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 dynamics D Some proofs and explicit computations
E Mathematical tools, conventions and notation
References
Index
Table of Contents:
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 dynamics.- D Some proofs and explicit computations.- E Mathematical tools, conventions and notation.- References.- Index.
About the Author :
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..
Review :
"A handbook of critically important mathematical concepts with broad utility in the applied and social sciences as well as pure sciences. Due to its applicability to a variety of disciplines this volume will likely see use in a wide array of academic institutions." (Ninah Moore, RUSA Update, rusaupdate.org, January 29, 2023)
"This book emphasizes the conceptual and foundational aspects of dynamics and probability. It tries to present these aspects as simply as possible without losing too much mathematical rigor. Some required mathematics is summarized in appendices, which is to provide quick access to a perhaps forgotten definition or theorem ... ." (N. N. Ganikhodjaev, Mathematical Reviews, November, 2022)
