信息与计算科学基础实验1

1、沈阳农业大学学生实验报告册2011 2012学年第1学期姓 名：刘秋洋学 号：年级专业：11级信息与计算科学一班课程名称：信息基础实验1任课教师：惠淑荣成 绩：怎样做数学实验及写实验报告做数学实验主要是培养学生发现问题和用计算机做实验去解决问题的意识和能力。一般情况 下，有如下5个过程：1. 提出要研究的数学问题或其它实际问题；2. 设计一定的实验方式对所提问题进行观察和分析(最好借助数学软件编程来做此事)；3. 发现问题的规律性；4. 根据实验结果提出自己的猜想或见解；5. 总结实验过程，写出实验报告。做了数学实验后，写数学实验报告的形式主要包含如下6项内容：(1)实验项日名称；(2)实验目

2、的；(3)实验原理；(4)实验所用主要仪器；(5)实验内容；(6)实验步骤与结果；(7)讨 论。其中写实验名称时只要写出对要实验问题取的名称即可，例如要进行曲线拟合的最小二乘法方 面的数学实验，可以将该实验的名称写为：曲线拟合的最小二乘法。写实验h的时只要写出要通过 实验达到的冃的即可，例如进行曲线拟合的最小二乘法数学实验是理解曲线拟合概念和原理，以及 曲线拟合与拟合基函数类有关的结论，可以将该实验的fl的写为：理解曲线拟合概念和原理、拟合 基函数类。实验原理是实验涉及的数学概念、数学模型(如与实验有关的数学公式及算法等)，写 此项内容时，只要列举出与要进行的数学实验有关的数学概念、数学公式及

3、算法等即可。写实验程 序时只耍写出进行实验用到的数学软件或计算机语言，所编写的程序或命令，且程序中的变量及功 能要给出说明。写实验步骤与结果时只要写出对要实验的问题的操作过程并输hi结果。写讨论时要 写出做了实验后口己对实验的问题有哪些更深入的理解、受到什么启发、澄清了哪些模糊概念及实 验屮遇到的问题等。讨论的内容可以不拘形式，只要把耍说的事情说清楚即可。实验一 mathematia数学软件的使用一、实验目的熟悉mathematia数学软件的启动和退出、notebook窗口、命令输入、常量、内部函数、语法 和基本注意事项。二、实验原理学习mathematia基础及数学软件教材的第一章mathe

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5、,1,99,21,3,5,7,9,13,15,17,19,21,23, 25,27,29,31, 33,35, 37,3 9, 41,43, 45,47, 49,51, 53, 55, 57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99b=tableia2zi,1,101,4,9,16,25,36,49,64,81,100c=tai,2,100(1/2z1/3,1/4,1/5,1/6,1/7,1/8z1/9,1/10,1/11,1/12,1/13,1/14, 1/15,1/16, 1/17,1/18, 1/ 19,

6、1/20,1/21,1/22,1/23,1/24,1/25,1/26,1/27,1/28,1/29,1/30,1/31,1/32,1/33,1/34,1/ 35,1/36, 1/37,1/38, 1/39, 1/4 0, 1/41,1/42, 1/43,1/44, 1/45, 1/46, 1/47,1/48, 1/49, 1/50, 1/ 51,1/52, 1/53,1/54, 1/55,1/56, 1/57,1/58,l/59r 1/60, 1/61,1/62, 1/63,1/64, 1/65r1/66, 1/ 67,1/68,1/69,1/70,1/71,1/72,1/73,1/74,1/

7、75,1/76,1/77,1/78,1/79,1/80,1/81,1/82,1/ 83,1/84,1/85,1/86,1/87,1/88,1/89,1/90,1/91,l/92z1/93,1/94z1/95,1/96,1/97,1/98z1/ 99,1/100d=tablei+j,i,0,900,100,j,100j1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23, 24,25,26,27,28,29, 30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,5

8、0,51,52,53,54,55,56 ,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,8 3, 84,85, 86, 87, 88,89, 90,91, 92,93, 94,95, 96, 97, 98,99,100,101, 102, 103, 104, 105, 106, 107,108,109,110,111,112,113,114,115, 116,117,118,119, 12 0z 121, 12 2, 12 3z 12 4, 12 5, 12 6, 127, 128,

9、129,130,131,132,133, 134, 135,136,137,138,139,140,141, 142, 143, 144,145, 146, 147,148,149z150,151f152,153,154,155,156,157,158,159,160,161,162,163,164,165,166, 167,168,169, 17 0,171, 17 2z 17 3z174r 17 5, 176, 17 7, 17 8z179z180z181z182z183z184z18 5z 186, 187,188,189,190,191,192,193,194,195,196,197,

10、198,199,200,201,202,203,204,205,20 6,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,24 6, 24 7, 24 8, 24 9, 25 0, 251, 252, 25 3, 25 4,255, 25 6, 257, 25 8, 25 9, 2 60, 2 61,2 62, 2 63, 2 64,

11、 2 65, 2 6 6,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,28 6,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305, 30 6, 30 7, 30 8, 30 9, 310,311,312,313,314,315,316,317,318,319, 32 0, 321, 322, 32 3, 32 4, 32 5, 32 6, 32 7, 32 8, 32 9, 33 0,

12、331, 332, 33 3, 33 4, 33 5, 33 6, 337, 33 8, 33 9, 34 0, 341, 34 2, 34 3, 34 4, 34 5, 346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365, 36 6, 367, 368, 3 6 9, 37 0, 371, 37 2, 37 3, 37 4, 37 5, 37 6, 37 7, 37 8, 37 9, 38 0, 381, 382, 38 3, 38 4, 38 5, 386, 387, 388,389

13、, 390,391,392,393,394, 395,396, 397,398,399, 400,401,402,403,404,40 5,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,42 5,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,44 5,446, 447,448,449, 450, 451,452,453, 454,455, 456, 457,458, 459, 460,

14、 461, 462, 463, 464, 46 5,466, 467,468,469, 470,471,472,473, 474,475,476, 477,478, 479, 480,481,482,483,484,48 5,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504, 505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524, 52 5, 52 6, 52 7, 52 8, 52 9,

15、 53 0, 531, 532, 533, 534,53 5, 53 6, 53 7, 538, 53 9, 54 0, 541,54 2, 54 3, 54 4, 545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564, 565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584, 58 5, 58 6, 58 7, 588, 58 9, 590, 591, 592, 593, 594,5

16、95, 59 6, 597, 598, 59 9, 600,601, 602, 60 3, 60 4,605,606,607,608,609,610,611,6丄2,613,614,615,616,617,618,619,620,621,622,623,62 4,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,64 4, 64 5, 64 6, 64 7, 64 8, 64 9, 650, 651, 652, 653, 65 4, 65 5, 65 6, 65 7, 65 8, 65 9,

17、660, 661, 6 62, 663, 6 6 4, 665, 66 6, 667, 668, 66 9, 67 0, 671, 67 2, 67 3, 67 4, 67 5, 67 6, 67 7, 67 8, 67 9, 68 0, 681, 682, 68 3, 68 4,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703, 704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723, 7

18、2 4,72 5, 72 6, 72 7, 72 8, 72 9, 730,731, 732, 733, 734, 735,73 6, 737, 73 8, 73 9, 74 0, 741, 74 2, 74 3, 74 4,74 5, 74 6, 74 7, 74 8, 74 9, 750, 751, 752, 753, 754, 755, 75 6, 757, 75 8, 75 9, 7 60, 7 61, 7 62, 7 63, 764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,

19、 784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,80 3, 804,805, 806,807, 808, 809, 810, 811,812,813,814,815,816,817, 818,819, 82 0,821, 822,823, 82 4, 82 5, 82 6, 82 7, 82 8, 82 9, 83 0, 831, 832,83 3, 834,83 5, 83 6,837, 83 8,83 9, 84 0,841, 84 2,843,844,845,846,847,848,

20、849,850,851,852,853,854,855,856,857,858,859,860,861,862,86 3, 8 64, 8 65, 86 6, 8 67, 8 68, 8 6 9, 87 0, 871, 87 2,87 3, 87 4,87 5, 87 6,87 7, 87 8,87 9, 88 0,881, 8 82,883,884,885, 886,887, 888, 889, 890,891,892,893,894,895,896,897, 898,899, 90 0, 901, 902,903,904,905,906,907,908,909,910,911,912,91

21、3,914,915,916,917,918,919,920,921,922, 923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942, 94 3, 94 4, 94 5, 94 6, 94 7, 94 8, 94 9, 95 0, 951, 952, 95 3, 954, 95 5, 95 6, 95 7, 95 8, 95 9, 9 6 0, 961, 962, 963, 964, 965, 96 6, 967, 968, 96 9, 97 0, 971, 972, 97 3, 97 4,

22、 97 5, 97 6, 97 7, 97 8, 97 9, 98 0, 981, 982, 983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000al,5,-31,9,95bl,5,31,25,64cl,5,31/2,1/6,1/98applyplus,a2500applytimes,a2725392139750729502980713245400918633290796330545803413734328823443106201171875applyplus,b385applytimes,b13168

23、189440000applyplus,c11677821270331852073640165685691639305439/2788815009188499086581352357412492142272 applytimes,c11677821270331852073640165685691639305439/2788815009188499086581352357412492142272 1/93326215443944152681699238856266700490715968264381621468592963895217599993229915608 9414639761565182

24、86253697920827223758251185210916864000000000000000000000000e=t able randomreal , 10 |0.230843,0.277505,0.658351,0.0668512,0.72291&0.15122,0.63301,0.253828,0.374543,0.742873sorte0.0668512,05122,0.230843,0.253828,0.277505,0.374543,0.63301,0.658351,0.722918,0.742873f=randomreal 11,20),1016.7045,18.

25、2893,16.031,11.9766,13.507&18.3714,12.6226,11.844&1&5671,18.5001reverse sort fjj18.5671,18.5001,18.3714,18.2893,16.7045,16.031,13.5078,12.6226,11.9766,11.8448六、讨论教师评语实验二用曲线图形研究函数特性一、实验目的熟悉基本初等函数的图形，熟悉mathematia数学软件的曲线绘图命令。二、实验原理知道基木初等函数概念、学习教材第二章2.2节、24节内容用mathematia数学软件绘制 平面及空间曲线。三、实验所用

26、主要仪器计算机四、实验内容1. 在习题二的14题中各任选1题绘制平面曲线图形。2. 每位同学随机给出一些平面点列，画出点列并连接点列为折线。3. 在习题二的8题中任选2题绘制空间曲线图形。四、实验步骤与结果p45-l.l=plotxa4-5xa3+7xa2-3x,x,-0.5,3.5set:write: tag_plus_in_-l.l+p45_is protected.p45-2.1 =implicitplotx4+y3 1,x,l .5,1.5set:write: tag _plus_ in _-2.1+p45_ is protected.p45-3.1=parametricplot3t/

27、(l+ta3),3ta2/(l+ta3),t,-6,6set:write: tag _plus_ in _-3.1+p45_is protected.p4541二polarplot2t,t,0,3piset:write: tag _plus_ in _-4.1 +p45_ is protected.mi二123,249,364,4,7.0,565,6,6.8,7，&0, 8,10.6listplotmi1,2.3,2,49,3,64,4,7,5,65,6,6.8,7,& ,8,10.6paramedic pio t3d=xh05*t>29yh0*t>39z=9*co

28、2£=to6)parametricplocsd 二 xhcos(t/10)诜 costly=coslxt/lo)*sintjnhsin(t/lo)=o24*7c =实验三函数变换对函数图形的影响一、实验目的熟悉函数于(处)、qf (x)、/(x + b)、fo) + b与./*(x)的图形变化特点，熟悉mathematia数学软 件的曲线绘图命令。二、实验原理知道函数概念、学习教材第二章2.2节内容。三、实验所用主要仪器四、实验内容1. 以函数f(x) = smxf-7r<x<7r为实验函数，用函数绘图命令分别就a = -1,-*,*,2画出f (ax), -71 <

29、;x< 71的图形，观察/(x)与/(gx)的图形变化特点。2. 以函数fx) = sinx , -7i <x< 7i为实验函数，用函数绘图命令分别就a - -1,-, ,2ih|出妙(兀)，-71 <x<7t的图形，观察于与af(x)的图形变化特点。3. 以函数/(x) = sinx, -7t<x<7t为实验函数，用函数绘图命令分别就2-2,21田i出f(x + b), -7t<x<7t的图形，观察/(兀)与f(x + b)的图形变化特点。4. 以函数/(x) = sinx,为实验函数，用函数绘图命令分别就b = -2,2画出/(%) +

30、 /? ,-71 < x< 7t 图形，观察/(x)与f(x) + h的图形变化特点。五、实验步骤与结果cl=plotsinx,xrpi,pi,plotstyleredjc2=plotsin-x, x,pi,pi plotstyle>greenc3=plotsin-l /2x, x 厂 pif i .plotstylebluec4=plot sin l/2x, xrpi,pi ,plotstyleb lackc5=plotsin2x,x,pi,pi,plotstyletcyanshowcl,c2,c3,c4，c5c6=plot-sinx, xrpi,pi .plotstyle

31、>magentac7=plot-l/2sinxj xrpi,pi .plotstyle yellow0.4c8=plot 1 /2sinx, xrpi,pi ,plotsty leb ro wnc9=plot2sinx, x,-pi，p i .plotstyleorangeshowlc 1 ,c6,c7，c&c9,plotranget allc10=plotsinx-2, x 厂 pif i ,plotstyle->pinkc11 =plotsinx+2, xrpi,pi .plotstylepurplejc12=plotsinx-2, x,-pi,pi ,plotstyl

32、e>darkery ellowjjc13=plotsinx+2j x,-pi,pi ,plotstyledarkergreen |showcl ,c 12,cl 3,plotrangeall六、讨论教师评语实验四 多项式、有理函数及方程求根一、实验目的理解多项式、有理函数、连续求和、连续求积运算、方程求根概念。熟悉mathematia数学软 件的多项式、有理函数运算命令、熟悉连续求和与连续求积运算命令、熟悉和方程求根命令。-x实验原理知道多项式、有理函数、连续求和与连续求积运算、方程求根概念、学习教材第三章3.1、3.6、 3.7内容。三、实验所用主要仪器四、实验内容1. 化简(1题)2

33、. 展开(2题)3. 分解因式(3题)4. 约分(4题)5. 通分后化简(5题)6. 分解分式为最简分式之和(6题)7. 求和式与积式(11题)8. 求下列方程的根(12题)五、实验步骤与结果simplify(x-2)(xa2+2x+4)+(x+5)(xa2-5x+25) 117+2 x3simplify(y-2)(ya2-6y-9)-y(ya2-2y-15)-6 (-3-3 y+y)expand(a+b)a3a3+3 a2 b+3 a b2+b3expand(x+y-2)a24-4 x+x2-4 y+2 x y+y2factorxa5+ya5(x+y) (x4-x3 y+x2 y2-x y3

34、+y4)factoraa8-ba8 (a-b) (a+b) (a2+b2) (a4+b4)cancel(xa3+ya3)/(xa2-ya2)(x2-x y+y2)/(x-y)cancel(xa2+ya2-za2+2xy)/(xa2-ya2+za2-2xy)j (x2+2 xy+y2-z2)/(x2-2 xy-y2+z2)together(b-c)/a+(c-a)/b+(a-b)/c (a2 b-a b2-a2 c+b2 c+a c2-b c2)/(a b c)together 1 /(x+ l)+2/(x-2)-3/(x+3)(6(1+2 x)/(2+x) (1+x) (3+x)apart(x

35、-3)/(xa3-x)(l/(l+x)+3/x2/(l+x)apart3/(l-xa3)-(1/(-1 +x)+(2+x)/( 1 +x+x2)apart6(l +2x)/( x+ l)(x-2)(x+3)j -72+6 x+12 x2+36/(1+x)apart2(l +xa2)/(x- l)(x+ 1)a2 144-16/(-1 +x)+10 x+6 x2+2 x31 2k 1 av 1兀2/8-(x(l+x)/(-l+x)3)11na21/211n n 2"12solvef xa2-5 x+3 x+6=0,xxl-、门,xt1+®solvexa4+xa2+m 0,x1

36、、 4m,xt("1、/t 亦)，xtsolve - +c,xxt(4+j)/(4 c2)solve -mx+1 o,xjxf，xt、彷. 2 mxmx'solve x-y=m,xa2+ya2=n, x,yxt1/2(m-"昭 2t )/2(-m- " m2 2t ),仪1/2(m+ 外心 2t ),yl/2(m+、)solvexa2-y a,x+y b,x,yxt1/2 (1、4a 41 ),yl/2+b+l/2、4 a 41 ,xt1/2 (1+、4a 41 ),yl/2 (1+2 b、 4a 41 )solvecosx-x 0,xsolve:nsme

37、t: this system cannot be solved with the methods available to solvesolve-x+cosx 0,x六、讨论教师评语实验五极限与导数计算一、实验目的理解极限、导数、微分概念。熟悉mathematia数学软件的求极限、求导数和求微分命令。二、实验原理知道函数极限、导数和微分概念、学习教材第三章3.2、3.3节内容。三、实验所用主要仪器四、实验内容1. /二里叮，分别取xo=o, 1,oo,求极限lim/(x),思考本题的实验结果使你对求极限问题的认识。x牙2. 在你学习的数学分析教材中，分别选择一道有关初等函数求导、隐函数求导、参

38、数方程求导、 求高阶导数和求微分的较难做的习题，用mathematia数学软件命令来计算。3. 利用口然数e的极限定义，实验当mtoo时(1 +丄)”£。n4. 选择一道与求导数有关的应用题用mathematia数学软件的命令來处理其中的导数计算问题。五、实验步骤与结果limitsinx/x,x>01limitsinx/x,x> 1 sinllimitsinx/x,xtoo 0dfv 1 xa3 ,xv=x*y+3 *xa2-5 *y-7dv,x-7+3 x2-5 y+x y6 x+yv=(l-x)/(l+x)dlv,x,20(1 -a cost)/(1 +a cost)

39、1 a cos ta cos t ,20 -1 a cos td©2*x+xa2jx,202 x2 x2 x670442572800*+3352212864000(2+2 x)2+2514159648000(2+22 x2 x2 xx)4+670442572800(2+2 x)6+83805321600(2+2 xf+5587021440(2+22 x2 x2 x'x)10+211629600(2+2x)v+4651200(2+2x)+58140(2+2 x)16+380 '(2+2 x)18+ $ 川(2+2 x)20limit(l +1 /n)n,ntoo

40、9;dsina*x+cosb*x, x,2 -b2 cosb x-a2 sina x六、讨论教师评语实验六泰勒公式的计算一、实验目的理解泰勒（taylor）公式、函数的n次近似多项式及余项概念，了解n次近似多项式随n增大 一般是逐步逼近原函数的结果。熟悉mathematia数学软件求函数的n阶泰勒公式命令和求函数的 n次近似多项式命令。二、实验原理知道泰勒（taylor）公式、苗数的n次近似多项式及余项概念，学习教材第三章3.5节内容。三、实验所用主要仪器四. 实验内容1. 取函数f(x) = xex为实验函数,用mathematia命令分别就xo=-l,0,2,将/(切按(x-x0)展开成

41、8阶泰勒公式和求出相应的8次近似多项式，在区间4, 4上画出这些近似多项式。从这个实 验屮，能给你提供哪些思考？2. 在你学习的数学分析教材屮，选择2道有关泰勒公式计算的习题，用mathematia数学软件命 令来计算。五、实验步骤与结果seriesx*©x, x,-l ,8(l/©)+(x+l)2/(2 ©)+(x+lf/(3 ©)+(x+l)4/(8 ©)+(x+1)5/(30 ©)+(x+1)6/(144 ©)+(x+1)7/(840 ©)+(x+1)8/(5760 ©)+ox+l9seriesx*©x, x,0,8 x+x2+x3/2+x4/6+x5/24+x6/1204-x7/720+x8/5040+0x9seriesx *©x,x,2,82 ©2+3 ©2 (x-2)+2 ©2 (x-2)2+5/6 ©2 (x2)*l/4 ©2 (x-2)4+7/120 ©2 (x-2)5+l/90 ©2 (x-2)6+1/560 ©2 (x-2)7+(©2 (x-2)8)/4032+ox-29a