An Informal Introduction To Stochastic Calculus With Applications (2版)

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Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory. The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus. The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods. This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises. This edition has also improved presentation from the first edition in several chapters, including new material.

An Informal Conceptual Introduction to Turbulence: Second Edition of An Informal Introduction to Turbulence (2版)

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The subject of turbulence remains and probably will remain as the most exciting one for the mind of researchers in a variety of ?elds. Since publication of the ?rst edition of this book in November 2001 a number of otherbooksonturbulencehaveappeared,forexampleBernardandWallace (2002), Oberlack and Busse (2002), Foias et al. (2001), Biskamp (2003), Davidson(2004),Jovanovich(2004),SagautandCambon(2008)tomention afew. Soonehastoaskagain thequestionwhyasecondeditionofonebook from a ?eld of so many on the same subject? Does it make any di?erence? Thereareadditionalreasonsapartofthosegiveninthe?rstedition. One of thebasic premises of this bookis thatWeabsolutelymustleave roomfor doubtor thereis noprogress and nolearning. Thereis nolearning without posing a question. And a question requires doubt. . . Now the freedom of doubt,whichisabsolutelyessentialforthedevelopmentofscience,wasborn from astruggle with constituted authorities. . . R. Feynmann (1964). This is closely related to the term ‘conceptual ’: the book has now a di?erent title An informal conceptual introduction to turbulence. One of the main f- tures of the ?rst edition was indeed its conceptual orientation. The second edition is an attempt to make this feature dominant. Consequently items whicharesecondaryfromthispointofview werereducedandeven removed in favour of those added which are important conceptually. This required addressing in more detail most common misconceptions, which are con- quencesoftheprofounddi?cultiesofthesubjectandwhichtravel fromone publication to another. Consequently a one page Appendix D listing some of these misconceptions in the ?rst edition became chapter 9 titled Ana- gies,misconceptions and ill de?ned concepts.