1 Model problem 1.1 Poisson Equation in 1D Boundary Value Problem(BVP) (x)=∫(x) (0,1),u(0)=(1)=0,f Describes many simple physical phenomena(e.g) Deformation of an elastic bar Deformation of a string under tension Temperature distribution in a bar The Poisson equation in one dimension is in fact an ordinary differ tion. When dealing with ordinary differential equations we Poisson equation will be used here to illastrate numerical techniques for elliptic PDE's in multi-dimensions. Other techniques specialized for ordinary differen tial equations could be used if we were only interested in the one dimension

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

Dirichlet Model Problems Strong Form Domain: Q =(0, 1) Find u such that (0)=(1)=0 for given f SMA-HPO⊙1999M Poisson in Rl. Formulation 1

Formulations Model problem Strong Formulation Find u such that Vu=f in n2 a =0 on I for a polygonal domain

理解功能/数据的目的，学会使用U/C矩阵的建立、校验、求解过程；掌握新的管理信息系统逻辑模型的含义和内容

一、概 述 生物碱是人类对植物药中有效成分研究得最早而较多的一类成分。从十九世纪德国学者 F.W.Sert. . u rner 从鸦片中分离出吗啡碱（morphine）以来，迄今已从自然界中分离得到约 10000种生物碱类化合物。在《全国医药产品大全》 中收载的生物碱药物及其制剂达六十余种

7.1概 在化工、轻工、食品、医药等工业中,通过化学反应或物 NGOLL 理性操作过程经常得到一些含溶质的稀溶液,为了得到符u 合标准的产品,常将含有不挥发溶质的溶液沸腾汽化并移 出蒸汽,从而使溶液中溶质浓度提高的单元操作称为蒸发

一.电流与电压的关系(u~i关系) 电阻、电感与电容元件的串联交流电路,各元件通过同一电流。若设定电流及电压的正方向以后,总电压瞬时值可由克希荷夫定律得到下式:

Background About the author: Floyd Dell (1887- 1969), U.S. versatile and prolific writer and an editor for several newspapers and magazines

一、例题精解 【例题3.1】在R、L、C元件串联的电路中,已知R=30,L=127mh,c=40uF, 电源电压u=2202sin(314t+20°)V.(1)求感抗、容抗和阻抗;(2)求电流的有效值1 与瞬时值i的表达式;(3)求功率因数cos;(4)求各部分电压的有效值与瞬时值的表 达式;(5)作相量图;(6)求功率P、Q和S