1 Motivation The Poisson problem has a strong formulation a minimization formulation and a weak formulation T weak formulations are more general than the strong formulation in terms of regularity and admissible data SLIDE 2 The minimization/weak formulations are defined by: a space X; a bilinear The minimization/weak formulations identify ESSENTIAL boundary conditions NATURAL boundary conditions ed in a The points of departure for the finite element method are the weak formulation(more generally) the minimization statement (if a is SPD) 2 The dirichlet problem 2.1 Strong Formulation Find u such that

一、线性变换的定义线性空间V到自身的映射称为V的一个变换定义1线性空间V的一个变换A称为线性变换,如果对于V中任意的元素a,B和数域P中任意数k,都有 (1) 一般用花体拉丁字母A,B,表示V的线性变换,A(a)或a代表元素a在 变换下的像定义中等式

1 The Number-Picking Game Here is a game that you and I could play that reveals a strange property of expectation. 3, First, you think of a probability density function on the natural numbers. Your distri- bution can be absolutely anything you like. For example, you might choose a uniform distribution on 1, 2, ... 6, like the outcome of a fair die roll. Or you might choose a bi- probability, provided that,...,n. You can even give every natural number a non-zero nomial distribution on 0, 1 he sum of all probabilities is 1

The expectation or expected value of a random variable is a single number that tells you a lot about the behavior of the variable. Roughly, the expectation is the average value, where each value is weighted according to the probability that it comes up. Formally, the expected value of a random variable r defined on a sample space s is: (B)=∑R()Pr(o) To appreciate its signficance, suppose S is the set of students in a class, and we select a student uniformly at random. Let r be the selected student's exam score. Then

一、选择题 (1)C)(2)A)(3)C)(4)D)(5)C(6)D)(7)A)(8)A) (9)B)(10)B)(11)C)(12)D)(13)C)(14)C)(15)C)(16)B) (17)A)(18)B)(19)B)(20)D)(1)B)(22)B)(23)A)(24)D) (25)C)(26)B)(27)B)(28)C)(29)D)(30)B)(31)A)(32)C) (33)B)(34)C)(35)A)

3.1-(A⊕B)⊕(C⊕D)奇偶校验器 (b)y-A+B+A+B=a+ab…或功能 3.2(a)y=ab+(+)+D= (b)y=A+AC+BC全加器 Y2=A⊕BC全加器

assets An asset is a commodity that provides a flow of services over time. +E.g. a house, or a computer. .A financial asset provides a flow of money over time -a security

16.322 Stochastic Estimation and Control Professor Vander Velde 1. P(ABCD.=P(A)P(B A)P(C|AB)P(D 1 ABC) Derive this by letting A=CD. Then P(BCD)= P(CD)P(B ICD)= P(C)P(DIC)P(DICD) 2. If A,, A2r.. is a set of mutually exclusive and collectively exhaustive events, then