在许多实际问题中,人们往往通过适当的变换把一个复杂的问题 化成简单的问题来研究.例如,通过对对数变换,把除法运算化为加 减运算,通过分式线性变换把复杂区域化为简单区域等.本张从 Fourier级数出发,引出在电学、力学、控制理论等许多工程和科学 领域中有广泛应用的积分变换 Fourier变换及其基本性质和一些简 单应用 Fourier级数的应用可在力学中振动和波动部分找到:任何振动 和波动都可表示为谐振动和谐波的叠加 Fourier级数展开 简谐振动是振动或周期运动的一种,许多实际的周期运动并不是 谐振动.例如,各种乐器的振动大多不是谐振动.对小提琴的锯齿振

留数在复变函数理论本身及实际应用中都具有重要意义本节主 要介绍留数概念、留数定理、留数计算及留数的应用

级数是研究解析函数的一个重要工具.将解析函数表示为级数不 仅有理论上的意义,而且也有使用意义,比如可利用级数计算函数的 近似值(截取幂级数的前面有限项可作为函数的近似表达式,项数取 决于要达到的近似程度)或解微分方程. 我们将看到,一个函数的解析性与一个函数可否展开成幂级数的 问题是等价的.这从另一个侧面揭示了解析函数的本质,因此我们可 以进一步地认识解析函数 本章研究复数项级数和复变函数的幂级数展开.对于某些和数学 分析中平行的结论,往往叙述而不证明

在许多工程技术领域(如电磁场理论、量子力学、固体物理、材 料物理、流体力学等)经常遇到复变量的函数.复变函数理论研究复 变量之间的对应关系,它是实变函数理论在复数域中的推广,因此两 者之间有许多相近之处,这有助于我们学习比较,但在学习中更要注 意它们之间的不同之处.本章主要讨论复变函数的一些基本概念

《博弈论》（英文版） ps5 Due Tuesday, November

1. Machines Extend Proposition 151. 1(the Perfect Folk Theorem with discounting)to arbitrary mixtures of payoff profiles of the original game G=(N, (Ai, lilieN Allow for both rational and real weights on the set of profiles u(a): aE A]; note that the statement of the result will involve an approximation of the payoff profile Construct a machine that implements the strategies in your proof

1. Asymmetric auctions Consider an interdependent-values auction with two bidders, each of whom observes an i.i.d uniform signal s; E [ 0, 1]. Bidder i' s valuation for the object is equal to

Player i is rational\;R=nieN Ri. Also, Bi(E) is the event \Player i is certain that E is true\ and B(E)=neN Bi(E). This is as in Lecture 7. Let me introduce the following notation for iterated mutual certainty: B()(E)=E B()(E)=B(B-I)(E)). Then the definition of Bk in Lecture 7 can be rewritten as Bk

NOTE: On the“ ethics” of problem sets Some of the theoretical exercise I will assign are actually well-known results; in other cases you may be able to find the answer in the literature. This is certainly the case for the current My position on this issue is that, basically, if you look up the answer somewhere it's your problem. After all, you can buy answer keys to most textbooks. The fact is, you will not have access to such, ehm, supporting material when you take your generals, or, in a more

Introduction: Invariance In their seminal contribution, Von Neumann and Morgenstern argue that the normal form of a game contains all\strategically relevant\information. This view, note well, does not invalidate or trivialize extensive-form analysis; rather, it leads those who embrace it to be uspicious of extensive-form solution concepts which yield different predictions in distinct