这是一本有关微分方程的启蒙读物,一位数学家仅仅用了初等三角学的知识,通过三角测量的实际例子,把微分方程的基本特征一步一步地展现出来。语言浅显,图例丰富,启发性强,非常值得孩子们和家长共同阅读。
Following Keller [119] we call two problems inverse to each other if the formulation of each of them requires full or partial knowledge of the other. By this definition, it is obviously arbitrary which of the two problems we call the direct and which we call the inverse problem. But usually, one of the problems haeen studied earlier and, perhaps, in more detail. This one is usually called the direct problem, whereas the other is the inverse problem. However, there is often another, more important difference between these two problems. Hadamard (see [91]) introduced the concept of a well-posed problem, originating from the philosophy that the mathematical model of a physical problem has to have the properties of uniqueness, existence, and stability of the solution. If one of the properties fails to hold, he called the problem iU-posed. It turns out that many interesting and important inverse problems in science lead to ill-posed problems,, while the corresponding direct problems are well-posed. Often, existenc
20世纪的数学可谓又深又广,皮耶尔乔治·奥迪弗雷迪编著的《数学世纪——过去100年间30个重大问题》在有限篇幅内深入浅出地概括了这个世纪数学的主要成就。特别适合那些对20世纪数学及其重要应用有兴趣并想了解概貌的读者阅读。
本书内容包括数理统计学最基本的理论和方法,文字简明易懂,概念清楚明确,推证逻辑严谨,显示出先生深厚的统计理论底蕴。 本书分为三部分。部分是绪论(章)。该章节论述了数理统计学的研究对象;阐述了数理统计学与概率论、数学和社会经济学统计学的关系;说明了数理统计学在自然界、技术界和社会经济领域广泛的应用性。 第二部分是论述数理统计学的数理基础概率论理论(第二章至第六章)。 第三部分是讲述数理统计的主要内容(第七章至第十二章)。 本书非常强调各种分布和方法的实际应用,特别是对工农业生产和科学试验中现象波动分析常用的方差分析,作者做了细微的论述。因此,此书可作为以教学参考用书,也可作为经济管理上进行预测决策分析的参考用书,还可作为工农业生产试验和科学试验的参考用书。