| 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 |
