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고려대학교zoom강의/calculus.m

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+clear; close all; clc;
+
+
+%% Fig 3. 한 점 (x,y)에서 순간 변화율과 평균 변화율 (동영상)
+for x1 = [1, 0.5, 0.1]+1
+    plotXY(-1,3,-1,3,true,20)
+    x = linspace(-1,3, 100);
+    y = 1/3*x.^2 + 1;
+    hold on;
+    plot(x,y,'k','linewidth',2)
+
+    x = linspace(-0.5, 2.5, 100);
+
+    plot(x, 2/3*x + 2/3,'b','linewidth',3)
+    plot(1, 4/3 ,'o','markerfacecolor','b','markeredgecolor','none','markersize',10)
+
+    y1 = 1/3 * x1^2  + 1;
+
+    y = (y1-4/3)/(x1-1) * (x-1) + 4/3;
+    h(1) = plot(x1, y1, 'o', 'markerfacecolor','r','markeredgecolor','none','markersize',10);
+    h(2) = plot(x, y, 'r','linewidth',3);
+
+end
+
+
+%% Fig 3. 한 점 (x,y)에서 순간 변화율과 평균 변화율 (동영상)
+clear v
+v = VideoWriter('fig3.mp4','MPEG-4');
+v.FrameRate = 30;
+v.Quality = 100;
+open(v);
+
+clear F
+
+plotXY(-1,3,-1,3,true,20)
+x = linspace(-1,3, 100);
+y = 1/3*x.^2 + 1;
+hold on;
+plot(x,y,'k','linewidth',2)
+
+x = linspace(-0.5, 2.5, 100);
+
+plot(x, 2/3*x + 2/3,'b','linewidth',3)
+plot(1, 4/3 ,'o','markerfacecolor','b','markeredgecolor','none','markersize',10)
+
+i=1;
+for x1 = linspace(3,1,100)
+
+
+    y1 = 1/3 * x1^2  + 1;
+
+    y = (y1-4/3)/(x1-1) * (x-1) + 4/3;
+    h(1) = plot(x1, y1, 'o', 'markerfacecolor','r','markeredgecolor','none','markersize',10);
+    h(2) = plot(x, y, 'r','linewidth',3);
+    drawnow;
+
+    F(i)=getframe(gcf);
+    if x1>1
+        delete(h)
+    end
+    i=i+1;
+end
+
+
+for i=1:length(F)
+    % convert the image to a frame
+    frame = F(i) ;
+    writeVideo(v, frame);
+end
+
+close(v)
+
+%% 3d plot
+
+close all;
+[X,Y] = meshgrid(linspace(-3,3,20));
+
+surf(X, Y, -X.^2-Y.^2+1)
+xlabel('$$x$$','interpreter','latex'); ylabel('$$y$$','interpreter','latex'); zlabel('$$z=-x^2-y^2+1$$','interpreter','latex');
+hold on;
+xx = -1 * ones(1,100);
+yy = linspace(-3,3,100);
+zz = -xx.^2 - yy.^2  + 1;
+plot3(xx,yy,zz,'r','linewidth',3)
+
+% tangential line
+% (-1, -1, -1)에서...?
+% round z round y = - 2y
+t = linspace(-0.5,1,100);
+
+x = -1 * ones(1, 100);
+y = -2 + 4 * t;
+z = -4 + 16*t
+
+plot3(x,y,z,'k','linewidth',3);
+plot3(-1,-2,-4,'o','markersize',7,'markerfacecolor','k','markeredgecolor','none')
+
+axis square
+

고려대학교zoom강의/plotXY.m

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+function plotXY(x1, x2, y1, y2,h_newfig, fontsize)
+
+% fontsize= 20;
+if h_newfig
+    figure;
+    set(gcf,'position',[500,100,1000,650])
+    set(gcf,'color','w');
+end
+
+mArrow2(x1,0,x2,0,{'color','k'});
+mArrow2(0,y1,0,y2,{'color','k'});
+xlim([x1,x2])
+ylim([y1,y2])
+set(gca,'visible','off');
+
+% (x1+1):10:(x2-1)
+for i = unique(round([linspace(x1*0.9, x2*0.9,7),0]))
+    line([i i],[-(y2-y1)*0.005 (y2-y1)*0.005],'color','k')
+    line([-(x2-x1)*0.005 (x2-x1)*0.005],[i i],'color','k')
+
+    % xticks
+    if i<=0
+        t= text(i-(y2-y1)*0.03, -(x2-x1)*0.025,num2str(round(i)));
+    else
+        t= text(i-(y2-y1)*0.02, -(x2-x1)*0.025,num2str(round(i)));
+    end
+    t.FontSize=fontsize;
+
+    % yticks
+    if i<0
+        t = text((y2-y1)*0.01, i, num2str(round(i)));
+    elseif i>0
+        t = text((y2-y1)*0.01, i, num2str(round(i)));
+    end
+    t.FontSize = fontsize;
+end
+
+t = text(x2*0.97,(y2-y1)*0.03,'$$x$$','Interpreter','latex');
+t.FontSize = fontsize;
+t = text(-(x2-x1)*0.03,y2*1,'$$y$$','Interpreter','latex');
+t.FontSize = fontsize;
+axis square
+
+end
+
+function [ h ] = mArrow2(x1,y1,x2,y2,props)
+
+h = annotation('arrow');
+set(h,'parent', gca, ...
+    'position', [x1,y1,x2-x1,y2-y1], ...
+    'HeadLength', 10, 'HeadWidth', 10, 'HeadStyle', 'cback1', ...
+    props{:} );
+end