MATLAB入门学习Matlab数值计算课件

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,11/7/2009,#,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Matlab,数值计算,第,10,讲,Matlab数值计算第10讲,6.1,多项式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,2,多项式的,M,A,T,L,A,B,表达,多项式由一个行向量表示,该向量元素是该多项式的系数,且按降幂次序排列,如：多项式,x,4,12x,3,25x,116,由行向量：,p=1,-,12,0,25,116,表示。,注意，必须包括具有零系数的项。,求解多项式的根？,r,oots,指令,6.1 多项式(polynomial)Application,6.1,多项式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,3,举例：求解多项式,x,4,12x,3,25x,116,的根,p,=,1,-12,0,25,116,p,=,1,-12,025116,r,=,r,oots(p),r,=,11,.,7473,2,.,7028,-1.2,251,+,1.4672i,-1.2,251,-,1.4672i,M,A,T,L,AB,按惯例规定，多项式是行向量，根是列向量,6.1 多项式(polynomial)Application,6.1,多项式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,4,已知多项式的根，求解多项式,？,能！,使用,po,l,y,指令,举例：由上例所得的根求其多,项,式,pp=po,l,y(r),p,p,=,1.0,0,00,-,12.,0,000,-,0.0000,25.0000,即：,x,4,12,x,3,25,x,116,116.0000,6.1 多项式(polynomial)Application,6.1,多项,式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,5,多项式的乘法,(,co,n,v,指令,),举例：多项式,a(x)=,x,3,2,x,2,3,x,4,和,b(x,),=,x,3,4,x,2,9,x,1,6,的乘积。,a=1234,;b=1,c=co,n,v(a,b),c,=,16205075,4916;,8464,两,个,以,上,的,多,项,式,的,乘,法,需,要,重,复,使,用,co,n,v,.,6.1 多项式(polynomial)Application,6.1,多项式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,6,多项式加法,:,M,A,T,L,AB,没有提供进行加法运算的函数。,如果两个多项式向量大小相同，标准的数组加法有效。,把多项式,a(x,),与,上,面给,出,的,b,(x,),相加。,d=a+b,d,=,261220,结果,:,d(x)=,2x,3,6x,2,1,2,x,20,当两个多项式阶次不同，低阶的多项式必须用首零填补，使其 与高阶多项式有同样的阶次。,考虑上面多项,式,c,和,d,相,加,：,e=c+,0,0,0,d,e,=,162052819684,结果,:,d(x,)=,x,6,+6x,5,+,2,0 x,4,+,5,2x,3,+,8,1x,2,+,9,6x,+,84,6.1 多项式(polynomial)Application,6.1,多项式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,7,问题：编写一个多项式加法运,算,的函数文件,明确需求,定义一个函数，需要有两个输入参数（比如：,p,1,、,p2,），一个输出参数,p_out,。,p,1,、,p,2,表示两个待计算的多项式。,p_out,表示两个多项式的求和结果,函数的内部处理,如,p,1,、,p,2,两参数大小相等，则直接相加,:,p_out=p1+p2,如,p,1,、,p,2,两参数大小不等：,If,length(,p,1)le,n,gt,h,(p2),P,2,前面要补,0,元素，使,p1,、,p2,两参数大小相等,否则,P,1,前面要补,0,元素，使,p1,、,p2,两参数大小相等,6.1 多项式(polynomial)Application,6.1,多项式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,8,函数文件的编写,f,unction,p_out=poly_sum(p1,p2),%,calculate,the,sum,of,two,polynomials,if,length(,p,1)=,=,length(,p,2),p_out=p1+p,2,;,elseif,length(,p,1),length(p2)p2=,z,e,r,os(1,length(p,1,),-length(,p,2),p2;,p_out=p1+p,2,;,else,p1=,z,e,r,os(1,length(p,2,),-length(,p,1),p1;,p_out=p1+p,2,;,end,6.1 多项式(polynomial)Application,6.1,多项式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,9,多项式的除法,(,deco,n,v,),举例说明：,c(x,)=,x,6,6,x,5,20,x,4,50,x,3,7,5,x,2,8,4,x,64,除以,b(x)=,x,3,4,x,2,9,x,16,c,=,1,b=1,4,6,2,0,50,75,84,64;,91,6,;,q,r,=,deco,n,v,(c,b),q=,1234,r,=,0000000,6.1 多项式(polynomial)Application,6.1,多项式,(polynomial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,10,多项式的导,数,(pol,y,der),举例：求,b(x)=,x,3,4,x,2,9,x,16,的导数。,b=149,d=pol,y,der(b),d,=,389,1,6,;,结果为：,3,x,2,8,x,9,另外两种形式为：,p,=,pol,y,der,(,P,Q),：求,P*Q,的导函数,p,q,=,pol,y,der,(,P,Q),：求,P/Q,的导函数，导数分子存入,p,分母存入,q,6.1 多项式(polynomial)Application,6.1,多项式,(polyno,m,ial),Application,of,Matlab,Langu,a,g,e,201,3,/9/10,11,多项式的估值,(poly,v,al),举例：绘制,p(x)=,x,3,4,x,2,7,x,10,在,-,1,3,段上的曲线。,x=li,nspace,(,-,1,3);,p=14,-,7,-,10;,v=p,o,ly,v,al(,p,x);,%choose,100,data,points,between,-,1and,3.,plot(x,v);,tit,le(x3,+,4x2,-,7,x,-,1,0,);xlabel(,x),6.1 多项式(polynomial)Application,6.1,多项式,(polynomial),p(x)=,x,3,4,x,2,7,x,10,在,-1,3,段上的曲线,:,Application,of,Matlab,Langu,a,g,e,201,3,/9/10,12,6.1 多项式(polynomial)p(x)=x34,6.,2,函数的数值导数,导数定义为：,则,y=f(x,),的导数可近似为：,h,0,f,(,x,h,),f,(,x,),(,x,h,),(,x,),lim,d,y,d,x,d,y,f,(,x,h,),f,(,x,),d,x,(,x,h,),(,x,),这里,h0,它是,y,的有限差分除以,x,的有限差,分,。,M,A,TLA,B,中没有直,接,提供数值导,数,的函数，只,有,计算向,前,差,分的,函,数,diff,，其调用,格,式为：,DX,=,diff(X),计算向量,X,的向前差分,DX,=,diff(X,，,n),计算向量,X,的,n,阶向前差分,Application,of,Matlab,Langu,a,g,e,201,3,/9/10,13,6.2 函数的数值导数导数定义为：则y=f(x)的导,例题,Application,of,Matlab,Langu,a,g,e,201,3,/9/10,14,设,x,由,0,2,间均匀分布,的,10,个点组成，,求,si,n,x,的,1-3,阶差分。,命令如下：,X=,linspace(0,2*pi,10,),;Y,=,sin(,X,);,D,Y,=,diff,(,Y),D2Y,=,di,f,f,(,Y,2),D3Y,=,di,f,f,(,Y,3),D,Y,=,0.64280.3420,0.6428,D2Y,=,-,0.1188-0.5240-0.6840-0.5240-0.11880.3420,-,0.3008,D3Y,=,-,0.1600,-,0.4608,-,0.4052,-,0.1600,0.1600,0.4052,0.4608,0.3008,0.0556,0.2452,0.3201,0.2452,0.0556,-,0.1600,例题Application of Matlab Langua,6.2,函数的数值导数（续）,例：设,f,(,x,),x,3,2,x,2,x,1,2,6,x,5,5,x,2,在,-,3,3,区间内,以,0.,0,1,为步长求数,值,导数。并画,出,导函,数图像。,程序如下：,f,=,in,line(,sqrt(x.3+,2,*x.,2,-,x+12)+(,x,+5,),.,(1/6,),+5*,x,+,2,),;,8,内联函数,7,.,5,%,定义式求导数,x,=,-,3:,0,.01,:,3;,dx=,di,f,f(f,(,x,3,.0,1,),)/0.01;,plot(x,dx),7,%,根,据,6,.,5,6,-3,-2,-1,0,1,2,3,4,.,5,5,.,5,5,Application,of,Matlab,Langu,a,g,e,201,3,/9/10,15,6.2 函数的数值导数（续）例：设 f(x)x3,6.3,数值积分,Application,of,Matlab,Langu,a,g,e,201,3,/9/10,16,一元函数的数值积分,常用积分指令：,qua,d,和,quadl,。,一般说来,，,qu,a,d,l,比,qu,a,d,更,有,效。,具体调用格式如下：,q=,quadl(,f,un,a,b),q=,quadl(,f,un,a,b,tol),q=,quadl(,f,un,a,b,tol,t,r,ace)q,f,cnt=,quadl(,f,un,a,b,.,.,),输入,量,f,un,为被积,函,数的,句,柄。,输入,量,a,b,分别是积分的下限、和,上,限，,都,必须,是,确定,的,数值,;,前,3,个输入参数是调用积,分,指令,所,必须,的,，其,他,可以,缺,省,;,输入,量,to,l,是一个标量，控制绝对,误,差,;,输入,量,t,r,ace,为非,0,值,时,，将,