Our time is characterized by an explosive growth in the use of ever more complicated and sophisticated (computer) models. These models rely on dynamical systems theory for the interpretation of their results and on probability theory for the quantification of their uncertainties. A conscientious and intelligent use of these models requires that both these theories are properly understood.
This book is to provide such understanding. It gives a unifying treatment of dynamical systems theory and probability theory. It covers the basic concepts and statements of these theories, their interrelations, and their applications to scientific reasoning and physics. The book stresses the underlying concepts and mathematical structures but is written in a simple and illuminating manner without sacrificing too much mathematical rigor.
The book is aimed at students, post-docs, and researchers in the applied sciences who aspire to better understand the conceptual and mathematical underpinnings of the models that they use. Despite the peculiarities of any applied science, dynamics and probability are the common and indispensable tools in any modeling effort. The book is self-contained, with many technical aspects covered in appendices, but does require some basic knowledge in analysis, linear algebra, and physics.
Peter Müller, now a professor emeritus at the University of Hawaii, has worked extensively on ocean and climate models and the foundations of complex system theories.
Inhaltsverzeichnis
Introduction
I Dynamics
Deterministic dynamical systems
Linear and integrable systems
Stability and long-time behavior
Ergodic theory
Numerical Algorithms
II Probability
Probability Theory
Discrete-time stochastic processes
Continuous-time stochastic processes
Information entropy
III Probability in dynamical evolution
Time evolution of broadened initial states
Stochastic processes generated by observables
Stochastic dynamical systems
IV Probability in scientific reasoning
Interpretations of probability
Parameter estimation and hypothesis testing
Bayesian inferences
V Probability in physics
Equilibrium statistical mechanics
Non-equilibrium statistical mechanics
Foundational issues of statistical mechanics
Quantum Mechanics
A Classical Mechanics
B Thermostatics
C Fluid dynamicsD Some proofs and explicit computations
E Mathematical tools, conventions and notation
References
Index
Über den Autor
Peter Müller studied physics and mathematics at the University of Hamburg. He received his Diplom degree (Physics) in 1970 , his Ph.D. (Geophysics) in 1974, and his habilitation (Geophysics) in 1981. He worked at Harvard University as a research associate before moving to the University of Hawaii in 1982, where he was a professor of Oceanography in the School of Ocean and Earth Science and Technology until his retirement in 2013. He is now a professor emeritus. His research interests cover a broad range of topics in oceanography and climate research, especially wave dynamics, stochastic (climate) models, and foundations of complex system theories. He has published two books and numerous articles. Peter Müller was the organizer of the ‚Aha Huliko’a Hawaiian Winter Workshop series and for ten years the chief editor of the Journal of Physical Oceanography..Ebooks vom selben Autor / Herausgeber
30.625 Ebooks in dieser Kategorie
