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Record Nr. |
UNINA9910784818103321 |
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Autore |
Wu Yong |
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Titolo |
Beyond nonstructural quantitative analysis [[electronic resource] ] : blown-ups, spinning currents, and modern science / / Yong Wu, Yi Lin |
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Pubbl/distr/stampa |
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River Edge, NJ, : World Scientific, c2002 |
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ISBN |
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Descrizione fisica |
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1 online resource (344 p.) |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. 303-310) and index. |
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Nota di contenuto |
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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 |
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; 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 |
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Sommario/riassunto |
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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 |
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