scientists will be fruitful for the solution of the great problems which remain to be treated, should they arise from the mathematical structure itself (for example from non-linearities) or from the architecture of computers, such as parallel computers

CONTENT

I. Physical Examples -- A. The Physical Models -- ยง 1. Classical Fluids and the Navier-Stokes System -- ยง2. Linear Elasticity -- ยง3. Linear Viscoelasticity -- ยง4. Electromagnetism and Maxwellโ{128}{153}s Equations -- ยง5. Neutronics. Equations of Transport and Diffusion -- ยง6. Quantum Physics -- Appendix โ{128}{156}Mechanicsโ{128}{157}. Elements Concerning the Problems of Mechanics -- ยง1. Indicial Calculus. Elementary Techniques of the Tensor Calculus -- ยง2. Notation, Language and Conventions in Mechanics -- ยง3. Ideas Concerning the Principle of Virtual Power -- B. First Examination of the Mathematical Models -- ยง 1. The Principal Types of Linear Partial Differential Equations Seen in Chapter IA -- ยง2. Global Constraints Imposed on the Solutions of a Problem: Inclusion in a Function Space; Boundary Conditions; Initial Conditions -- Review of Chapter IB -- II. The Laplace Operator Introduction -- ยง1. The Laplace Operator -- ยง2. Harmonic Functions -- ยง3. Newtonian Potentials -- ยง4. Classical Theory of Dirichletโ{128}{153}s Problem -- ยง5. Capacities -- ยง6. Regularity -- ยง7. Other Methods of Solution of the Dirichlet Problem -- ยง8. Elliptic Equations of the Second Order -- Review of Chapter II -- Table of Notations -- of Volumes 2โ{128}{147}6

Mathematics
Partial differential equations
Numerical analysis
Mechanics
Applied mathematics
Engineering mathematics
Mathematics
Partial Differential Equations
Numerical Analysis
Appl.Mathematics/Computational Methods of Engineering
Mechanics