An introduction to partial differential equations偏微分方程概论
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作者： Michael Renardy等著
出 版 社：
出版时间： 2004-1-1字数：版次： 1页数： 434印刷时间： 2004/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387004440包装： 精装内容简介
Partial differential equations are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis and algebraic topology. Like algebra, topology, and rational mechanics, partial differential equations are a core area of mathematics. This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in Chapter 10, and the necessary tools from functional analysis are developed within the course. The book can be used to teach a variety of different courses. This new edition features new problems throughout and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded.
目录
Preface
1Competing Risk Modeling in Reliability
Tim Bedford
1.1 Introduction
1.2 Independent and Dependent Competing Risks .
1.3 Characterization of Possible Marginals
1.4 Kolmogorov-Smirnov Test
1.5 Conservatism of Independence
1.6 The Bias of Independence
1.7 Maintenance as a Censoring Mechanism
1.7.1 Dependent copula model
1.7.2 Random clipping
1.7.3 Random signs
1.7.4 LBL model...
1.7.5 Mixed exponential model
1.7.6 Delay time model
1.8 Loosening the Renewal Assumption
1.9 Conclusion
References
2 Game-Theoretic and Reliability Methods in Counter-Terrorism and Security Vicki Bier
2.1 Introduction
2.2 Applications of Reliability Analysis to Security
2.3 Applications of Game Theory to Security
2.3.1 Security as a game between defenders
2.4 Combining Reliability Analysis and Game Theory
2.5 Directions for Future Work
2.6 Conclusion
Acknowledgments
References
3 Regression Models for Reliability Given the Usage Accumulation History Thierry Duchesne
3.1 Introduction
3.1.1 Definitions and notation
3.1.2 Common lifetime regression models
3.2 Other Approaches to Regression Model Building
3.2.1 Models based on transfer functionals
3.2.2 Models based on internal wear
3.3 Collapsible Models
3.3.1 Two-dimensional prediction problems
3.4 Discussion
Acknowledgments
References
4 Bayesian Methods for Assessing System Reliability: Models and Computation Todd Graves and Michael Hamada
4.1 Challenges in Modern Reliability Analyses
4.2 Three Important Examples
4.2.1 Example 1: Reliability of a component based on biased sampling
4.2.2 Example 2: System reliability based on partially informative tests
4.2.3 Example 3: Integrated system reliability based on diverse data
4.3 YADAS: a Statistical Modeling Environment
4.3.1 Expressing arbitrary models
4.3.2 Special algorithms
4.3.3 Interfaces, present and future
4.4 Examples Revisited
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