This is a pletely revised edition, with more thafifty pages of new material scattered throughout. Ikeeping with the conventional meaning of chapters and sections, I have reorgaruzed the book into twenty-nine sections isevechapters. The maiadditions are Sectio20 0the Lie derivative and interior multiplication, two intrinsic operations oa manifold too important to leave out, new criteria iSectio21 for the boundary orientation, and a new appendix oquaternions and the symplectic group. Apart from correcting errors and misprints, I have thought through every proof again, clarified many passages, and added new examples, exercises, hints, and solutions. Ithe process, every sectiohas beerewritten, sometimes quite drastically. The revisions are so extensive that it is not possible to enumerate them all here. Each chapter now es with aintroductory essay giving aoverview of what is to e. To provide a timeline for the development ofideas, I have indicated whenever possi- ble the historical origiof the concepts, and hav

This book is intended as a textbook for a first course in the theory offunctions of one plex variable for students who are mathematicallymature enough to understand and execute arguments. The actual pre-requisites for reading this book are quite minimal; not much more than astiff course in basic calculus and a few facts about partial derivatives. Thetopics from advanced calculus that are used (e.g., Leibniz's rule for differ-entiating under the integral sign) are proved in detail.

本书是《高等数学：一元微积分及其实验（MATLAB版）》的续本，共分6章，主要内容包括向量代数与空间解析几何、多元函数微积分、曲线积分与曲面积分、无穷级数和常微分方程的基本理论和方法，以及与各个知识点匹配的MATLAB的符号解读、数值解法及其图形显示程序。 《高等数学多元微积分及其实验（MATLAB版）》各章均安排了演示与实验，增加了用MATLAB计算多元函数微积分、级数、常微分方程的数值解法、符号解法及其图形显示，数学建模的基本内容和基本方法等，在每章末附有上机实验的课题。作者把多年在大学数学实验教学中编写的大量MATLAB程度和算例融入到本书中，为高等数学中的每种方面都配备了MATLAB数值计算、符号计算及其图形可视化的MATLAB程序，许多程度具有科研和使用价值。 《高等数学多元微积分及其实验（MATLAB版）》可作为高等院校工

代数K理论在代数拓扑、数论、代数几何和算子理论等现代数学各个领域中的作用越来越大。这门学科的广泛性往往使人感觉望而生畏。本书以1990年秋天Maryland大学讲义为基础，不仅为数学领域研究生提供很好的学习代数K理论的基本知识，也讲述其在各个领域的应用。全书结构完整，了解代数基础知识、基本代数拓扑和几何拓扑知识就可以完全读懂这本书。该书也涉及到不少代数拓扑、拓扑代数和代数数论的知识。最后一章简明地介绍了循环同调以及其与K理论的关系。目次：环的K0群；环的K1群；范畴的K0、K1群，MilnorK2群；QuillenK理论和 -结构；循环同调及其与K理论的关系。 读者对象：数学系高年级学生及研究生的教材，也可供高校数学教师及数学研究人员阅读或参考。

This book is intended as a textbook for a first course in the theory offunctions of one plex variable for students who are mathematicallymature enough to understand and execute arguments. The actual pre-requisites for reading this book are quite minimal; not much more than astiff course in basic calculus and a few facts about partial derivatives. Thetopics from advanced calculus that are used (e.g., Leibniz's rule for differ-entiating under the integral sign) are proved in detail.