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1、1求函数在指定点的导数值>>symsx>>a=[xx^2x^3;12*x3*x^2;026*x];>>f=det(a);>>diff(f,1)ans=6*x^2>>diff(f,2)ans=12*x>>diff(f,3)ans=122符号法求下列函数的导数或积分1）y=x10+10x+logx10,求y’f=('x^10+10^x+log(10)/log(x)')f=x^10+10^x+log(10)/log(x)>>diff(f)ans=10*x^9+10^x*log(10)-log(10)/log(x)^2/x2）y=ln(1+x),求y’’∣x=1f
2、=('log(1+x)/log(e)')f=log(1+x)/log(e)>>diff(f,1,2)ans=-1/(1+x)^2/log(e)3)y=ex/cosx,求y’f=('exp(x)/cos(x)')f=exp(x)/cos(x)>>diff(f)ans=exp(x)/cos(x)+exp(x)/cos(x)^2*sin(x)4）functionf=fun0(t)f=t*sin(t)int('fun0','0','pi')ans=1/2*pi^25)已知函数z=sin(xy),计算symsxy>>z=('sin(x*y)')z=sin(x*y)>
3、>diff(diff(z,y,2),x)ans=-cos(x*y)*y*x^2-2*sin(x*y)*x3用数值方法求定积分1）functionf=fun(x)f=x.^2.*sqrt(2.*x.^2+3)quad('fun',1,5)ans=232.80572）functionf=fun(x)f=x./sin(x).^2quad('fun',pi/4,pi/3)ans=0.38354已知数据[x,y]如下表，试求2次拟合多项式f(x)，然后求x=0.05,0.25,0.45,0.65,0.85,1.05各点的函数近似值，并绘出拟合曲线及求得的函数点。x0
4、.00.10.20.30.40.50.60.70.80.91.0y-0.4471.9783.286.167.087.347.669.569.489.311.2>>x=[0.00.10.20.30.40.50.60.70.80.91.0];>>y=[-0.4471.9783.286.167.087.347.669.569.489.311.2];>>a=polyfit(x,y,2)a=-9.810820.1293-0.0317>>x0=[0.0:0.1:1.0];>>y0=a(3)+a(2).*x0+a(1).*x0.^2;>>plot(x,y,'*')>>h
5、oldon>>plot(x0,y0,'-r')>>x1=[0.050.250.450.650.851.05];>>y1=interp1(x0,y0,x1)y1=Columns1through50.92574.36297.01538.88289.9654Column6NaN5求方程exsinx=0在区间[-4,-3]上的一个根。x=fzero('exp(x).*sin(x)',[-4,-3])x=-3.14166已知某函数的离散点列如下X-4-3-2-101234y0.972793.42343.81861.84150-0.15853-0.18141-2.57
6、66-7.0272分别使用hermite插值、三次样条插值、三次方插值估算在x在2.5，1.5，0.5，-0.5，-1.5，-2.5的函数值，并在同一张图上绘制出三条曲线。>>x0=[-4-3-2-101234];>>y0=[0.972793.42343.81861.84150-0.15853-0.18141-2.5766-7.0272];>>x=[-4:1:4];>>y=pchip(x0,y0,x);>>plot(x,y,'-r')>>holdon>>y=spline(x0,y0,x);>>plot(x,y,'-b')>>holdon>>a=polyfi
7、t(x0,y0,3)a=0.0000-0.2395-1.00001.6092>>y=a(4)+a(3).*x+a(2).*x.^2+a(1).*x.^3;>>plot(x,y,'-k')>>t=[2.51.50.5-0.5-1.5-2.5];>>g=interp1(x0,y0,t,'pchip')g=Columns1through5-0.9954-0.1693-0.11080.71893.0684Column63.7061>>f=interp1(x0,y0,t,'spline')f=Columns1through5-1.05380.0011-0.24990
8、.75013.0011Column63.9462>>h=inter
