Vector calculus is the fundamental language of mathematical physics. It provides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These topics include fluid dynamics， solid mechanics and electromagnetism， all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However， it is assumed that the reader has a knowledge of basic calculus， including differentiation， integration and partial differentiation. Some knowledge of linear algebra is also required， particularly the concepts of matrices and determinants.

ADVANTAGE has been taken of the prearation of the fourth edition of this work to add a few additional referens and to make a number of corrections of minor errors.Our thanks are bue to a number of our readers for pointing out errors and misprints，and in particular we are grateful to Mr E.T.Copson，Lecturer in mathematics in　the University Edinburgh，for the trouble which he has taken in supplying us with a somewhat lenthy list.

Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic settheoretic facts of life， and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups， or integrals， or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here。

The object of this book is to familiarize the reader with the basic language of and some fundamental theorems in Riemannian Geometry. To avoid referring to previous knowledge of differentiable manifolds， we include Chapter 0， which contains those concepts and results on differentiable manifolds which are used in an essential way in the rest of the book。The first four chapters of the book present the basic concepts of Riemannian Geometry （Riemannian metrics， Riemannian connections， geodesics and curvature）. A good part of the study of Riemannian Geometry consists of understanding the relationship between geodesics and curvature. Jacobi fields， an essential tool for this understanding， are introduced in Chapter 5. In Chapter 6 we introduce the second fundamental form associated with an isometric immersion， and prove a generalization of the Theorem Egregium of Gauss. This allows us to relate the notion of curvature in Riemannian manifolds to the classical concept of Gaussian curvature for surfaces。

《高中数学竞赛专题讲座》（第一辑）12种出版以来，反响强烈，深受广大读者喜爱，并收到了大量反馈信息。很多读者，包括一线竞赛辅导的教师和竞赛研究人员提出了许多宝贵的建设性意见，希望我们再组织出版一套以解题方法和解题策略为主的丛书。为了满足广大读者的需求，我们在全国范围‘内组织优秀的数学奥林匹克教练编写了《高中数学竞赛专题讲座》（第二辑）共8种：《图论方法》、《周期函数与周期数列》、《代数变形》、《极值问题》、《染色与染色方法》、《递推与递推方法》、《组合构造》；考虑到配套，把’第一辑中《数学结构思想及解题方法》放在第二辑出版。丛书的起点是高中阶段学生必须掌握的数学基本知识和全国数学竞赛大纲要求的一些基本的数学思想、方法，凡是对数学爱好的高中学生都有能力阅读。丛书的特点是：1．充分吸收了世界各地的优秀数学竞赛试题，通过对典型例题的解剖，传授数学思想方法，侧重培养学生的逻辑思维能力，不唯解题而解题；2．本着少而精的原则选择材料，不搞题海战术，不追求大而全，而是以点带面，举一反三；3．以数学修养和能力培养为立意，通过深刻剖析问题的数学背景，挖掘数学内涵，培养学生的数学品格和解决实际问题的能力；4．在注重基础知识训练同时，有适当程度的拨高，对参加冬令营甚至是更高层次的竞赛都有相当的指导作用和参考价值。

《21世纪经济学教材：计量经济学实验基础》计量经济学实验是经济管理类本科生和研究生的秘修课或公共专业基础课的重要组成部分。《21世纪经济学教材：计量经济学实验基础》是专门为这门课程撰写的教材，共由7章组成：第1章为回归分析实验，第2章为虚拟变量模型回归实验，第3章为Logistic回归实验，第4章为共线性问题实验，第5章为异方差问题实验，第6章为自相关问题实验，第7章为线性时间序列回归分析实验。

《集值映象与微分包含》内容主要包括：集值分析基础和微分包含理论两个板块。前者包括集值映的连续性理论和选取理论，是后者存在的基础；后者是微分方程理论的推广，主要包括微分包含解的存性理论与定性理论，并对极大单词调的微分包含理论和应用做了比较详细的介绍.两个板块都建立在泛函分析的基础之上，要求读者掌握点集拓扑学和泛函分析基础理论.为了让数学与应用数学专业高年级学生也能读懂《集值映象与微分包含》的基本内容，作者特意将学生在本科阶段难以学到或难以学好的上、下半连续，弱收敛和紧（或弱紧）致性等部分内容做了归纳和加深，这些内容连同其他必备知识组成第一章.不管是本科还在研究生，要读懂《集值映象与微分包含》都得先仔细读好这一章。

《数学模型与实验》分为上、下两篇，共11章。上篇以介绍数学建模方法为主线，内容包括：数学建模概论、初等数学模型、微分与差分方程模型、数学规划模型、概率统计模型、图论模型、模糊数学和灰色系统模型；下篇以介绍数学实验方法为主线，内容包括：Matlab软件介绍、LINGO软件简介、SAS软件主要功能模块介绍、具有代表性的数学实验。《数学模型与实验》适合高等学校本、专科学生作为数学建模课程教材，也可作为大学生数学建模竞赛科技活动的培训教材，还可供科技工作者和学习应用数学知识的自学者参考。

本书以讲授思想和方法为主，并以初值问题解的唯一性和非唯一性作为出发点，分别讨论线性和非线性问题，书中以算子法贯穿于求解线性问题的全过程。 本书主要内容包括：基本概念和预备知识，微分方程和微分系统的基本理论，线性微分方程和线性微分系统的解，一阶非线性微分方程的解，非线性微分系统和非线性现象，二阶微分方程边值问题。本书可作为数学及相关专业常微分方程课的教材或作自学之用，也可供有关科研人员阅读参考。

《李群，李代数及其表示》是一部学习李群，李代数及其表示论的优秀的研究生教材。与其他一些同类著作相比，《李群，李代数及其表示》有两大特点，第一大特点是：作者以一种尽可能少地运用流形知识的方法来研究李群。这种方法十分清晰易懂，使读者可以快速地掌握知识的核心内容。第二大特点是：《李群，李代数及其表示》在给出半单李群及李代数的理论框架之前，通过详尽地介绍SU（2）和SU（3）的表示理论来引入即将介绍的一般内容，这种方式使得读者能够在了解一般理论之前已经有了对根系、权，及Weyl群的简单认识。同时，书中众多的例子和图示可以很好地协助学习并理解一些内容。《李群，李代数及其表示》分为两部分，第一部分主要介绍了李群与李代数，以及它们之间的相互关系，同时还介绍了基础的表示论。第二部分则阐述了半单李群与李代数理论。This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups （which is the basis of many texts） and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups， the Peter-Weyl theorem， conjugacy of maximal tori （two proofs）， Weyl character formula and more are covered. The book continues with the study of complex analytic groups， then general noncompact Lie groups， including the Coxeter presentation of the Weyl group， the Iwasawa and Bruhat decompositions， Cartan decomposition， symmetric spaces， Cayley transforms， relative root systems， Satake diagrams， extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a "topics" section giving depth to the students understanding of representation theory， taking the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme， with many applications in diverse areas such as random matrix theory， minors of Toeplitz matrices， symmetric algebra decompositions， Gelfand pairs， Hecke algebras， representations of finite general linear groups and the cohomology of Grassmannians and flag varieties.