本书不仅对偏微分方程的古典理论作了严谨的介绍和论证，而且在内容、概念与方法等方面注意了与现代偏微分方程知识的内在联系，对现代知识作了基本的阐述，注意了各数学分支知识在偏微分方程中的应用。内容丰富，方法多样，技巧性强，并配有大量的例题与习题，难易兼顾，雅俗共赏。 本书可作为综合性大学数学专业教材或教学参考书、理工科大学非数学专业的参考书和高等师范院校数学专业本科生选修课的教材或研究生教材。另外，可供一般的数学工作者、物理工作者和工程技术人员作为参考书。
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.
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。
