MATLAB基礎(chǔ)實(shí)驗(yàn)三及求解

1、實(shí)驗(yàn)三、符號(hào)運(yùn)算的應(yīng)用1、簡(jiǎn)化"壯+夕+乎+8（比較simple和simplify指令的區(qū)別）clear;syms xf = (1/xa3+6/xa2+8)a(1/3)f =(l/xx3+6/x2+8)人(1/3)simple(f) %simple不返回指定的變量時(shí)，給出所有簡(jiǎn)化的結(jié)果，最 后結(jié)果是最簡(jiǎn)的形式simplify:(l+6*x+8*xa3)/x3)"(1/3)radsimp:1/x*(l+6*x+8*x3)(1/3)combine(trig):(l+6*x+8*x3)/x3)人(1/3)factor:(l + 6*x+8*xa3)/xa3)a(1/3)expan

2、d:(1/xx3+6/xa2+8)人(1/3)combine:(l/x3+6/xx2+8)人(1/3)convert(exp):(1/xx3+6/xa2+8)人(1/3)convert(sincos):(1/xx3+6/xa2+8)人(1/3)convert(tan):(1/x"3 + 6/xa2 + 8)人(1/3)collect(x):(l/x3+6/xx2+8)人(1/3)mwcos2sin:(1/xx3+6/xa2+8)a(1/3)ans =(l/x3+6/xx2+8)人(1/3)=simple(f) %把最簡(jiǎn)的形式賦給變量b =(1/xa3 + 6/xa2 + 8)人(1/

3、3)c = simplify(f) %數(shù)學(xué)上的恒等式化簡(jiǎn)c =(l+6*x+8*xa3)/xa3)a(1/3)2、尸sinor,求心空，叟c = © 、dx da dx2clear;syms x a y = sin(a*x)y =sin(a*x)a = diff(y)a = cos(a*x)*ab = diff(y3a)b = cos(a*x)*xc = diff(y,2)-sin(a*x)*ax29.j (x2 - 2x+2)23、計(jì)算不定積分.定積分、反常積分k訂；ujoat rk/ 2 cos兀.dx j =dxjo sinx+cosxclear;syms xf1 = (xa2

4、+1)/(xa2-2*x+2)a2fl =(xa2+1)/(xx2-2*x+2)x21/4*(2*x-6)/(xx2-2*x+2)+3/2*atan(x-l)f2 = cos(x)/(sin(x)+cos(x)f2 =cos(x)/(sin(x)+cos(x)j =int(f250,pi/2)l/4*pif3 = exp(-xa2)f3 =exp(-x2)k = int(f3,0,inf)k =l/2*pix(l/2)k = vpa(k,4).88654、求級(jí)數(shù)工飛的和s，以及前十項(xiàng)的部分和sl n= “clear;syms ns = symsum(1/na2,15inf)l/6*pix2s1

5、 = symsum(1/na2,1,10)si =1968329/1270080s1 = vpa(s1,4)si =1 5505、求一元二次方程or，+bx + c = 0的根.f = sym(a*xa2+b*x+c=0)clear;syms a b c xf = a*xa2+b*x+cf =a*x2+b*x+cx = solve l/2/a*(-b+(b'2-4*a*c)(1/2)1/2/a*(b2-4*a*c)入(1/2)6、求微分方程y =兀的通解.dsolve(vdy = xjxjans = l/2*x2+cl7、求微分方程+x(o) = l,y(o) = o的特解.y=dso

6、lve(,d2y=dy+x,；y(0)=1,dy(0)=07x,)-l/2*x2+exp(x)-xx - y + x8、求微分方程組.的通解u =2兀x3y=dsolve(,dx =y+x,dy = 2*xf)-l/2*cl*exp(-t)+c2*exp(2*t)cl*exp(-t)+c2*exp(2*t)9、求下列聯(lián)立方程的解(用數(shù)值和符號(hào)運(yùn)算兩種方法)3x + 4y -7z -12w = 45x - 7y + 4z + 2w = -3vx + 8z 5w =9-6x + 5y - 2z + low = -8法一：數(shù)值方法a = 3 4 -7 -12;5 -7 4 2;1 0 8 -5;-6

7、 5 -2 10; b = 4;-3;9;-8;x = ab14841-068160 5337-12429法二：符號(hào)方法clear;syms x y z wf1 = 3*x+4*y-7*z-12*w-4 f2 = 5*x-7*y+4*z+2*w+3 f3 = x+8*z-5*w-9f4 = -6*x+5*y-2*z+10*w+8fl =3*x+4*y-7*z-12*w-4f2 =5*x-7*y+4*z+2*w+3f3 =x+8*z-5*w-9f4 =-6*x+5*y-2*z+10*w+8w x y z=solve(f 1 ,f2,f3,f4)w =-2932/2359-3501/2359-16

8、08/2359 z =1259/2359x= vpa(x;y;z;w,4)x =14846816 5337-1.24310、求極限m = limt ln(x + /z)-ln(x)l = lim力tohclear;syms x h nf1 = (log(x+h) log(x) / hfl =(log(x+h)-log(x)/hl = limit(f1,h,0)l =1/xf2 = (1 - x/n)an(1-x/n)人!1m = iimit(f2,n,inf)exp(-x)11、設(shè)a、b定義如下，試上機(jī)輸出factor(a)和factor(b)的結(jié)果，并指 出那個(gè)結(jié)果才是12345678901

9、234567890的因式分解，為件么？ a=symc12345678901234567890*); % 直接創(chuàng)建符號(hào)常量 b=sym(12345678901234567890); %將數(shù)值常量轉(zhuǎn)換為符號(hào)常量， 有誤差x1=factor(a)xl =(2)* (3)x2* (5)* (101)* (3803)* (3607)* (27961)* (3541)x2=factor(b)x2 = (2)11* (7)*(7324703)*(117570121)isequal(x1,x2)ans12、求函數(shù)/(x) = x4-3x + 8的函數(shù)值，其中x = l：10 (用數(shù)值和符號(hào)運(yùn)算三種方法)符號(hào)，

10、置換f = sym(,xa4 -3*x + 8)xa4 -3*x + 8 fx = subs(f/x1:10)fx =columns1through561880252618columns6through1012862388408065429978f = symfxa4 -3*x + 81)f =xa4 -3*x + 8p = sym2poly(f)p =100-38fx = polyval(p,1:10)fx6188025261812862388408065429978逾亙:飆位,多項(xiàng)式求值p=10 0 -3 8p =10 0-38fx = polyval(p,1:10)fx =618802526181286238840806542997813、把(s +1)3(3, + 4屛+ 7)展成多項(xiàng)式的形式。(用數(shù)值和符號(hào)運(yùn)算兩種方法)毅仏$項(xiàng)式相乘n = conv(conv(1 151 1),conv(1 1,3 4 0 7)n =313212225217f = poly2sym(n/s,)f =3*s6+13*sx5+21*sa4+22*sa3+25*sa2+21*s+