2015/10/16 例3]单变量函数线性化 y=0.2x3 x=2 5 Nonlinear Linearized 4 =[1:0.01:3]: y=0.2*x.3: y2=1.6+2.4*(x-2): 1 plot (x,y,'r',x,y2,'b-.') xlabel('x');ylabel('y') grid legend('Nonlinear','Linearized') 1.5 2 2.5 School of Mechanical Engineering ME369-lecture 5.3 Shanghai Jiao Tong University Fall 2015 [例4]多变量函数线性化 z=x2+4y+6y2 in the region8≤x≤10,2≤y≤4 400 350 [x,y]=meshgrid(8:0.04:10, 2:0.04:4): z=.^2+4.*x.*y+6.*y.^2; N 250 z2=243+30.*(x-9)+72.*(y-3): mesh (x,y,z) 150 xlabel('x');ylabel('y');zlabel('z') grid;hold on;mesh(x,y,z2) 100 3.5 3 2.5 210 School of Mechanical Engineering ME369-lecture 5.3 Shanghai Jiao Tong University Fall 2015 52015/10/16 5 ME369-lecture 5.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 3 y x  0.2 0 x  2 1 1.5 2 2.5 3 -1 0 1 2 3 4 5 6 x y Nonlinear Linearized [例3]单变量函数线性化 x=[1:0.01:3]; y = 0.2*x.^3; y2 = 1.6+2.4*(x-2); plot(x,y, 'r', x, y2, 'b-.') xlabel('x'); ylabel('y') grid legend('Nonlinear','Linearized') ME369-lecture 5.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [例4] 多变量函数线性化 2 2 z x xy y    4 6 in the region 8 10, 2 4     x y [x,y]=meshgrid(8:0.04:10, 2:0.04:4); z = x.^2+4.*x.*y+6.*y.^2; z2 = 243+30.*(x-9)+72.*(y-3); mesh(x,y,z) xlabel('x'); ylabel('y'); zlabel('z') grid; hold on; mesh(x,y,z2) 8 9 10 2.5 2 3.5 3 4 100 150 200 250 300 350 400 y x z