1.1 
implicitplot(x^2+4*x+2*y^2-12*y = 18, x = -10 .. 5,y = -2 .. 10);
1.2 
implicitplot(64*x^2-36*y^2-2304 = 0, x = -15 .. 15,y = -15 .. 15);
1.3 
plot([x, -2*x^2+1], x = -1.2 .. 1.2);
1.4 
implicitplot([x-2*y = 5, x = 2, (x-2)^2+y^2 = 9],x = -4 .. 6, y = -5 .. 5);
1.5 
implicitplot(x^2+y^2 = 1, x = -10 .. 10,y = -10 .. 10);
1.6 
implicitplot(x^2+y^2 = 1, x = -10 .. 10,y = -10 .. 10, grid=[100,100]);
1.7 
implicitplot((x-2)^2+(y+1)^2 = 25, x = -5 .. 10,y = -8 .. 7, filledregions);
1.8 
plot(sqrt(2*cos(2*v)), v = 0 .. 2*Pi, coords = polar, numpoints = 1000);
1.9 
implicitplot3d(x+y+z = 1, x = -1 .. 1, y = -1 .. 1,z = -1 .. 1);
1.10 
implicitplot3d([x=0,y=0,z=0],x=-5..5,y=-5..5,z=-5..5);
implicitplot3d([x+y+z = 1, x = 0, y-z = 1], x = -2 .. 2,y = -1 .. 1, z = -1 .. 1);

1.11 
implicitplot3d(r = 1, r = 0 .. 1.5, v = 0 .. 2* Pi,z = -2 .. 2,coords =cylindrical);
1.12 
implicitplot3d([r = 1, v = 3*Pi*1/4, z = 1, r = 0 .. 2,v = 0 .. 2*Pi, z = 0 .. 2,coords =cylindrical, grid = [10, 20, 20]);
1.13 
implicitplot3d(r = v, r = 0 .. 10, v = 0 .. 4*Pi,z = 0 .. 10,coords =cylindrical, grid = [15, 40, 15]);
1.14 
implicitplot3d(r = 1, r = 0 .. 1.1, u = 0 .. 2*Pi,v = 0 .. Pi,coords = spherical, grid = [10,15,15]);
1.15 
implicitplot3d([u = Pi, v = (1/4)*Pi], r = 0 ..2,u = 0 .. 2*Pi, v = 0 .. (1/2)*Pi,coords = spherical,grid = [10,15,15]);
1.16 
implicitplot3d(x^2+y^2-z^2 = 0, x = -5 .. 5, y = -5 .. 5,z = -5 .. 5, grid = [20, 20, 20]);
1.17 
implicitplot3d(sin(v)^2-cos(v)^2 = 0, r = 0 .. 2,u = 0 .. 2*Pi, v = 0 .. Pi, grid = [10, 20, 10],coords = spherical);
1.18 
implicitplot3d(z = x^2+y^2, x = -3 .. 3, y = -3 .. 3,z = 0 .. 9);
1.19 
implicitplot3d(z = 5*cos(x^2+y^2)/(1+x^2+y^2),x = -3 .. 3, y = -3 .. 3, z = -1.5 .. 5,grid = [35, 35, 35]);
1.20 
plot3d(sqrt(z), v = 0 .. 2*Pi, z = 0 .. 3,coords =cylindrical);
1.21 
plot3d(exp(z)+exp(-z), v = 0 .. 2*Pi, z = -2 .. 2,coords =cylindrical);
1.22 
plot3d(x^2+y^2, x = -5 .. 5, y = -5 .. 5);
1.23 
plot3d(x^2+y^2, x = -y .. y, y = 0 .. 5);
plot3d(x^2+y^2, x = -sqrt(25-y^2) .. sqrt(25-y^2),y = -5 .. 5);
1.24 
g :=(x,y)-> x*y ; plot3d(g(x, y), x = -5 .. 5,y = -5 .. 5);
1.25 
h := (x, y) -> x-(1/4)*y^2+10: plot3d(h(x, y),x = -5 .. 5, y = -5 .. 5);
1.26 
F := (x, y)-> sqrt(100-x^2-y^2):
plot3d(F(x, y), x = -10 .. 10, y = -10 .. 10);
1.27 
plot3d([h(x, y), F(x, y)], x = -5 .. 5, y = -5 .. 5);
1.28 
plot3d(1/(x^2+y^2), x = -2 .. 2, y = -2 .. 2,view = 0 .. 4);
1.29 
plot3d(1/x, x = -1 .. 1, y = -1 .. 1, grid = [16, 16]);
1.30 
f:=(x,y)->(x^3+2*y^3)/(1+x^2+3*y^2):
implicitplot(f(x,y)=0,x=-10..10,y=-10..10,grid=[50,50]);
1.31 
N0:=implicitplot(f(x,y)=0,x=-10..10,y=-10..10,grid=[50,50]):
1.32 
display(N0,N2,Nm2,N4,Nm4,N6,Nm6);
1.33
contourplot(x^2+y^2, x = -sqrt(25-y^2) .. sqrt(25-y^2),y = -5 .. 5, grid = [30, 30],contours = 10);
1.34 
f:=(x,y)->(x^3+2*y^3)/(1+x^2+3*y^2):
contourplot(f(x, y), x = -10 .. 10, y = -10 .. 10,grid = [50, 50],contours = 7);
1.35 
plot3d(x^2+y^2, x = -sqrt(25-y^2) .. sqrt(25-y^2),y = -5 .. 5, style=contour,contours = 10, grid =[50,50]);
1.36 
with(plots):with(plottools):
f := (x, y)->4*x^2-5*y^2+200:
gf := plot3d(f(x, y), x = -5 .. 5, y = -5 .. 5,contours = 15, style =contour):
cf :=contourplot(f(x, y), x = -5 .. 5, y = -5 .. 5,contours = 15):
tf := transform((x, y)->[x, y, 0]):
display(cf);
display(gf, tf(cf));
1.37 
plot([t-sin(t), 1-cos(t), t = 0 .. 6*Pi]);
with(plots):
spacecurve([4*cos(6*Pi*t), 4*sin(6*Pi*t), 1.5*t],t = 0 .. 1, numpoints=1000);
1.38 
spacecurve([(4+sin(20*t))*cos(t), (4+sin(20*t))*sin(t),2*cos(20*t)], t = 0 .. 7, numpoints = 1000);
1.39 
animatecurve([65*cos((2*Pi*1/30)*t-(1/2)*Pi),65*(1+sin((2*Pi*1/30)*t-(1/2)*Pi)), t = 0 .. 30]);
1.40 
fieldplot([x/(x^2+y^2+4)^(1/2), -y/(x^2+y^2+4)^(1/2)],x = -2 .. 2, y = -2 .. 2,grid=[8,8]);
1.41 
fieldplot([-y, x], x = -2 .. 2, y = -2 .. 2,grid = [10,10]);
1.42 
fieldplot3d([ x,2* (y+z),z/2+1], x = -1 .. 1,y = -1 .. 1, z = -1 .. 1,arrows = SLIM,grid = [5, 5, 5]);
1.43 
plot3d([r*cos(v), r*sin(v), 2*r], r = 0..2, v = 0..2*Pi);
1.44 
plot3d([5*cos(v)*sin(u),5*sin(v)*sin(u),5*cos(u)],u=0..Pi,v=0..2*Pi);
2.1 
implicitplot3d(z-sin(2*v), r = 0 .. 1, v = 0 .. 2*Pi,z = -1.5 .. 1.5, grid = [30, 30, 20],coords =cylindrical);
2.2 
g := (x, y)->2*x*y/(x^2+y^2);
contourplot(g(x, y), x = -1 .. 1, y = -1 .. 1,grid = [100, 100]);
3.1 
f:=(x,y) -> (x+1)^2+(x+1)(y+2)+(y+2)^2:
plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1,orientation =[-148, 60]);
3.2 
fx := diff(exp(2*x*y)*sin(x* y^2),x);
3.3 
fy := diff(exp(2*x*y)*sin(x*y^2),y);
3.4 
subs(x=1,y=3,fx);
3.5 
g := unapply(fx, x, y); g(1, 3);
3.6 
f:=(x,y) -> exp(2*x*y)*sin(x*y^2);
3.7 
fx:=D[1](f); dfx(1,3):=fx(1,3);
3.8 
f := (x,y) -> (x+1)^2+(x+1)*(y+2)+(y+2)^2:
mtaylor(f(x, y), [x = 0, y = 0], 2);
3.9 
with(VetorCalculus): with(plots):
f := (x,y) -> (x+1)^2+(x+1)*(y+2)+(y+2)^2:
v := Gradient(f(x, y), [x, y]);
3.10 
subs(x = 0, y = 0, v);
3.11 
gradplot(f(x, y), x = -2 .. 2, y =-2 .. 2);
3.12 
f := (x, y)-> x^2*y^3:
h := (u,v)->f(u^2+v^2,u*v):
hu := diff(h(u,v),u):uderivatan:=subs(u=2,v=-2,hu);
hv := diff(h(u,v),v):vderivatan:=subs(u=2,v=-2,hv);
3.13 
h:= (u,v)->f(x(u,v),y(u,v)):
D[1](h)(a,b);
3.14 
f := (x, y) -> x^2+y^3:
ex := 12/sqrt(12^2+5^2):ey := 5/sqrt(12^2+5^2):
gt := diff(f(1+t*ex, 1+t*ey), t); subs(t = 0, gt);
3.15 
with(plots):
f := (x, y) -> 3*x-5*y+10:
A := gradplot(f(x, y), x = -2 .. 2, y = -2 .. 2):
B :=contourplot(f(x, y), x = -2 .. 2, y = -2 .. 2):
display(A,B);
3.16 
f := (x,y,z)->(x^2+y^2)*z/(2-z^2):
fx := D[1](f): fy := D[2](f): fz := D[3](f):
fx(-1,2, 1); fy(-1, 2, 1); fz(-1, 2, 1);
4.1 
f:=(x,y)->x*(1-y): g:=(x,y)->x^2+y^2:
a11:=diff(f(x,y),x): a21:=diff(f(x,y),y):
a12:=diff(g(x,y),x): a22:=diff(g(x,y),y):
eq1:=a11* a22-a21* a12=0: eq2:=x^2+y^2=1:
solve(eq1,eq2,x,y);
4.2 
g:=(x,y)->(x+2*y)*exp(-(x^2+y^2)):
eq1:=diff(g(x,y),x)=0:
eq2:=diff(g(x,y),y)=0:
allvalues(solve({eq1,eq2},{x,y}));
4.3 
f:=(x,y)-> -4*x*y-2*y^2-x^4:
solve({diff(f(x,y),x)=0,diff(f(x,y),y)=0},{x,y});
5.1 
dsolve(diff(f(x), x)+4*x*f(x) = x);
5.2 
dsolve({diff(f(x), x)+4*x*f(x) = x,f(0)=1});
5.3 
pdsolve(diff(f(x,y),x)+2*x*y*f(x,y)=4*x*y^2);
5.4 
sol:=solve(y^2=2*y+e^(-4*y)*h(y), h(y)):
h:=unapply(sol,y);
5.5 
pdsolve(diff(f(x, y), x)+diff(f(x, y), y) = 0);
5.6 
with(PDEtools):
PDE :=diff(f(x,y),x)+diff(f(x,y), y)=0;
5.7 
tr := {v=x-y, u=x+y}; tr1:= solve(tr,{x, y});
5.8 
PDE1 := dchange(tr1, PDE);
5.9 
pdsolve(PDE1);
6.1 
f:=x->x^2:
riemannsumma:=n-> sum(f(k/n)*1/n,k=1..n):
simplify(riemannsumma(n));
limit(riemannsumma(n),n=infinity);
6.2 
int(x^2,x=0..1);
6.3 
S:=sum(sum((i+j),j=1..8),i=1..5);
6.4 
S:=sum(sum((i+j),j=1..m),i=1..n);
6.5 
S:=sum(sum(sum(i*(j+k),k=1..n),j=1..n),i=1..n);
6.6 
summa:=n->sum(1/k^2,k=1..n):
limit(summa(n),n=infinity);
6.7 
f:=(x,y)->x*y^2:
summa:=n->sum(sum(f(i/n,j/n)*1/n*1/n,i=1..2*n),j=1..n):
simplify(summa(n));
limit(summa(n),n=infinity);
6.8 
with(plots):
f:=(x,y)->4-(x^2+y^2):
fplus:=(x,y)->max(4-(x^2+y^2),0):
fminus:=(x,y)->min(4-(x^2+y^2),0):
plot3d(f(x,y),x=-3..3,y=-2..2);
plot3d(abs(f(x,y)),x=-3..3,y=-2..2);
plot3d(fplus(x,y),x=-3..3,y=-2..2);
plot3d(fminus(x,y),x=-3..3,y=-2..2);
6.9 
int(int(exp(x^2),y=0..x),x=0..1);
6.10 
int(int(r*cos(phi)*(r*sin(phi))^2*r,r=1..3),phi=-Pi/4..Pi/4);
6.11 
f:=(x,y)-> x* y^2:
int(int(f(r*cos(phi),r*sin(phi))*r,phi=-Pi/4..Pi/4),r=1..3);
6.12 
int(r^4,r=1..3)*int(cos(phi)*(sin(phi))^2,phi=-Pi/4..Pi/4);
6.13 
int(2*r*ln(r),r=0..1);
6.14 
int(1/sqrt(x), x = 0 .. 1); int(1/x^2, x = 0 .. 1);
int(1/x^2, x = 1 .. infinity); int(sin(x),x = 1 .. infinity);
6.15 
int(int(1/(x^2+y^2)^2, x = 1 .. infinity),y = 1 .. infinity);
6.16 
int(int(1/(x^2+y^2)^2, x = 0 .. 1), y = 0 .. 1);
6.17 
int(int(int(exp(x-y+z),z=0..(1-x-y)),y=0..(1-x)),x=0..1);
6.18
int(int(int(ln(x+y+z), x = 0 .. 1/3), y = 0 .. 1/3),z = 0 .. 1/3);
evalf(%);
6.19 
int(int(int(x*y*z/(x^2+y^2+z^2), x = 0 .. 1),y = 0 .. 1), z = 0 .. 1);
evalf(%);
6.20 
V:= int(r^2,r=0..2)*int(sin(v),v=0..Pi/4)*int(1,w=0..2*Pi);
Tz:=int(r^3,r=0..2)*int(cos(v)*sin(v),v=0..Pi/4)*int(1,w=0..2*Pi);
zkoord:= Tz/V;
simplify(%);
zkoord:=evalf(%);
7.1 
pdsolve({diff(U(x,y),x)=x/(x^2+y^2),diff(U(x,y),y)=y/(x^2+y^2)},{U(x,y)});
8.1 
with(plots):with(plottools):
V := fieldplot([-y, x], x = -2 .. 2, y = -2 .. 2,grid = [8, 8]):display(V);
8.2 
V := fieldplot([-y+1, x-1], x = 0.5 .. 1.5,y = 0.5 .. 1.5,grid = [8, 8]):
V1 := fieldplot([-y+1, x-1], x = .5 .. 1.5,y = .5 .. 1.5, grid = [8, 8]):
PIL := arrow([1+.3/sqrt(2), 1+.3/sqrt(2)],[1+.9*.3/sqrt(2),1+1.1*.3/sqrt(2)], 0, 0.03, 1.5);
display(V);
display([V1, C, PIL]);
8.3 
with(plots): with(plottools):
P := (x, y)-> ln((x-1)^2+y^2)-ln((x+1)^2+y^2) :
A := gradplot(P(x, y), x = -2.5 .. 2.5, y = -2.5 .. 2.5,grid = [12, 12], scaling =constrained, arrows = slim,fieldstrength = fixed):
B :=contourplot(P(x, y), x = -2.5 .. 2.5, y = -2.5 .. 2.5,grid = [100, 100],contours = 20, scaling =constrained):
display(A, B);
9.1 
with(PDEtools):
PDE:=diff(diff(f(x,t),t),t) -c^2*diff(diff(f(x,t),x),x)=0;
9.2 
tr:={u = x+c*t, v = x-c*t}; 
tr1:= solve(tr,{x,t});
9.3 
PDE1 := simplify(dchange(tr1, PDE,[u,v],params=c));
9.4 
pdsolve(PDE1);
9.5 
f(x,t):=subs(u=x+c*t,v=x-c*t,%);