Applied and Computational Complex Analysis Vol 1 - P. Henrici
- Auteur Peter Henrici
- Édition illustrée, réimprimée
- Éditeur Wiley, 1974
- Original provenant de l'Université de Californie
- Numérisé 2 avr. 2007
- ISBN 0471372447, 9780471372448
- Longueur 682 pages
This book constitutes the first installment of a projected three-volume
work that will present applications as well as the basic theory of analytic
functions of one or several complex variables. Applications are made to
other branches of mathematics, to science and engineering, and to compu-
tation. The algorithmic attitude toward mathematics--not to consider a
problem solved unless an.algorithm for constructing the solution has been
found--prevails not only in the sections devoted to computation but forms
one of the work's unifying themes.
A short overview of the three volumes is in order. The first volume, after
laying the necessary foundations in the theory of power series and of
complex integration, discusses applications and basic theory (without the
Riemann mapping theorem) of conformal mapping and the solution of
algebraic and transcendental equations. The second volume will cover
topics that are broadly connected with ordinary differential equations:
special functions, integral transforms, asymptotics, and continued frac-
tions. The third volume will center similarly around partial differential
equations and will feature harmonic functions, the construction of confor-
mal maps, the Bergman-Vekua theory of elliptic partial differential equa-
tions with analytic coefficients, and analytical. techniques for solving
three-dimensional potential problems.
In collecting all these topics under one cover, I have been guided by the
idea that for today's applied mathematician it is not enough to specialize,
however deeply, in any single narrowly restricted area. He should also be
made aware as forcefully as possible of the light that radiates from the
basic theories of mathematics into the neighboring fields of science. What
1 have tried to do here for complex analysis, should as part of an applied
mathematics curriculum also be done, for instance, in real analysis and
linear algebra.
work that will present applications as well as the basic theory of analytic
functions of one or several complex variables. Applications are made to
other branches of mathematics, to science and engineering, and to compu-
tation. The algorithmic attitude toward mathematics--not to consider a
problem solved unless an.algorithm for constructing the solution has been
found--prevails not only in the sections devoted to computation but forms
one of the work's unifying themes.
A short overview of the three volumes is in order. The first volume, after
laying the necessary foundations in the theory of power series and of
complex integration, discusses applications and basic theory (without the
Riemann mapping theorem) of conformal mapping and the solution of
algebraic and transcendental equations. The second volume will cover
topics that are broadly connected with ordinary differential equations:
special functions, integral transforms, asymptotics, and continued frac-
tions. The third volume will center similarly around partial differential
equations and will feature harmonic functions, the construction of confor-
mal maps, the Bergman-Vekua theory of elliptic partial differential equa-
tions with analytic coefficients, and analytical. techniques for solving
three-dimensional potential problems.
In collecting all these topics under one cover, I have been guided by the
idea that for today's applied mathematician it is not enough to specialize,
however deeply, in any single narrowly restricted area. He should also be
made aware as forcefully as possible of the light that radiates from the
basic theories of mathematics into the neighboring fields of science. What
1 have tried to do here for complex analysis, should as part of an applied
mathematics curriculum also be done, for instance, in real analysis and
linear algebra.
