信息与计算科学基础实验1

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沈阳农业大学 学生实验报告册

2011 2012姓 名:学 号:年级专业:课程名称:任课教师:成 绩:

学年第1学期

刘秋洋

11级信息与计算科学一班 信息基础实验1 惠淑荣

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)实验项目名称;(2) 实验目的;(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。写实验目的时只要写出要通过实验达到的目的即可,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,可以将该实验的目的写为: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、数学公式及算法等即可。写实验程序时只要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出结果。写讨论时要写出做了实验后自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中遇到的问题等。讨论的内容可以不拘形式,只要把要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Mathematia简介与基本量 三、实验所用主要仪器 计算机

四、实验内容 1.建立下面各表

(1)?1,3,5,?,99?;(2)?1,4,9,16,?,100?;(3)?,,,?,?234?1111?? 100?(4)??1,2,3,?,100?,?101,102,103,?,200?,?,?901,902,903,?,1000??。

2.取出1题(1),(2),(3)表中第1、第5与倒数第3个元素。 3.将1题(1),(2),(3)表中的所有元素加在一起,乘在一起。

4.随机生成10个元素、数值范围在(0,1)之间的表,并将元素从小到排序。

5.随机生成10个元素、数值范围在(11,20)之间的表,并将元素从大到小排序。 五、实验步骤与结果

a=Table[i,{i,1,99,2}]

{1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99}

b=Table[i^2,{i,1,10}]

{1,4,9,16,25,36,49,64,81,100}

c=Table[1/i,{i,2,100}]

{1/2,1/3,1/4,1/5,1/6,1/7,1/8,1/9,1/10,1/11,1/12,1/13,1/14,1/15,1/16,1/17,1/18,1/19,1/20,1/21,1/22,1/23,1/24,1/25,1/26,1/27,1/28,1/29,1/30,1/31,1/32,1/33,1/34,1/35,1/36,1/37,1/38,1/39,1/40,1/41,1/42,1/43,1/44,1/45,1/46,1/47,1/48,1/49,1/50,1/51,1/52,1/53,1/54,1/55,1/56,1/57,1/58,1/59,1/60,1/61,1/62,1/63,1/64,1/65,1/66,1/67,1/68,1/69,1/70,1/71,1/72,1/73,1/74,1/75,1/76,1/77,1/78,1/79,1/80,1/81,1/82,1/83,1/84,1/85,1/86,1/87,1/88,1/89,1/90,1/91,1/92,1/93,1/94,1/95,1/96,1/97,1/98,1/99,1/100}

d=Table[i+j,{i,0,900,100},{j,100}]

{{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100},{101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200},{201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,22

6,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300},{301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400},{401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500},{501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600},{601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700},{701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800},{801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900},{901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000}}

a[[{1,5,-3}]] {1,9,95}

b[[{1,5,-3}]] {1,25,64}

c[[{1,5,-3}]] {1/2,1/6,1/98}

Apply[Plus,a] 2500

Apply[Times,a]

2725392139750729502980713245400918633290796330545803413734328823443106201171875

Apply[Plus,b] 385

Apply[Times,b] 13168189440000

Apply[Plus,c]

11677821270331852073640165685691639305439/2788815009188499086581352357412492142272 Apply[Times,c]

11677821270331852073640165685691639305439/2788815009188499086581352357412492142272 1/93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

e=Table[RandomReal[],{10}]

{0.230843,0.277505,0.658351,0.0668512,0.722918,0.15122,0.63301,0.253828,0.374543,0.742873}

Sort[e]

{0.0668512,0.15122,0.230843,0.253828,0.277505,0.374543,0.63301,0.658351,0.722918,0.742873}

f=RandomReal[{11,20},10]

{16.7045,18.2893,16.031,11.9766,13.5078,18.3714,12.6226,11.8448,18.5671,18.5001}

Reverse [Sort[ f]]

{18.5671,18.5001,18.3714,18.2893,16.7045,16.031,13.5078,12.6226,11.9766,11.8448} 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

知道基本初等函数概念、学习教材第二章2.2节、2.4节内容——用Mathematia数学软件绘制平面及空间曲线。

三、实验所用主要仪器 计算机

四、实验内容

1.在习题二的1-4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

P45-1.1=Plot[x^4-5x^3+7x^2-3x,{x,-0.5,3.5}]

Set::write: Tag _Plus_ in _-1.1+P45_ is Protected. ?

?13246 p45-2.1=

ImplicitPlot[x4+y3?1,{x,-1.5,1.5}]

Set::write: Tag _Plus_ in _-2.1+p45_ is Protected. ?

?1.50.51.0

P45-3.1=ParametricPlot[{3t/(1+t^3),3t^2/(1+t^3)},{t,-6,6}] Set::write: Tag _Plus_ in _-3.1+P45_ is Protected. ?

421.00.50.51.01.52.024 P45-4.1= PolarPlot[2t,{t,0,3Pi}] Set::write: Tag _Plus_ in _-4.1+P45_ is Protected. ? ?51015 Mi={{1,2.3},{2,4.9},{3,6.4},{4,7.0},{5,6.5},{6,6.8},{7,8.0},{8,10.6}} ListPlot[Mi] {{1,2.3},{2,4.9},{3,6.4},{4,7.},{5,6.5},{6,6.8},{7,8. },{8,10.6}} 246810

ListPlot[Mi,PlotJoined?True]

2 46810

ParametricPlot3D[{x=0.5*t^2,y=0.1*t^3,z=9*Cos[2*t]},{t,0,6}]

101520?05 ParametricPlot3D[{x=Cos[(t/10)]*Cos[t],y=Cos[(t/10)]*Sin[t],z=Sin[(t/10)]},{t,0,24*?}]

?0.00.51.0 五、讨论

教师评语

实验三 函数变换对函数图形的影响

一、实验目的

熟悉函数f(ax)、af(x)、f(x?b)、f(x)?b与f(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)?sinx,用函数绘图命令分别就a??1,?,,2画出 f(ax),???x??为实验函数,

22???x??11 的图形, 观察f(x)与f(ax)的图形变化特点。

11222.以函数f(x)?sinx,???x??为实验函数,用函数绘图命令分别就a??1,?,,2画出af(x),

???x??的图形, 观察f(x)与af(x)的图形变化特点。

3.以函数f(x)?sinx,???x??为实验函数,用函数绘图命令分别就b??2,2画出 f(x?b),???x?? 的图形, 观察f(x)与f(x?b)的图形变化特点。

4.以函数f(x)?sinx,???x??为实验函数,用函数绘图命令分别就b??2,2画出 f(x)?b, ???x??的图形, 观察f(x)与f(x)?b的图形变化特点。 五、实验步骤与结果

C1=Plot[Sin[x],{x,-Pi,Pi},PlotStyle?Red]

1230.51.0?

C2=Plot[Sin[-x],{x,-Pi,Pi},PlotStyle?Green]

?1230.51.0

C3=Plot[Sin[-1/2x],{x,-Pi,Pi},PlotStyle?Blue]

1231.00.5?

C4=Plot[Sin[1/2x],{x,-Pi,Pi},PlotStyle?Black]

?1230.51.0

C5=Plot[Sin[2x],{x,-Pi,Pi},PlotStyle?Cyan]

?1230.51.0

Show[C1,C2,C3,C4,C5]

1230.51.0? C6=Plot[-Sin[x],{x,-Pi,Pi},PlotStyle?Magenta]

123?0.51.0 C7=Plot[-1/2Sin[x],{x,-Pi,Pi},PlotStyle?Yellow]

?1230.20.4 C8=Plot[1/2Sin[x],{x,-Pi,Pi},PlotStyle?Brown]

1230.20.4? C9=Plot[2Sin[x],{x,-Pi,Pi},PlotStyle?Orange]

312?

Show[C1,C6,C7,C8,C9,PlotRange?All]

3?12

C10=Plot[Sin[x-2],{x,-Pi,Pi},PlotStyle?Pink]

?1230.51.0

C11=Plot[Sin[x+2],{x,-Pi,Pi},PlotStyle?Purple]

1 23?0.51.0 Show[C1,C10,C11]

?1230.51.0

C12=Plot[Sin[x]-2,{x,-Pi,Pi},PlotStyle?Darker[Yellow]]

?1232.52.01.51.0

C13=Plot[Sin[x]+2,{x,-Pi,Pi},PlotStyle?Darker[Green]]

?1231.52.02.53.0

Show[C1,C12,C13,PlotRange?All]

?123

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。 二、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. 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)(x^2+2x+4)+(x+5)(x^2-5x+25)] 117+2 x3

Simplify[(y-2)(y^2-6y-9)-y(y^2-2y-15)] -6 (-3-3 y+y2)

Expand[(a+b)^3] a3+3 a2 b+3 a b2+b3

Expand[(x+y-2)^2] 4-4 x+x2-4 y+2 x y+y2

Factor[x^5+y^5]

(x+y) (x4-x3 y+x2 y2-x y3+y4)

Factor[a^8-b^8]

(a-b) (a+b) (a2+b2) (a4+b4)

Cancel[(x^3+y^3)/(x^2-y^2)] (x2-x y+y2)/(x-y)

Cancel[(x^2+y^2-z^2+2xy)/(x^2-y^2+z^2-2xy)] (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+1)+2/(x-2)-3/(x+3)] (6 (1+2 x))/((-2+x) (1+x) (3+x))

Apart[(x-3)/(x^3-x)] -(1/(-1+x))+3/x-2/(1+x)

Apart[3/(1-x^3)]

-(1/(-1+x))+(2+x)/(1+x+x2) Apart[6(1+2x)/(x+1)(x-2)(x+3)] -72+6 x+12 x2+36/(1+x)

Apart[2(1+x^2)/(x-1)(x+1)^2] 14+16/(-1+x)+10 x+6 x2+2 x3

1/4 n2 (1+n)2

k?1

k?1?2/8

k?1-((x (1+x))/(-1+x)3)

n?10

n?21/2

?n?1??????????????????????????nk^3?12k1^2

?k^2x^k

?1n?2

?11n^2

11nn2

2

Solve[x^2-5x+3x+6==0,x] {{x?1-?

5},{x?1+?

5}}

Solve[x^4+x^2+m?0,x] {{x?-(

114m/2)},{x?

114m/2},{x?-(

114m/2)},{x?

114m/2}}

Solve[

x1+

x1?c,x]

{{x?(4+c4)/(4 c2)}}

Solve[{{x?-x^21-mx+1?0,x]

22mxmx2},{x?22mxmx2}}

Solve[{x-y==m,x^2+y^2==n},{x,y}] {{x?1/2 (m-(-m+

m22n),y?1/2

(-m-

m22n)},{x?1/2 (m+

m22n),y?1/2

m22n)}}

Solve[{x^2-y?a,x+y?b},{x,y}] {{x?1/2 (-1-14a4b),y?1/2+b+1/2

14a4b},{x?1/2 (-1+

14a4b),y?1/2

(1+2 b-14a4b)}}

Solve[Cos[x]-x?0,x]

Solve::nsmet: This system cannot be solved with the methods available to Solve. ? Solve[-x+Cos[x]?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.f(x)?sinxx,分别取x0?0,1,?,求极限limf(x),思考本题的实验结果使你对求极限问题的认识。

x?x02.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.利用自然数e的极限定义,实验当n??时(1?)n?e。

n14.选择一道与求导数有关的应用题用Mathematia数学软件的命令来处理其中的导数计算问题。

五、实验步骤与结果 Limit[Sin[x]/x,x?0] 1

Limit[Sin[x]/x,x?1] Sin[1]

Limit[Sin[x]/x,x??] 0 D[

1x^3,x]

(3 x2)/(2

1x3)

v=x*y+3*x^2-5*y-7 D[v,x]

-7+3 x2-5 y+x y 6 x+y

v=(1-x)/(1+x) D[v,{x,20}]

(1-a Cos[t])/(1+a Cos[t])

?aCos????t,20410

18

1aCost1aCost x22x+3352212864000 ?x26

D[?2*x+x^2,{x,20}]

2x670442572800 ?????x22x (2+2 x)+2514159648000 ?2

x2 (2+2

x22xx)+670442572800 ?2x (2+2 x)+83805321600 ?12

x22x (2+2 x)+5587021440 ?8

14

(2+2

2xx2x)+211629600 ?2x(2+2 x)+?x22xx2 (2+2 x)+4651200 ?2xx2 (2+2 x)+58140 ?2xx2 (2+2 x)+380 ?16

(2+2 x)20

Limit[(1+1/n)n,n??] ?

D[Sin[a*x]+Cos[b*x],{x,2}] -b2 Cos[b x]-a2 Sin[a 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、函数的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x0??1,0,2,将 f(x)按(x?x0)展开成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。从这个实验中,能给你提供哪些思考?

2. 在你学习的数学分析教材中,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 Series[x*?x,{x,-1,8}]

-(1/?)+(x+1)2/(2 ?)+(x+1)3/(3 ?)+(x+1)4/(8 ?)+(x+1)5/(30 ?)+(x+1)6/(144 ?)+(x+1)7/(840 ?)+(x+1)8/(5760 ?)+O[x+1]9 Series[x*?x,{x,0,8}]

x+x2+x3/2+x4/6+x5/24+x6/120+x7/720+x8/5040+O[x]9 Series[x*?x,{x,2,8}]

2 ?2+3 ?2 (x-2)+2 ?2 (x-2)2+5/6 ?2 (x-2)3+1/4 ?2 (x-2)4+7/120 ?2 (x-2)5+1/90 ?2 (x-2)6+1/560 ?2 (x-2)7+(?2 (x-2)8)/4032+O[x-2]9

a=x+x2+x3/2+x4/6+x5/24+x6/120+x7/720+x8/5040

Plot[a,{x,-4,4}]

x+x2+x3/2+x4/6+x5/24+x6/120+x7/720+x8/5040

2015105-4-22 ? Graphics ?

Series[?x,{x,0,6}]

1+x+x2/2+x3/6+x4/24+x5/120+x6/720+O[x]7 Series[Sin[x],{x,1,10}]

Sin[1]+Cos[1] (x-1)-1/2 Sin[1] (x-1)2-1/6 Cos[1] (x-1)3+1/24 Sin[1] (x-1)4+1/120 Cos[1] (x-1)5-1/720 Sin[1] (x-1)6-(Cos[1] (x-1)7)/5040+(Sin[1] (x-1)8)/40320+(Cos[1] (x-1)9)/362880-(Sin[1] (x-1)10)/3628800+O[x-1]11

b=2 ?2+3 ?2 (x-2)+2 ?2 (x-2)2+5/6 ?2 (x-2)3+1/4 ?2 (x-2)4+7/120 ?2 (x-2)5+1/90 ?2 (x-2)6+1/560 ?2 (x-2)7+(?2 (x-2)8)/4032 Plot[b,{x,-4,4}]

2 ?2+3 ?2 (-2+x)+2 ?2 (-2+x)2+5/6 ?2 (-2+x)3+1/4 ?2 (-2+x)4+7/120 ?2 (-2+x)5+1/90 ?2 (-2+x)6+1/560 ?2 (-2+x)7+(?2 (-2+x)8)/4032

20015010050-4-22 ? Graphics ?

c=-(1/?)+(x+1)2/(2 ?)+(x+1)3/(3 ?)+(x+1)4/(8 ?)+(x+1)5/(30 ?)+(x+1)6/(144 ?)+(x+1)7/(840 ?)+(x+1)8/(5760 ?) Plot[c,{x,-4,4}] 六、讨论 教师评语

实验七 求函数的极值

一、实验目的

理解一元函数极值和极值点、最值和最值点概念。熟悉Mathematia数学软件的求函数极值和极值点命令。 二、实验原理

知道函数极值和极值点概念,学习教材第七章7.3节、第二章2.2节内容。 三、实验所用主要仪器

四、实验内容

1.在你学习的数学分析教材中,分别选择2道有关求函数极值和极值点、最值和最值点的习题,

用Mathematia数学软件命令来计算。

2.选择一道与求极值有关的应用题,用Mathematia数学软件的命令来处理其中的极值计算问题。 五、实验步骤与结果 w=?.3*x*Sin[2*x] FindMinimum[w,{x,6}] ?0.3 x Sin[2 x]

{-5.26217,{x?5.57223}} w=x*(5-2*x)*(8-2*x) FindMinimum[w,{x,8}] (5-2 x) (8-2 x) x

{-7.40741,{x?3.33333}} a=x^4+3*x^3-5*x^2-8*x+6 FindMinimum[a,{x,5}] 6-8 x-5 x2+3 x3+x4

{-3.54268,{x?1.20442}} 六、讨论 教师评语

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