國立虎尾科技大學 |

Handbook of Dynamics and Probability

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Handbook of Dynamics and Probability/ by Peter Müller.
Author:	Müller, Peter.
Description:	XIV, 543 p. 68 illus., 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Earth sciences. -
Online resource:	https://doi.org/10.1007/978-3-030-88486-4
ISBN:	9783030884864

Handbook of Dynamics and Probability
Müller, Peter.

Handbook of Dynamics and Probability[electronic resource] /by Peter Müller. - 1st ed. 2022. - XIV, 543 p. 68 illus., 1 illus. in color.online resource.

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.

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.

ISBN: 9783030884864

Standard No.: 10.1007/978-3-030-88486-4doiSubjects--Topical Terms:

580242
Earth sciences.

LC Class. No.: G1-922

Dewey Class. No.: 550

Handbook of Dynamics and Probability
LDR:03816nam a22003975i 4500 001 1090858
003 DE-He213
005 20220121012140.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783030884864 $9 978-3-030-88486-4
024 7 $a 10.1007/978-3-030-88486-4 $2 doi
035 $a 978-3-030-88486-4
050 4 $a G1-922
072 7 $a RB $2 bicssc
072 7 $a SCI019000 $2 bisacsh
072 7 $a RB $2 thema
082 0 4 $a 550 $2 23
100 1 $a Müller, Peter. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1257225
245 1 0 $a Handbook of Dynamics and Probability $h [electronic resource] / $c by Peter Müller.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a XIV, 543 p. 68 illus., 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a 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.
520 $a 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.
650 0 $a Earth sciences. $3 580242
650 0 $a Geography—Mathematics. $3 1387745
650 0 $a Climatology. $3 554822
650 0 $a Geography. $3 654331
650 0 $a Mathematics. $3 527692
650 0 $a Statistics . $3 1253516
650 1 4 $a Earth Sciences. $3 683879
650 2 4 $a Mathematics of Planet Earth. $3 1141729
650 2 4 $a Climate Sciences. $3 1365898
650 2 4 $a Earth and Environmental Sciences. $3 1387959
650 2 4 $a General Mathematics. $3 1365847
650 2 4 $a Statistics. $3 556824
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030884857
776 0 8 $i Printed edition: $z 9783030884871
776 0 8 $i Printed edition: $z 9783030884888
856 4 0 $u https://doi.org/10.1007/978-3-030-88486-4
912 $a ZDB-2-EES
912 $a ZDB-2-SXEE
950 $a Earth and Environmental Science (SpringerNature-11646)
950 $a Earth and Environmental Science (R0) (SpringerNature-43711)