1、电子一班王申江实验十 符号计算基础与符号微积分一、实验目的1、掌握定义符号对象的方法2、掌握符号表达式的运算法则及符号矩阵运算3、掌握求符号函数极限及导数的方法4、掌握求符号函数定积分和不定积分的方法二、实验内容1、已知 x=6,y=5，利用符号表达式求 13xzy提示：定义符号常数 。6,5xsymsmx=sym(6),y=sym(5)x =6y =5 z=(x+1)/(sqrt(3+x)-sqrt(y)z =7/(3-5(1/2)2、分解因式（1） 4xyx=sym(x)x =x y=sym(y)y =y A=x4-y4A =x4-y4 factor(A)ans =(x-y)*(x+y)*
2、(x2+y2)（2）5135factor(sym(5135)ans =(5)*(13)*(79)3、化简表达式（1） 1212sincosinbyte1=sym(byte1)byte1 =byte1 byte2=sym(byte2)byte2 =byte2 S=sin(byte1)*cos(byte2)-cos(byte1)*sin(byte2)S =sin(byte1)*cos(byte2)-cos(byte1)*sin(byte2) simplify(S)ans =sin(byte1)*cos(byte2)-cos(byte1)*sin(byte2)（2）24831xx=sym(x)x =
3、x S=(4*x2+8*x+3)/(2*x+1)S =(4*x2+8*x+3)/(2*x+1) simple(s) simple(S)simplify:2*x+3radsimp:2*x+3combine(trig):2*x+3factor:2*x+3expand:4/(2*x+1)*x2+8/(2*x+1)*x+3/(2*x+1)combine:(4*x2+8*x+3)/(2*x+1)convert(exp):(4*x2+8*x+3)/(2*x+1)convert(sincos):(4*x2+8*x+3)/(2*x+1)convert(tan):(4*x2+8*x+3)/(2*x+1)coll
4、ect(x):(4*x2+8*x+3)/(2*x+1)ans =2*x+34、已知 12010,abcPAdefghi完成下列运算：（1） B=P1 P2 AP1=0 1 0;1 0 0;0 0 1P1 =0 1 01 0 00 0 1 P2=1 0 0;0 1 0;1 0 1P2 =1 0 00 1 01 0 1 a=sym(a);b=sym(b);c=sym(c);d=sym(d);e=sym(e);f=sym(f);g=sym(g);h=sym(h);i=sym(i); A=a b c;d e f;g h iA = a, b, c d, e, f g, h, iB=P1*P2*AB =
5、d, e, f a, b, c a+g, b+h, c+i（2） B 的逆矩阵并验证结果C=inv(B)C = (i*b-c*h)/(i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b), (-e*c-i*e+f*b+f*h)/(i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b), -(-e*c+f*b)/(i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b) -(i*a-c*g)/(i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b), -(-d*c-i*d+f*a+f*g)/(i*d*b-d*c*h-i*a*
6、e+a*f*h+g*e*c-g*f*b), (-d*c+f*a)/(i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b) (a*h-b*g)/(i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b), (-d*b-d*h+e*a+e*g)/(i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b), -(-d*b+e*a)/(i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b)（3）包括 B 矩阵主对角线元素的下三角阵tril(B)ans = d, 0, 0 a, b, 0 a+g, b+h, c+l（4）B 的行列式值
7、det(B)ans =i*d*b-d*c*h-i*a*e+a*f*h+g*e*c-g*f*b5、用符号方法求下列极限或导数2sintan313 2222 0,121limircos2li1s23,4cosln5, ,xxxxxy xyeeyyatdAdAxttt yffxye 求已 知 ， 分 别 求 、 、已 知 求 、(1)x=sym(x)x =x f=(x*(exp(sin(x)+1)-2*(exp(tan(x)-1)/sin(x).3f =(x*(exp(sin(x)+1)-2*exp(tan(x)+2)/sin(x)3 limit(f)ans =-1/2（2）x=sym(x)x =x
8、 f=(sqrt(pi)-sqrt(acos(x)/sqrt(x+1)f =(3991211251234741/2251799813685248-acos(x)(1/2)/(x+1)(1/2) limit(f,x,-1,right) ans =-inf（3）x=sym(x)x =x y=(1-cos(2*x)/xy =(1-cos(2*x)/x diff(y,x,1)ans =2*sin(2*x)/x-(1-cos(2*x)/x2 diff(y,x,2)ans =4*cos(2*x)/x-4*sin(2*x)/x2+2*(1-cos(2*x)/x3（4）x=sym(x)x =x y=(1-co
9、s(2*x)/xy =(1-cos(2*x)/x diff(y,x,1)ans =2*sin(2*x)/x-(1-cos(2*x)/x2 diff(y,x,2)ans =4*cos(2*x)/x-4*sin(2*x)/x2+2*(1-cos(2*x)/x3 syms a t x; f=sym(ax,t3;t*cos(x),log(x)f = ax, t3 t*cos(x), log(x) diff(f,x,1); diff(f,x,1)ans = ax*log(a), 0 -t*sin(x), 1/x diff(f,t,2)ans = 0, 6*t 0, 0 diff(f,x)/diff(f,
10、t)ans = 0, 1/cos(x)*ax*log(a) 1/3/t2/x, -1/cos(x)*t*sin(x)（5）syms x y f=(x.2-2.*x).*exp(-x.2-y.2-x.*y)f =(x2-2*x)*exp(-x2-y2-x*y) diff(y,x)ans =0 a=diff(f,x)/diff(f,y)a =(2*x-2)*exp(-x2-y2-x*y)+(x2-2*x)*(-2*x-y)*exp(-x2-y2-x*y)/(x2-2*x)/(-2*y-x)/exp(-x2-y2-x*y) x=0;y=1; eval(a)ans =Inf6、用符号方法求下列积分48
11、222042ln2012arcsin1314xxdxxxde（1）sym(x)ans =x f=1/(1+x4+x8)f =1/(1+x4+x8) int(f,x)ans =1/6*3(1/2)*atan(1/3*(2*x-1)*3(1/2)+1/6*3(1/2)*atan(1/3*(1+2*x)*3(1/2)-1/12*3(1/2)*log(-x2+3(1/2)*x-1)+1/12*3(1/2)*log(x2+3(1/2)*x+1)（2）sym(x)ans =x f=1/(asin(x).2.*sqrt(1-x.2)f =1/asin(x)2/(1-x2)(1/2) int(x)ans =1/2*x2（3）syms x f=(x.2+1)/(x.4+1)f =(x2+1)/(1+x4) int(f,x,0,inf)ans =1/2*pi*2(1/2)（4）syms x f=exp(x).*(1+exp(x).2f =exp(x)*(1+exp(x)2 int(f,x,0,log(2)ans =-7/3+exp(6243314768165359/9007199254740992)+exp(6243314768165359/9007199254740992)2+1/3*exp(6243314768165359/9007199254740992)3
