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Mathematical Analysis, Second Edition
It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis. -
Visual Complex Analysis
Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians. -
Introduction to Mathematical Thinking
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线性代数与矩阵论
《线性代数与矩阵论》是将矩阵论和线性空间理论溶合在一起编写的。先以中学时熟悉的多项式为基础,将多项式理论交代清楚。接下去讲多元多项式。然后是矩阵论和线性空间理论的基本工具:行列式、矩阵以及线性方程组求解理论。从而引进线性空间、线性不等式和它上面的线性变换,以及求复方阵的Jordan标准形的代数理论和几何解释,Jordan标准形的应用,它包含了方阵函数和方阵在复相似下的标准型理论。给出了线性函数和它的推广,即多重线性函数,Grassmann代数以及张量场。接着转向内积空间(即实和复Euclid空间的结构和二次型的分类)。最后三章是广义逆矩阵的几何基础和矩阵处理,非负矩阵的基本性质和复矩阵偶在相抵下的标准形。《线性代数与矩阵论》的特点是充分发挥矩阵技巧在矩阵论和线性空间理论中的应用,涉及面也比较广。《线性代数与矩阵论》的另一个特点是书中的例题和习题比较难一点,虽然《线性代数与矩阵论》的一些习题已经被一些作者选为例题,但是《线性代数与矩阵论》的目的是使同学有一个良好的严格训练环境,可以自由地选择这些习题来做。 -
随机微分方程
《随机微分方程》(第6版)是《Universitext》丛书之一,是一部理想的研究生教材,内容做了较大的修改和补充,包括鞅表示论、变分不等式和随机控制等内容,书后附有部分习题解答和提示。随机微分方程在数学以外的许多领域有着广泛的应用,它对数学领域中的许多分支起着有效的联结作用。 -
Brownian Motion and Stochastic Calculus
A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.