2004 456 p. 152 illus. Hardcover
3-7643-4308-7
Modern finite element analysis has grown
into a basic
mathematical tool for almost every field
of engineering and the
applied sciences. This introductory textbook
fills a gap in the
literature, offering a concise, integrated
presentation of
methods, applications, software tools, and
hands-on projects.
Included are numerous exercises, problems,
and Mathematica/Matlab-based
programming projects. The emphasis is on
interdisciplinary
applications to serve a broad audience of
advanced undergraduate/graduate
students with different backgrounds in applied
mathematics,
engineering, physics/geophysics. The work
may also serve as a
self-study reference for researchers and
practitioners seeking a
quick introduction to the subject for their
research.
Keywords: Analysis, Applied Mathematics,
Design, Engineering,
Mathematical Methods in Engineering, Physics
Contents: Preface * Notation * Introduction
* One-Dimensional
Shape Functions * One-Dimensional Second-Order
Equations * One-Dimensional
Fourth-Order Equations * Two-Dimensional
Elements * Two-Dimensional
Problems * More Two-Dimensional Problems
* Axisymmetric Heat
Transfer * Transient Problems * Single Nonlinear
One-Dimensional
Equations * Plane Elasticity * Stokes Equations
and Penalty
Method * Vibration Analysis * Computer Codes:
Mathematica Codes,
Ansys Codes, MatLab Codes, Fortran Codes
* Appendix A:
Integration Formulas * Appendix B: Special
Cases * Appendix C:
Temporal Approximations * Appendix D: Isoparametric
Elements *
Appendix E: Green's Identities * Appendix
F: Gaussian Quadrature
* Appendix G: Gradient-Based Methods * Bibliography
* Index
2003 XVI, 220 p. Hardcover
3-7643-2169-5
This volume is based on the lecture notes
of six courses
delivered at a CIMPA Summer School in Temuco,
Chile, in January
2001. The courses are: asymptotic of the
heat kernel in unbounded
domains; spin systems with long range interactions;
non-linear
Dirichlet problem and non-linear integration;
first-passage
percolation; central limit theorem for Markov
processes;
stochastic orders and stopping times in Brownian
motion. The
level of each course is that of a graduate
course, but the
material will also be of interest for the
specialist.
Keywords: Stochastic Processes, Mathematical
Physics, Dirichlet
Problem, Spin Glasses, Central Limit Theorem
Series: Progress in Probability. Vol.. 54
2nd ed. 2003 Approx. 320 p. Hardcover
3-7643-6907-8
The main subject of the book is the full
understanding of Weyl's
formula for the volume of a tube, its roots
and its implications.
Another discussed approach to the study of
volumes of tubes is
the computation of the power series of the
volume of a tube as a
function of its radius. The chapter on mean
values, besides its
intrinsic interest, shows an interesting
fact: methods which are
useful for volumes are also useful for problems
related with the
Laplacian. Historical notes and Mathematica
drawings have been
added to this revised second edition.
Keywords: Differential geometry, projective
geometry
Series: Progress in Mathematics. 221
2003 VIII, 440 p. Hardcover
3-7643-2168-7
This volume focuses on recent developments
in non-linear and
hyperbolic equations.
In the first contribution, the singularities
of the solutions of
several classes of non-linear partial differential
equations are
investigated. Applications concern the Monge-Ampere
equation,
quasi-linear systems arising in fluid mechanics
as well as
integro-differential equations for media
with memory.
There follows an article on L_p-L_q decay
estimates for Klein-Gordon
equations with time-dependent coefficients,
explaining, in
particular, the influence of the relation
between the mass term
and the wave propagation speed. The next
paper addresses
questions of local existence of solutions,
blow-up criteria, and
C^8 regularity for quasilinear weakly hyperbolic
equations.
Spectral theory of semibounded selfadjoint
operators is the topic
of a further contribution, providing upper
and lower bounds for
the bottom eigenvalue as well as an upper
bound for the second
eigenvalue in terms of capacitary estimates.
Keywords: Partial Differential Equations,
Wavelets, Operator
Theory, Spectral Theory, Functional Analysis,
Mathematical
Physics
Contents:
Contributions: Nonlinear PDE. Singularities,
Propagation,
Applications (P.R. Popivanov).- From Wave
to Klein-Gordon Type
Decay Rates (F. Hirosawa and M. Reissig).-
Local Solutions to
Quasilinear Qeakly Hyperbolic Differential
Equations (M. Dreher).-
S(M,g)-pseudo-differential Calculus of Manifolds
(F. Baldus).-
Domain Perturbations and Capacity in General
Hilbert Spaces and
Applications to Spectral Theory (A. Noll).-
An Interpolation
Family between Gabor and Wavelet Transformations
(B. Nazaret and
M. Holschneider).- Formes de Torsion Analytique
et Fibrations
Singulieres (Xiaonan Ma).- Regularisation
of Secondary
Characteristic Classes and Unusual Index
Formulas for Operator-Valued
Symbols (G. Rozenblum).
Series: Operator Theory: Advances and Applications.
Vol.. 145