2022年学习matlab笔记 .pdf

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1、学习必备欢迎下载Matlab 的数学运算功能1 数据分析：约定：1 若 x 是矢量，不论是行矢量还是列矢量，运算是对整个矢量进行。2 若 x 是数组，则命令运算是按列进行的，即默认每个列是由一个变量的不同“观察”所得数据组成。max(x)找 x 各列的最大元素，mean(x)平均值median(x)中位元素，min 最小元素std（x）各列的标准差，prod(x)元素之积，sum(x)之和，S=cumsum(x)p=cumprod(x)累计和，累计积sort(x)各列元素按递增排序。2 离差分析var(x)各列方差，std(x)range(x)标准差，极差，cov(x)协方差阵，cov(x,y

2、)2 个矩阵的协方差阵corrcoef(x)自相关阵，corrcoef(x.,y)3 数值分析：p=poly(A),p=a0,a1,，an 创建多项式格式，roots(p)求 根，polyval(P,A),polyvalm(P,m)求 值conv(a,b)相 乘q,r=deconv(a,b)除法p=polyder(p),p=polyder(p1,p2)q,r=polyder(p1,p2)多顶式求导4 数值插值一维：interp1 二维：interp2 ZI=interp2(X,Y,Z,XI,YI)ZI=interp2(Z,XI,YI)ZI=interp2(Z,n)ZI=interp2(X,Y,

3、Z,XI,YI,method)三维：VI=inter3(x,y,z,v,x1,y2,z3)VI=inter3(v,x1,y2,z3)VI=inter3(v,n)VI=inter3(x,y,z,v,x1,y2,z3,method)Nearest linear spline pchip=cubic 最近，线性（默认）三次样条，分段三次 hermite 学习必备欢迎下载5 利用 matlab 内建函数进行线性曲线按拟合p,e=polyfit(x,y,n)6 极小值 一维；X=fminbnd(fun,a,b)x,y=fminbnd(fun,a,b)多：X=fminsearch(fun,a)x,y=fm

4、insearch(fun,a)零点：X=fzero(fun,a)X=fzero(fun,a,b)X,y=fzero(fun,a)X.y=fzero(fun,a,b)7 常微分方程的求解：x,y=ode23(f,x0,xn,y0)x,y=ode45(f,x0,xn)二，符号运算1 变量的定义sym（变量名）或 sym(表达式)定义一个符号变量或符号表达式格式：syms 变量 1 变量 n 定义这些变量为符号变量符 号 运 算 函 数：symadd(s1,s2)symsub()symmul()symdiv()sympow()，s1+s2,-,*,/,2 符号表达式的化简函数：collect(s,x

5、)合并自变量 x 的同幂系数expand(s)符号表达式 x 的展开factor(s)因式分解numden(s)s 的分式通分simple(s)寻找表达式的最简型文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N

6、6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9

7、L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8

8、U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8

9、P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ

10、6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W

11、3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9学习必

12、备欢迎下载simplify(s)符号表达式的化简radsimp(s)对含根式的表达式的化简horner(s)符号表达式的嵌套形式替代函数：R,SYM=subexpr(s,SYM)用变量 symr 的值代替符号表达式s 中重复出现的字符串，r 是返回替换后的结果。R=subs(S,old,new)用 new 代替 old vpa()强制求值极限函数：limit(F,x,a)F=F(x)的极限值，当 x-a limit(F,a)用 findsym(F)确定 F 中的自变量，设为变量x，再计算 F 的极限值，当 x-a 时。limit(F,x,a，right)limit(F,x,a,left)计算单

13、侧极限。求导函数：diff(S,v,n)对表达式 s 中指定的符号变量v 计算 s的 n 阶导数。积分函数：R=int(S,v,a,b)对 v 从 a 到 b 定保积分，R=int(S,v)计算不定积分，R=int(S)v=findsym(S)R=int(S,a,b)对 v 从 a到 b 定保积分,v=findsym(S)numeric()可以计算积分的数值。傅里叶函数：F=fourier(f)文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5

14、 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6

15、X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P1

16、0 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M

17、2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T

18、9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:

19、CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J

20、10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9学习必备欢迎下载F=fourier(f,v)对 v 进行。F=fourier(f，u,v)fu Fv f=ifourier(F)拉普拉斯：L=laplace(F)F=ilaplace(L)F=ilaplace(L,y)F=ilaplace(L,y,x)Z 变换：F=ztrans(f)F=ztrans(f,w)F=ztrans(f,k,w)f=ztrans(F)f=zt

21、rans(F,w)f=ztrans(F,k,w)代数方程的符号解函数：g=solve(eq,var)g=solve(eq)g=solve(eq1)g=solve(eq1,，var1)eg:g=solve(x+z=3,x+2*z=5)求出的如：x：1x1 sym 表示 g 是一个结构数组，其中每一个元素为一符号类型的向量。用x1=g.x 可查看数值。注意：用.来查看。文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 Z

22、J6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1

23、W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档

24、编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1

25、N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S

26、9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH

27、8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E

28、8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9学习必备欢迎下载常微分的：r=dsolve(eq1,eq2,，cond1,cond2 ，v)D:表示对自变量的微分算子。如：Dy,例如：s=dsolve(Dy=3*x2 ,y(2)=0.5)D2=d2/dx2 D 后面的字母则表示为因变量。v 为指定变量。泰勒级数：r=taylor(f,n,v)r=taylor(f,n,v,a)r=taylor(f)可视化符号计算函数：funtool functi

29、on 函数的函数名要与保存的文件名一致，本章中fminbnd fzero ode23 ode45中可用。文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1

30、W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档

31、编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1

32、N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S

33、9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH

34、8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9文档编码:CE1N6J10S9L5 HH8U6X3E8P10 ZJ6M2N1W3T9