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1.

図書

図書
В. Вазов ; перевод с английского В.Ф. Бутузова, А.Б. Васильевой и М.В. Федорюка ; под редакцией А.Б. Васильевой
出版情報: Москва : Изд-во "Мир", 1968  464 p. ; 22 cm
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2.

図書

図書
R.B. Paris, D. Kaminski
出版情報: Cambridge ; New York : Cambridge University Press, 2001  xvi, 422 p. ; 25 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 85
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目次情報: 続きを見る
Introduction / 1:
Fundamental results / 2:
Properties of Mellin transforms / 3:
Applications of Mellin transforms / 4:
Asymptotic expansions / 5:
The Stokes phenomenon and hyperasymptotics / 6:
Multiple Mellin-Barnes integrals / 7:
Application to some special functions / 8:
Introduction / 1:
Fundamental results / 2:
Properties of Mellin transforms / 3:
3.

図書

図書
Victor Ivrii
出版情報: Berlin ; New York : Springer, c1998  xv, 731 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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4.

図書

図書
A. Erdélyi
出版情報: New York : Dover Publications, 1956  vi, 108 p. ; 21 cm
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5.

図書

図書
M.V. Fedoryuk (ed.)
出版情報: Berlin : Springer-Verlag, c1999  247 p. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 34 . Partial differential equations ; 5
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6.

図書

図書
Daniel B. Dix
出版情報: Berlin ; New York : Springer, c1997  xiv, 203 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1668
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7.

図書

図書
A N Shiryaev, V G Spokoiny
出版情報: Singapore : World Scientific, c2000  xvi, 283 p. ; 26 cm
シリーズ名: Advanced series on statistical science & applied probability ; vol. 8
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8.

図書

図書
by Igor V. Andrianov, Leonid I. Manevitch ; with help from Michiel Hazewinkel
出版情報: Dordrecht ; London : Kluwer Academic, c2002  xvii, 252 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 551
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目次情報: 続きを見る
Foreword
Preface
Acknowledgments
Synopsis
Introduction / 1.:
General Remarks
What does "Popular Science Book" Mean? / 2.:
Why "Asymptology"? / 3.:
What Are Asymptotic Methods?
Reduction of the System's Dimension
Regular Asymptotics and Boundary Layers
Asymptotic Series
Averaging and Homogenization / 4.:
Continuous limits / 5.:
Local and Nonlocal Linearization / 6.:
Estimation of Asymptotic Solution Errors / 7.:
Summation Procedures / 8.:
"Padeons" / 9.:
How to Make Both Ends Meet / 10.:
Renormalization / 11.:
Asymptotics and Computers / 12.:
Are Asymptotic Methods a Panacea? / 13.:
A Little Mathematics
Basic Formalism
A Simple Example
Regular and Singular Asymptotics
Asymptotic Decomposition
Supplementary Asymptotics
Continuous Approximation of a Chain of Masses
Search for Small Parameters
Newton Polyhedron
Catastrophe Theory
How Asymptotic Methods Work
Celestial Mechanics
Theory of Plates and Shells
Polymer Physics
Asymptotics and Engineering
Theory of Composite Materials
Biology
Et Cetera
Asymptotics and Art
Asymptotics in Pictures
Formation of New Concepts
Is Understanding an Asymptotic Process?
Asymptotic Methods and Physical Theories
Asymptotic Correspondence of Physical Theories
Mechanics by Aristotle and Galileo-Newton
Newton Mechanics and Special Relativity Theory
Geometrical and Wave Optics
Classical and Quantum Mechanics
"Simple Theories" in Physics
"The Cube of Theories"
Asymptotic Ways of Thinking for Beginners
Phenomenology and First Principles
Basic Relations of Shell Theory
How to Construct Consistent Phenomenological Theories
Some Conclusions
A Little History
Method of Averaging
Triumphs of Perturbation Methods
Galileo and the Principle of Idealization
Fathers of Asymptotic Methods
Leonhard Euler
Alexis-Claude Clairaut
Jean Le Rond d'Alembert
Joseph-Louis Lagrange
Pierre-Simon Laplace
Carl Friedrich Gauss
Jules-Henri Poincare
Alexander M. Lyapunov
Henri Eugene Pade
Ludwig Prandtl
Balthasar Van der Pol
Nickolay M. Krylov
Nickolay N. Bogoliubov
Conclusion
Appendices
Linear and Nonlinear Mathematical Physics: from Harmonic Waves to Solitons / A:
The Quasi-Linear World
On the Way to Nonlinear Physics
How Solitons Work
Certain Mathematical Notions of Catastrophe Theory / B:
Representation of Functions by Jets
Equivalency of a Function and its k-th Jet
Representation of Functions by Jets in Ordinary Points
Jets at Non-Degenerate Critical Points
Jets at Degenerate Critical Points
Control Parameters
Asymptotics and Scaling Transformations / C:
Estimation of Variables
Subsequent Approximations
Asymptotic Approaches: Attempt at a Definition / D:
Asymptotic Methods or a New Mathematics?
Uncertainty-Complementarity-Compatibility
Some Web-Pages / E:
References
About the Authors
Author Index
Topic Index
Foreword
Preface
Acknowledgments
9.

図書

図書
Harold Widom
出版情報: Berlin ; New York : Springer-Verlag, c1985  149 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1152
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10.

図書

図書
J.D. Murray
出版情報: New York ; Tokyo : Springer-Verlag, c1984  vi, 164 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 48
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