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金融数学方法 英文版 Methods of Mathematical Finance/Ioannis Karatzas
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现代 PDE 理论框架 ：以椭圆型、双曲型、抛物型三大类方程为主线，既涵盖经典方程，又深入介绍泛函分析、加权索伯列夫空间等现代分析工具，帮助读者建立完整的理论体系。 应用紧密结合 ：包含大量来自物理与工程领域的实际问题，如守恒律、非线性扩散等，并配有丰富例题与图表，有效提升读者解决实际问题的能力。 前沿内容并重 ：由偏微分方程与几何应用领域杰出学者McOwen教授撰写，融入其多年研究成果，既适合数学专业本科高年级学生和研究生学习，也可为相关领域科研人员提供参考。
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inverseproblemsariseinanumberofimportantpracticalapplications,rangingfrombiomedicalimagingtoseismicprospecting.thisbookprovidesthereaderwithabasicunderstandingofboththeunderlyingmathematicsandthecomputationalmethodsusedtosolveinverseproblems.italsoaddressesspecializedtopicslikeimagereconstruction,parameteridentification,totalvariationmethods,nonnegativityconstraints,andregularizationparameterselectionmethods. becauseinverseproblemstypicallyinvolvetheestimationofcertainquantitiesbasedonindirectmeasurements,theestimationprocessisoftenill-posed.regularizationmethods,whichhavebeendevelopedtodealwiththisill-posedness,arecarefullyexplainedintheearlychaptersofcomputationalmethodsforinverseproblems.thebookalsointegratesmathematicalandstatisticaltheorywithapplicationsandpracticalcomputationalmethods,includingtopicslikemaximumlikelihoodestimationandBayesianestimation.
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inverseproblemsariseinanumberofimportantpracticalapplications,rangingfrombiomedicalimagingtoseismicprospecting.thisbookprovidesthereaderwithabasicunderstandingofboththeunderlyingmathematicsandthecomputationalmethodsusedtosolveinverseproblems.italsoaddressesspecializedtopicslikeimagereconstruction,parameteridentification,totalvariationmethods,nonnegativityconstraints,andregularizationparameterselectionmethods. becauseinverseproblemstypicallyinvolvetheestimationofcertainquantitiesbasedonindirectmeasurements,theestimationprocessisoftenill-posed.regularizationmethods,whichhavebeendevelopedtodealwiththisill-posedness,arecarefullyexplainedintheearlychaptersofcomputationalmethodsforinverseproblems.thebookalsointegratesmathematicalandstatisticaltheorywithapplicationsandpracticalcomputationalmethods,includingtopicslikemaximumlikelihoodestimationandBayesianestimation.
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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics （TAM）. The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos,mix with and reinforce the traditional methods of applied mathematics. Thus. the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math- ematical Sciences （AMS） series, which will focus on ad
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Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics （TAM）. The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos,mix with and reinforce the traditional methods of applied mathematics. Thus. the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math- ematical Sciences （AMS） series, which will focus on ad
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Superconvergence Analysis and a Posteriori Error Estimation
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