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1、实验 1 1 (log(pi)+log10(pi)-exp(1.2)2/81 ans = 0.0348 2 syms x y z = x2+exp(x+y)-y*log(x)-3 z = exp(x + y) - y*log(x) + x2 - 3 x = 2; y = 4; eval(z) ans = 401.6562 3 (1) f = 3 -1 2 1 0 3; r = roots(f) r = 0.7330 + 0.7416i 0.7330 - 0.7416i -0.8952 + 0.0000i -0.1188 + 1.0066i -0.1188 - 1.0066i (2) g = (
2、x) 1/3*x.3+x.2-3*x-1; minimizer,minimum = fminbnd(g,-1,2) minimizer = 1.0000 minimum = -2.6667 4 clear a = 5.3; b = 1 3; 2 5; who Your variables are: a b whos Name Size Bytes Class Attributes a 1x1 8 double b 2x2 32 double save D:exe01.mat 5 (1) 用 plot 作图的 m-文件 % ex1_5_1_plot x = -2:0.01:2; y = x.2.
3、*sin(x.2-x-2); plot(x,y) 用 fplot 作图的 m-文件 % ex1_5_1_fplot y = (x) x.2.*sin(x.2-x-2); fplot(y,-2 2) (2) 作图的 m-文件 % ex1_5_2 x = 0:pi/180:2*pi; y1 = x.2.*sin(x.2-2); y2 = x.2.*cos(x.2-2); y3 = 2*sin(2*x); y4 = 2*cos(2*x); subplot(2,2,1); plot(x,y1) subplot(2,2,2); plot(x,y2) subplot(2,2,3); plot(x,y3)
4、subplot(2,2,4); plot(x,y4) 实验 2 1 结果是在 Command Window. 输出结果是 (文件名是 “ex2_1”) ex2_1 sum = 11 product = 40 2 函数的 m-文件 (函数名改为 “ex2_2”) function y = ex2_2(x) y = 1+x+x.2+x.3+x.4+x.5; 计算 ex2_2(-3), ex2_2(2), ex2_2(5), ex2_2(7) y = ex2_2(-3 2 5 7) y = -182 63 3906 19608 3 函数的 m-文件 (函数名改为 “ex2_3”) function
5、y = ex2_3(x) if x ex2_3(-7), ex2_3(1), ex2_3(5), ex2_3(9) ans = 43 ans = 8.2305 ans = 8.0396 ans = 9.9984 4 函数的 m-文件 (函数名改为 “ex2_4”) function y = ex2_4(x) y = exp(ex2_2(x)+2*sin(ex2_2(x)+ex2_2(x).2; 计算 ex2_4(2), ex2_4(4), ex2_4(6), ex2_4(10) y = ex2_4(2 4 6 10) y = 1.0e+27 * 2.2938 Inf Inf Inf 5 % e
6、x2_5 clc n = input(请输入次数: ); r = 100/2n; d = 100+r; i = n-2; while i = 0 d = d+100/2i; i = i-1; end fprintf(皮球在第%d次的反弹高度是%fn,n,r) fprintf(皮球在第%d次反弹到达最高点时经过的总路程是%fn,n,d) 程序 ex2_5 输出样例 请输入次数: 3 皮球在第 3 次的反弹高度是 12.500000 m 皮球在第 3 次反弹到达最高点时经过的总路程是 262.500000 m 实验 3 1 zeros(size(A) ans = 0 0 0 0 2 (1) A(1
7、,:) ans = 1 -2 2 (2) A(:,2) ans = -2 0 5 (3) A(2 3,2 3) ans = 0 5 5 3 3 (1) det(A) ans = 13.0000 rank(A) ans = 3 inv(A) ans = -1.9231 1.2308 -0.7692 -0.3077 0.0769 0.0769 1.1538 -0.5385 0.4615 (2) 2*A-B ans = 1 -7 0 4 0 13 0 11 5 A*B ans = 1 1 12 13 4 17 17 0 -8 A.*B ans = 1 -6 8 6 0 -15 2 -5 3 A an
8、s = 1 3 1 -2 0 5 2 5 3 4 A+B ans = 2 5 10 5 4 9 3 -6 8 2*A-B ans = 1 1 8 1 8 3 0 -9 13 A*B ans = 19 -3 20 22 2 32 0 -4 -14 A.*B ans = 1 6 24 6 0 20 2 5 7 A/B ans = 0.0714 1.5000 -1.7857 1.8571 -1.0000 1.5714 -3.6429 5.5000 -5.9286 AB ans = 2.0714 -2.8571 0.7857 -0.1607 0.6786 0.4821 -0.1250 0.7500 0
9、.3750 A.B ans = 1.0e+03 * 0.0010 0.0080 1.2960 0.0080 0.0010 1.0240 0.0010 -0.0002 0.0070 5 (1) A = -1 2 0; -2 3 0; 3 0 2; V,D = eig(A), r = rank(V) V = 0 0.3015 0.3015 0 0.3015 0.3015 1.0000 -0.9045 -0.9045 D = 2 0 0 0 1 0 0 0 1 r = 2 不可以对角化. (2) B = -2 1 1; 0 2 0; -4 1 3; V,D = eig(B), r =rank(V)
10、V = -0.7071 -0.2425 0.3015 0 0 0.9045 -0.7071 -0.9701 0.3015 D = -1 0 0 0 2 0 0 0 2 r = 3 可以对角化, = 1. 6. A = 1 2 0 1; 1 3 0 -1; -1 -1 1 0; r = rank(A) r = 3 线性无关. 7 方法 1 A = 2 5 -8; 4 3 -9; 2 3 -5; 1 8 -7; b = 8; 9; 7; 12; x = linsolve(A,b) x = 3.0000 2.0000 1.0000 方法 2 R = rref(A,b) R = 1 0 0 3 0 1
11、 0 2 0 0 1 1 0 0 0 0 即 = (3,2,1). 8 A = 2 -1 3; 2 1 1; 4 1 2; x = linsolve(A,zeros(3,1) x = 0 0 0 实验 4 1 (1) syms n limit(sqrt(n+sqrt(n)-sqrt(n),n,inf) ans = 1/2 (2) syms x limit(1-2/x)(3*x),x,inf) ans = exp(-6) (3) syms x limit(sin(x)/(x3+3*x) ans = 1/3 2 (1) syms x y = x10+10x+log10(x); diff(y) an
12、s = 1/(x*log(10) + 10x*log(10) + 10*x9 (2) syms x y = log(1+x); x = 1; eval(diff(y,2) ans = -0.2500 (3) syms x y z = exp(2*x)*(x+y2+2*y); diff(z,x),diff(z,y) ans = exp(2*x) + 2*exp(2*x)*(y2 + 2*y + x), exp(2*x)*(2*y + 2) (4) syms x y z = sin(3*x+2*y)2; diff(z,x),diff(z,y) ans = 6*cos(3*x + 2*y)*sin(
13、3*x + 2*y), 4*cos(3*x + 2*y)*sin(3*x + 2*y) (5) syms x y u dx dy du z = log(x2+y2+u2); dz = simplify(diff(z,x)*dx+diff(z,y)*dy+diff(z,u)*du) dz = (2*(du*u + dx*x + dy*y)/(u2 + x2 + y2) 3 (1) syms x int(cos(2*x)*cos(3*x) ans = sin(5*x)/10 + sin(x)/2 (2) syms x a b simplify(int(1/(x*(sqrt(log(x)+a)+sq
14、rt(log(x)+b),x) ans = (2*(a + log(x)(3/2) - (b + log(x)(3/2)/(3*(a - b) 4 (1) fun = (x) sqrt(sin(x).3-sin(x).5); q = integral(fun,0,pi) q = 0.8000 (2) fun = (x) exp(-x.2/2); q = integral(fun,0,1) q = 0.8556 (3) syms x q = int(x2+5)/(x2+2),x,0,2) q = (3*2(1/2)*atan(2(1/2)/2 + 2 5 (1) fun = (x) x.2.*log(x); q = integral(fun,1,exp(1) q = 4.5746 (2) fun = (x,y) y.2./x.2; q = integral2(fun,1/2,2,1,2) q = 3.5000 (3) 方法 1 fun = (x,y) x.*y; ymin = (x) x.2; ymax = (x) x+2; q = integral2(fun,-1,2,ymin,ymax) q = 5.6250 方法 2 syms x y q = int(int(x*y,y,x2,x+2),x,-1,2) q = 45/8 6 (1) y = dsolve(1
