plot   Linear plot. plot(X,Y) plots vector Y versus vector X. If X or Y is a matrix,then the vector is plotted versus the rows or columns of the matrix,whichever line up.  If X is a scalar and Y is a vector, disconnectedline objects are created and plotted as discrete points vertically atX.plot(Y) plots the columns of Y versus their index.If Y is complex, plot(Y) is equivalent to plot(real(Y),imag(Y)).In all other uses of plot, the imaginary part is ignored.Various line types, plot symbols and colors may be obtained withplot(X,Y,S) where S is a character string made from one elementfrom any or all the following 3 columns:b     blue          .     point              -     solidg     green         o     circle             :     dottedr     red           x     x-mark             -.    dashdot c     cyan          +     plus               --    dashed   m     magenta       *     star             (none)  no liney     yellow        s     squarek     black         d     diamondw     white         v     triangle (down)^     triangle (up)<     triangle (left)>     triangle (right)p     pentagramh     hexagramFor example, plot(X,Y,'c+:') plots a cyan dotted line with a plus at each data point; plot(X,Y,'bd') plots blue diamond at each data point but does not draw any line.plot(X1,Y1,S1,X2,Y2,S2,X3,Y3,S3,...) combines the plots defined bythe (X,Y,S) triples, where the X's and Y's are vectors or matrices and the S's are strings.  For example, plot(X,Y,'y-',X,Y,'go') plots the data twice, with asolid yellow line interpolating green circles at the data points.The plot command, if no color is specified, makes automatic use ofthe colors specified by the axes ColorOrder property.  By default,plot cycles through the colors in the ColorOrder property.  Formonochrome systems, plot cycles over the axes LineStyleOrder property.Note that RGB colors in the ColorOrder property may differ fromsimilarly-named colors in the (X,Y,S) triples.  For example, the second axes ColorOrder property is medium green with RGB [0 .5 0],while plot(X,Y,'g') plots a green line with RGB [0 1 0].If you do not specify a marker type, plot uses no marker. If you do not specify a line style, plot uses a solid line.plot(AX,...) plots into the axes with handle AX.plot returns a column vector of handles to lineseries objects, onehandle per plotted line. The X,Y pairs, or X,Y,S triples, can be followed by parameter/value pairs to specify additional properties of the lines. For example, plot(X,Y,'LineWidth',2,'Color',[.6 0 0]) will create a plot with a dark red line width of 2 points.Examplex = -pi:pi/10:pi;y = tan(sin(x)) - sin(tan(x));plot(x,y,'--rs','LineWidth',2,...'Markerfdgecolor','k',...'Markerfacecolor','g',...'MarkerSize',10)

x = 0:pi/1000:2*pi;            % x取值范围由0到2π，pi/1000是递增的步长
y =sin( 2*x + pi/4);          %表示y的函数表达式是sin类型
plot(x,y)

x=linspace(-2, 2, 25);         %在-2到2取25个点
y=linspace(-2, 2, 25);         %在-2到2取25个点
[xx, yy]=meshgrid(x, y);       %生成网格采样点
zz=sqrt( xx.^2 + yy.^2);      %生成矩阵Z
surf( xx,yy,zz);                %画出着色的三维曲面

[X,Y,Z]=meshgrid(linspace(-10,10));       %形成网格数据(X,Y,Z)
V=X.^2+Y.^2-Z.^2;                     %形成体数据V
isosurface(X,Y,Z,V,1);                  %绘制三维隐函数图形X.^2+Y.^2-Z.^2=1
axis equal
colormap([1 0 0]);                      %改变图形颜色为红色
brighten(0.5);                          %进行增亮
camlight right;                         %设置光源位置
lighting phong;                         %设置光照模式
figure(2);
fv=isosurface(X,Y,Z,V,1);                  %计算等值面所对应的面元和顶点
p=patch(fv);                           %绘制等值面
set(p,'FaceColor','red','EdgeColor','none');    %修饰等值面
axis equal                              %等比例显示  

x=-3:1:3;
y=-2:1:2;
[X,Y]=meshgrid(x,y)

x = [0 0 0 0];
y = x;
u = [1 -1 0 0];
v = [0 0 1 -1];
quiver(x, y, u, v);

u = [1 1 1; 1 1 1];
v = u;
quiver(u, v);

[x,y]=meshgrid(-3:.5:3,-3:.5:3);         %生成所需的网格采样点，x与y在-3到3区间
z=y.^2-x.^2;        %定义函数
[u,v,w]= surfnorm(z);         %取三维曲面的法线
quiver3(z,u,v,w) ;    %绘制三维矢量场图

syms x y z                    %定义符号变量
f = 2*y*z*sin(x) + 3*x*sin(z)*cos(y);     %定义函数
gradient(f, [x, y, z])              %利用符号计算函数的梯度

syms x y                        %定义符号变量
F = -(sin(x) + sin(y))^2;             %定义函数
g = gradient(F, [x, y])            %计算梯度的表达式
[X, Y] = meshgrid(-1:.1:1,-1:.1:1);    %产生网格
G1 = subs(g(1), [x y], {X,Y});     %用{X,Y}替换所有出现的[x,y]，然后计算g(1)
G2 = subs(g(2), [x y], {X,Y});     %用{X,Y}替换所有出现的[x,y]，然后计算g(2)
quiver(X, Y, G1, G2);       %绘制梯度对应的箭头图

v = -2:0.2:2;          %定义向量v
[x,y]=meshgrid(v);         %利用v产生网格
z = x.* exp(-x.^2 - y.^2);     %计算网格格点上的函数值
[px,py] = gradient(z,.2,.2);       %数值方法计算梯度
figure
contour(x,y,z);         %绘制函数z的等高线
hold on;                %保持模式打开
quiver(x,y,px,py);          %绘制梯度的箭头图
hold off;               %保持模式关闭

syms x y z real  %定义符号变量
F = [ cos(x+2*y), sin(x-2*y) ];   %定义函数F
g = divergence(F,[x y])                    %求函数F的散度，符号形式
divF=matlabFunction(g);    %将散度转换为函数形式
x=linspace(-2.5,2.5,20);
[X,Y]=meshgrid(x,x);   %定义网格
Fx=cos(X+2*Y);    %F的x分量
Fy=sin(X-2*Y); %F的y分量
div_num=divF(X,Y); %散度的数值形式
pcolor(X,Y,div_num);    %绘制散度
shading interp; %差值
colorbar;   %绘制色条
hold on;    %保持绘图模式打开
quiver(X,Y,Fx,Fy,'k','linewidth',1);    %绘制箭头图

syms x y z
V = [x^3*y^2*z, y^3*z^2*x, z^3*x^2*y];
X = [x y z];
curl(V,X)

syms x y z
f = x^2 + y^2 + z^2;
vars = [x y z];
curl(gradient(f,vars),vars)

%%计算一个余弦函数的一维拉普拉斯矩阵
syms x y z real %定义符号变量
F = [ cos(x+2*y), sin(x-2*y) ];   %定义函数F
G = curl([F,0],[x y z])                    %计算F的旋度，并赋予G
curlF=matlabFunction(G(3));    %将G的z分量，赋予curlF
x=linspace(-2.5,2.5,20);
[X,Y]=meshgrid(x,x);   %定义网格
Fx=cos(X+2*Y);    %计算F的x分量
Fy=sin(X-2*Y); %计算F的y分量
rot=curlF(X,Y);    %计算旋度的值
pcolor(X,Y,rot);    %绘制旋度
shading interp; %颜色做插值
colorbar;   %绘制色条
hold on;    %保持模式打开
quiver(X,Y,Fx,Fy,'k','linewidth',1);    %绘制箭头图，并设置颜色为黑色，线宽为1
%%
syms x y z
V = [x^2*y, y^2*z, z^2*x];
vars = [x y z];
gradient(divergence(V,vars)) - curl(curl(V,vars),vars)

syms x y z
V = [x^2*y, y^2*z, z^2*x];
vars = [x y z];
gradient(divergence(V,vars)) - curl(curl(V,vars),vars)

x = linspace(-2*pi,2*pi);  %定义x向量
U = cos(x);    %计算cos(x)
L = 4*del2(U,x);   %计算U的拉普拉斯，注意系数4
plot(x,U,x,L)       %画出U和U的拉普拉斯曲线
legend('U(x)','L(x)','Location','Best') %给出图例

[x,y] = meshgrid(-5:0.25:5,-5:0.25:5);   %定义函数在x，y方向的区域
U = 1/3.*(x.^4+y.^4);                %定义函数U
h = 0.25;         %U中各点的间距在所有方向上都相等，所以可以指定一个间距h
L = 4*del2(U,h);  %计算U的拉普拉斯变换
surf(x,y,L);
grid on;
title('Plot of $Delta U(x,y) = 4x^2+4y^2$','Interpreter','latex')
xlabel('x');
ylabel('y');
zlabel('z');
view(35,14);