Beyond nonstructural quantitative analysis : blown-ups, spinning currents, and modern science / Yong Wu, Yi Lin.

Format:

Book

Author/Creator:

Wu, Yong.

Contributor:

Forrest, Jeffrey Yi-Lin, 1959-

Language:

English

Subjects (All):

Nonlinear theories.

Physical Description:

1 online resource (344 p.)

Edition:

1st ed.

Place of Publication:

River Edge, NJ : World Scientific, c2002.

Language Note:

English

Summary:

This book summarizes the main scientific achievements of the blown-up theory of evolution science, which was first seen in published form in 1994. It explores - using the viewpoint and methodology of the blown-up theory - possible generalizations of Newtonian particle mechanics and computational schemes, developed on Newton's and Leibniz's calculus, as well as the scientific systems and the corresponding epistemological propositions, introduced and polished in the past three hundred years. The authors briefly explain the fundamental concepts, then analyze a series of topics and problems of t

Contents:

Contents ; Foreword ; Chapter 1 Introduction ; 1.1 Scientific Discoveries ; 1.2 Nonlinear Science ; 1.3 Some Ancient Thoughts of the East and the West ; 1.4 Determinacy and Randomness ; 1.5 Equal Quantitative Effects ; 1.6 Organization of This Book ; 1.7 References

Chapter 2 Nonlinearity: The Conclusion of Calculus 2.1 A Brief History of Calculus ; 2.2 The Method of Differential Analysis ; 2.2.1 Functions and Their Properties ; 2.2.1.1 Representations of Functions ; 2.2.1.2 General Properties of Function ; 2.2.2 Limits of Functions

2.2.3 Continuous Functions 2.2.4 The Concept and Properties of Differentials ; 2.3 The Well-Posedness and Singularity of Differential Equations ; 2.4 Discontinuity: The Mathematical Characteristic of Nonlinear Evolutions ; 2.5 Question the Traditional Treatments of Nonlinearity

2.5.1 Linearization 2.5.2 Stabilization ; 2.5.3 Comparison between Spectral Method and Numerical Schemes ; 2.5.4 Limitations of Lyapunov Exponents ; 2.6 References ; Chapter 3 Blown-Up Theory: The Beginning of the Era of Discontinuity ; 3.1 Looking at Whole Evolutions

3.2 Mathematical Physics Meanings of Blown-Ups 3.3 Nonlinear Transitional Changes: A Mathematical Character of Blown-Ups ; 3.3.1 Blown-Ups of Quadratic Nonlinear Models ; 3.3.2 Blown-Ups of Cubic Polynomial Models ; 3.3.3 Blown-Ups of nth Degree Polynomial Models

3.3.4 Blown-Ups of Higher Order Nonlinear Evolution Systems

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 303-310) and index.

ISBN:

9789812778093

9812778098

OCLC:

879025122