An introduction to stochastic processes in physics
著者
書誌事項
An introduction to stochastic processes in physics
The Johns Hopkins University Press, c2002
- : hbk.
- : pbk.
- タイトル別名
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An introduction to stochastic processes in physics : Containing 'On the theory of brownian motion' by Paul Langevin, translated by Anthony Gythiel
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注記
"Containing 'On the theory of brownian motion' by Paul Langevin, translated by Anthony Gythiel"
Includes bibliograpgical refrences (p. [107]-108) and index
内容説明・目次
内容説明
An accessible introduction to stochastic processes in physics which describes the basic mathematical tools of the trade: probability, random walks, and Wiener and Ornstein-Uhlenbeck processes. It includes end-of-chapter problems and emphasizes applications. The book builds directly upon early-20th-century explanations of the "peculiar character in the motions of the particles of pollen in water" as described, in the early 19th century, by the biologist Robert Brown. Lemons has adopted Paul Langevin's 1908 approach of applying Newton's second law to a "Brownian particle on which the total force included a random component" to explain Brownian motion. This method builds on Newtonian dynamics and provides an accessible explanation to anyone approaching the subject for the first time. Students should find this book a useful aid to learning the unfamiliar mathematical aspects of stochastic processes while applying them to physical processes that they have already encountered.
目次
Preface and Acknowledgments
Chapter 1. Random Variables
Chapter 2. Expected Values
Chapter 3. Random Steps
Chapter 4. Continuous Random Variables
Chapter 5. Normal Variable Theorems
Chapter 6. Einstein's Brownian Motion
Chapter 7. Ornstein-Uhlenbeck Processes
Chapter 8. Langevin's Brownian Motion
Chapter 9. Other Physical Processes
Chapter 10. Fluctuations without Dissipation
Appendix A. "On the Theory of Brownian Motion," by Paul Langevin, translated by Anthony Gythiel
Appendix B. Kinetic Equations
Answers to Problems
References
Index
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