山东大学数学系2018年PDE期末试题

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分类号：单位代码：10422密级：学号：硕士学位论文论文题目：作者姓名X X X 学院名称X X X 专业名称X X X 指导教师X X X X X X 合作导师 2016年6月26日

原创性声明本人郑重声明：所呈交的学位论文，是本人在导师的指导下，独立进行研究所取得的成果。除文中已经注明引用的内容外，本论文不包含任何其他个人或集体已经发表或撰写过的科研成果。对本文的研究做出重要贡献的个人和集体，均已在文中以明确方式标明。本声明的法律责任由本人承担。论文作者签名：日期：关于学位论文使用授权的声明本人同意学校保留或向国家有关部门或机构送交论文的印刷件和电子版，允许论文被查阅和借阅；本人授权山东大学可以将本学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或其他复制手段保存论文和汇编本学位论文。 (保密论文在解密后应遵守此规定) 论文作者签名：导师签名：日期：

目录中文摘要.........................................................................................................................I ABSTRACT..................................................................................................................II 符号说明......................................................................................................................III 第一章绪论.. (1) 1.1"[点击输入一级标题××××标题2]" (3) 1.1.1"[点击输入二级标题××××标题3]" (3) 1.1.2"[点击输入二级标题××××标题3]" (3) 1.1.3"[点击输入二级标题××××标题3]" (3) 1.2"[点击输入一级标题××××标题2]" (3) 1.2.1"[点击输入二级标题××××标题3]" (3) 1.2.2"[点击输入二级标题××××标题3]" (4) 1.3"[点击输入一级标题××××标题2]" (4) 1.3.1"[点击输入二级标题××××标题3]" (4) 1.3.2"[点击输入二级标题××××标题3]" (4) 1.4"[点击输入一级标题××××标题2]" (4) 第二章"[点击输入大标题××××标题1]" (5) 2.1"[点击输入一级标题××××标题2]" (5) 2.1.1"[点击输入二级标题××××标题3]" (5) 2.1.2"[点击输入二级标题××××标题3]" (5) 2.2"[点击输入一级标题××××标题2]" (5) 2.2.1"[点击输入二级标题××××标题3]" (5) 2.2.2"[点击输入二级标题××××标题3]" (5) 2.3"[点击输入一级标题××××标题2]" (5) 2.3.1"[点击输入二级标题××××标题3]" (5) 2.3.2"[点击输入二级标题××××标题3]" (5) 第三章"[点击输入大标题××××标题1]" (6) 3.1"[点击输入一级标题××××标题2]" (6) 3.1.1"[点击输入二级标题××××标题3]" (6)

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题目摘要 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXX 关键词：XXXX XXXXX XXXXXX

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分类号：单位代码：10422 密级：学号：硕士学位论文论文题目：作者姓名 X X X 学院名称 X X X 专业名称 X X X 指导教师 X X X X X X 合作导师

目录中文摘要........................................................................................................................ I ABSTRACT .................................................................................................................. I I 符号说明...................................................................................................................... I II 第一章绪论.. (1) 1.1"[点击输入一级标题××××标题2]" (3) 1.1.1"[点击输入二级标题××××标题3]" (3) 1.1.2"[点击输入二级标题××××标题3]" (3) 1.1.3"[点击输入二级标题××××标题3]" (3) 1.2"[点击输入一级标题××××标题2]" (3) 1.2.1"[点击输入二级标题××××标题3]" (3) 1.2.2"[点击输入二级标题××××标题3]" (4) 1.3"[点击输入一级标题××××标题2]" (4) 1.3.1"[点击输入二级标题××××标题3]" (4) 1.3.2"[点击输入二级标题××××标题3]" (4) 1.4"[点击输入一级标题××××标题2]" (4) 第二章"[点击输入大标题××××标题1]" (5) 2.1"[点击输入一级标题××××标题2]" (5) 2.1.1"[点击输入二级标题××××标题3]" (5) 2.1.2"[点击输入二级标题××××标题3]" (5) 2.2"[点击输入一级标题××××标题2]" (5) 2.2.1"[点击输入二级标题××××标题3]" (5) 2.2.2"[点击输入二级标题××××标题3]" (5) 2.3"[点击输入一级标题××××标题2]" (5) 2.3.1"[点击输入二级标题××××标题3]" (5) 2.3.2"[点击输入二级标题××××标题3]" (5) 第三章"[点击输入大标题××××标题1]" (6) 3.1"[点击输入一级标题××××标题2]" (6) 3.1.1"[点击输入二级标题××××标题3]" (6) I

山东大学《高等数学》期末复习参考题 (1)

山东大学《数学分析III 》期末复习参考题一、选择题（共 5 小题，20 分） 1、若曲线x t y t z t ===cos ,sin ,22在对应于t =π 2 点处的一个切向量与oz 轴正方向成钝角，则此向量与yz 平面夹角的正弦值为（）（A ） 112 +π （B ）- +112 π （C ） ππ 12 + （D ）- +ππ 12 2、设L 是圆周 x 2+y 2=a 2 (a >0)负向，则 ( ) 3、设u y x =arctan ，则????2222 u x u y +＝（） (A) 4222 xy x y ()+ (B) -+4222 xy x y () (C) 0 (D) 2222 xy x y ()+ 4、曲面x y z xyz x z 2 2 2 2426-+--+=在点(,,)012处的切平面方程为（）（A ）31223110()()x y z -+--+= （B ）3234x y z +-= （C ） x y z 312230+-+--= （D ）x y z 31223 =-=-- 5、设u f r =(),而r x y z = ++222，f r ()具有二阶连续导数，则 ??????222222 u x u y u z ++ =（） (A)f r r f r " '()()+ 1 (B)f r r f r "'()()+ 2 (C) 112r f r r f r "'()()+ (D) 122r f r r f r "' ()()+ 二、填空题（共 10 小题，40 分）

1、函数f x y e x y x (,)sin()=+-2在点（0，π 4 ）处沿y 轴负向的方向导数是。 2、曲面xe y e z e e y z x ++= +2 2332 1在点(,,)210-处的法线方程为。 3、设u x y =2，则???2u x y = 。 4、设f (x ,y )在具有连续的二阶偏导数，L 是椭圆周的顺时针方向，则的值等于 ________________. 5、设u x y z =?? ? ? ? 1/，则 ??u z (,,) 111= 。 6、曲面arctan y xz 14 +=π 在点(,,)-210处的切平面方程是。 7、设L 为xoy 面上有质量的曲线，在曲线L 上的点(x ,y )处的质量线密度为ρ(x ,y )。则这条曲线L 的质量的计算表达式为_______________. 8、设是M (1，3)沿圆(x －2)2+(y －2)2=2到点N (3，1)的半圆，则积分 . 9、设是由A (－2，3)沿y =x 2－1到点M (1，0)，再沿y =2(x －1)到B (2，2)的路径，则 ________. 10、设，根据二重积分的几何意义，三、计算题（共 3 小题，30 分） 1、设y y x =()由方程arctan()xy y -=20所确定，求d d y x 。 2、计算曲线积分其中r 是从点O (0，0，0) 到A (1，2，3)的直线段。 3、求函数u x y z = ++22223在点（1,1,4）处沿曲线?? ? ??+===1332t z t y t x 在该点切线方向的方向导数。四、证明题（10 分）设z x y =arctan ，其中x u v y u v =+=-,，求证 ????z u z v u v u v +=-+22.

2014山东大学网络教育高起专期末考试英语模拟2

COLLEGE ENGLISH TEST FOR NON-ENGLISH MAJORS OF CONTINUING EDUCATION （英语一） I. Choose the correct pronunciation to each of the following words. (B)1. absorb: A. [bs b] B. [?b s:b] (A)2. enjoy: A. [in d i] B. [end i] (A)3. obvious: A. [bvi s] B. [b vi s] II. Mark the stress for each of the following words. (B)1. amount A. 第一个音节 B. 第二个音节 (A)2. midnight A. 第一个音节 B. 第二个音节 (A)3. possible A. 第一个音节 B. 第二个音节 C. 第三个音节 III. Each of the following sentences is provided with two answers. Choose the one that identifies its correct sentence type and its nuclear tone type. (B)1. Is the flower red or blue? A. 一般疑问句——升调 B. 选择疑问句——升、降调 (A)2. Must I leave right now? A. 一般疑问句——升调 B. 特殊疑问句——降调 (B)3. You don’t have to come tomorrow, A. don’t you?——升调 B. do you?——升调 IV. Fill in each of the following blanks with a word in its proper form. (1) He hoped the passenger would Mary be and indeed _she___ was __Mary__. (2) _Which__ way shall we go? By the stream or through the wood? (3) Let’s go and have a drink. We’ve got _much___ time before the train leaves. (4) Look at these pears. This seems to be a nice ripe _one__. (5) He remembers __what__ London of _in__ past and says it was gayer than _what_ London of __in___ today. (6) Let’s sing a song, ___shall___ we? (7) Don’t stand _under____ a tree during a thunderstorm. (8) _After___ all, they have nothing _in____ common. It’s only natural that they can’t get along well. (9) Last night I came back late __for___ the meeting. (10) They came __by___ the 9 o’clock train. V. Each of the following sentences is provided with four answers labeled A, B, C, and D. Choose the one that best completes it. (C) (1) _______, it is quite easy to drill a hole in it with laser. a. As diamond is hard b. Although hard diamond is c. Hard as diamond is d. However diamond is hard (C) (2) Not all the children will visit ________ parents on Sunday. a. his b. its c. their d. his or her (B) (3) If you get up ________, you will miss the plane. a. lately b. late c. latter d. later (C) (4) “Did you say that our neighbor in the accident?”

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