数学
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氧化硅郭晨峰 著本书以SiO为活性物质,石墨烯为缓冲载体,制备了二元复合材料—纳米氧化硅-石墨烯(SiO-石墨烯)复合物、电极体系—纳米三维(3D)氧化硅-石墨烯多层电极、三元复合材料—纳米碳包覆氧化硅-石墨烯(SiOx@C/RGO)复合物以及三元复合材料—纳米氧化硅@氮掺杂碳/氮掺杂石墨烯(SiO@NC/NG)复合物。对SiO基-石墨烯复合材料的制备方法、物理性质、电化学储锂性能及其储锂机制进行了深入的研究。 -
时变随机系统郭雷 著时变随机系统广泛存在于客观实际中,许多随机递推算法也可当作此类系统来研究.《时变随机系统:稳定性与自适应理论(第二版)》从理论上对这类系统的稳定性、自适应估计与自适应控制问题进行了统一的论述.《时变随机系统:稳定性与自适应理论(第二版)》共8章,既包含常用的稳定性与镇定性的经典结果,又侧重介绍基本的自适应估计、滤波与控制问题及相应算法的理论基础,其中多数属于作者的研究成果. 在保留原来内容的基础上,第二版进行了一些必要修订。特别地,进一步丰富了第1 章和第2 章的内容,并且增加了第7 章和第8 章两章新内容。将书的副标题修改为“稳定性与自适应理论”,其中自适应理论包括自适应估计与自适应控制两部分。第7 章讨论Markov 跳变线性随机系统的自适应控制问题,给出了这类系统可被自适应反馈镇定的充分必要条件。该条件与非自适应情形下的相应条件并不相等,这揭示了当系统的跳变参数未知时,不确定性对反馈机制能力的本质影响。第8 章讨论一般切换线性系统的镇定性问题,通过证明一个加强的Squashing 引理,分别研究了切换规律已知和未知情形下的反馈镇定性。 -
数值数学实验教程陈兴同.王海军.凌思涛 著本书为普通高等学校理工科各个专业有关数值计算类课程的配套教材。全书共分9章,内容包括:MATLAB编程基础、计算机数系、数值方法的基本思想、函数方程求根、线性方程组求解、数据插值与拟合、数值积分法、常微分方程的数值解法。对各种算法的详细理论分析可以参考有关数值计算教材,本书只列出相关结果,着重分析如何编程和实验。 -
离散数学刘铎 著离散数学是现代数学的一个重要分支,是计算机和软件科学理论的基础。《离散数学:翻转课堂适用教材》是针对“碎片化”教学和“翻转课堂”教学模式改革编写的新型教材,共包括4部分内容:基础知识、逻辑、关系与函数、图与树。每部分都包含大量习题,扫描二维码可获取部分习题的参考答案。《离散数学:翻转课堂适用教材》着重讲解离散数学的基本概念、基本方法及应用,内容精练、语言流畅、习题丰富,可作为高等院校计算机或软件工程专业不同方向、采用“翻转课堂”教学模式的“离散数学”课程师生教学使用,特别适合在学生自学及教学课时偏少(32~48 课时)的情况下使用,也可供其他专业学生和科技人员阅读参考。 -
实用时间序列分析Aileen Nielsen随着物联网、数字医疗、智慧城市的兴起,时间序列数据分析变得越来越重要,持续监测和数据收集变得越来越普遍,对通过统计和机器学习技术进行时间序列分析的需求将会增长。 -
微分方程数值方法王汉权,成蓉华《微分方程数值方法——有限差分法》介绍了微分方程数值求解方法——有限差分法。内容涉及有限差分法的基本设计过程与具体的实现过程,有限差分法在工程、科学和数学问题中的应用以及MATLAB程序,涵盖了有限差分法的很多内容:常微分方程的数值解法;二阶椭圆型、二阶抛物型及二阶双曲型方程的数值算法;各种非线性偏微分方程以及非线性偏微分方程组的数值方法; 数值积分与数值微分在偏微分方程求解过程中的应用等。《微分方程数值方法——有限差分法》的一大特色是给出大量的应用实例并附MATLAB程序。 -
图上独立圈若干问题的结构参数高云澍The study of graph theory started over two hundreds years ago. The earliest known paper is due to Euler(1736) about the seven bridges of Korugsberg. Since 1960s, graph theory has developed very fast and numerous results on graph theory sprung forth. There are many nice and celebrated problems in graph theory, such as Hamiltonian problem, four-color problem, Chinese postman problem, etc. Moreover, graph theory is widely applied in chemistry, computer science, biology and other disciplines. As a subfield in discrete mathematics, graph theory has attracted much attention from all perspectives.All graphs are considered only finite, simple, undirected graphs with no loops and no multiple edges. Let G be a graph. The Hamiltonian cycle problem is one of the most well-known problems in graph theory. A cycle which contains every vertex of G is called a Hamiltonian cycle. A cycle is called a chorded cycle if this cycle contains at least one chord. A k-factor in a graph G is a spanning k-regular subgraph of G, where k is a positive integer. There exists many interesting results about the existence of k-factor, by applying Tuttes Theorem, however, we mainly focus on the existence of 2-factor throughout this thesis. Clearly, a Hamiltonian cycle is a 2-factor with exactly one component. From this point of view, it is a more complex procedure to find the condition to ensure the existence of 2-factor in a given graph. The most usual technique to resolve 2-factor problems is to find a minimal packing and then extend it to a required 2-factor.The book is concerned with structural invariants for packing cycles in a graph and partitions of a graph into cycles, i.e., finding a prescribed number of vertex-disjoint cycles and vertex-partitions into a prescribed number of cycles in graphs. It is well-known that the problem of determining whether a given graph has such partitions or not, is NP-complete. Therefore, many researchers have investigated degree conditions for packing and partitioning. This book mainly focuses on the following invariants for such problems: minimum degree, average degree (also extremal function), degree sum of independent vertices and the order condition with minimum degree. -
贝叶斯数据分析 第3版(美)安德鲁·格尔曼This book is intended to have three roles and to serve three associated audiences: anintroductory text on Bayesian inference starting from first principles, a graduate text oneffective current approaches to Bayesian modeling and computation in statistics and relatedfields, and a handbook of Bayesian methods in applied statistics for general users of andresearchers in applied statistics. Although introductory in its early sections, the book isdefinitely not elementary in the sense of a first text in statistics. The mathematics usedin our book is basic probability and statistics, elementary calculus, and linear algebra. Areview of probability notation is given in Chapter 1 along with a more detailed list of topicsassumed to have been studied. The practical orientation of the book means that the reader'sprevious experience in probability, statistics, and linear algebra should ideally have includedstrong computational components.To write an introductory text alone would leave many readers with only a taste of theconceptual elements but no guidance for venturing into genuine practical applications, be-yond those where Bayesian methods agree essentially with standard non-Bayesian analyses.On the other hand, we feel it would be a mistake to present the advanced methods with-out first introducing the basic concepts from our data-analytic perspective. Furthermore,due to the nature of applied statistics, a text on current Bayesian methodology would beincomplete without a variety of worked examples drawn from real applications. To avoidcluttering the main narrative, there are bibliographic notes at the end of each chapter andreferences at the end of the book. -
解析几何马慧龙《解析几何》一方面内容充实,通俗易懂,是学习几何学的入门教材。书中既讲解了空间解析几何的基本内容和方法(向量代数,仿射坐标系,空间的直线和平面,常见曲面等),又讲解了仿射几何学中的基本内容和思想(仿射坐标变换,二次曲线的仿射理论,仿射变换和等距变换等),还介绍了射影几何学中的基本知识,较好地反映了几何学课程的全貌。该书突出几何思想的教育,强调形与数的结合;方法上强调解析法和综合法并重;内容编排上采用“实例一理论一应用”的方式,具体易懂;内容选取上兼顾各类高校的教学情况,具有广泛的适用性。《解析几何》表达通顺,说理严谨,阐述深入浅出。另一方面注意培养读者的空间想象能力,这尤其体现在第三章中关于旋转面、柱面和锥面方程的建立。《解析几何》论证严谨,同时又力求简明;叙述上深入浅出,条理清楚,注意讲清所讨论问题的来龙去脉。 -
概率论林正炎,苏中根,张立新 著《概率论》系浙江大学出版社版的《概率论》教材的配套英文教材,内容主要包括四大部分:一、随机事件及其概率;二、随机变量和分布函数;三、数字特征;四、极限定理。通过学习,使学生掌握概率论的基本概念和主要结果,了解定量地处理随机现象的基本思想,了解它在其它学科和实际部门的广泛应用,也为学习数理统计等后续课程奠定基础。
