%% Задание 1

a=6;
b=6;
c=3;
u = (-pi:0.05*pi:pi)';
v = -pi:0.05*pi:pi;
X = a*sin(u)*cos(v);
Y = b*sin(u)*sin(v);
Z = c*cos(u)*ones(size(v));
figure;
grid on;
hold on;
view(102,15);
surf(X, Y, Z)
[U, V, W] = surfnorm(X, Y, Z);
quiver3(X, Y, Z, U, V,W, 4, 'k');
%% Задание 2

u = (-4*pi:0.1*pi:4*pi).';
v = (-4*pi:0.1*pi:4*pi);
x = 2 .* u .* cos(v);
y = 3 .* u .* sin(v);
z = u .* ones(length(v));

figure;
grid on;
hold on;
view(102,15);
surf(x,y,z);
%% Задание 3

%% Задание 4

z = exp(y.^2)+cos(2*pi.*y)+exp(x.^2)+cos(2*pi.*x);
x = -1:0.01:1;
y = (-1:0.01:1)';
figure;
grid on;
hold on;
view(102,15);
surf(x, y, z);
[x_min1, y_min1] = fminbnd(f6, -1, -0.5)
[x_min2, y_min2] = fminbnd(f6, -0.5, 0)
[x_min3, y_min3] = fminbnd(f6, 0, 1)
[x_min4, y_min4] = fminbnd(f6, 1, 1.5)

%% Задание 5

x = [1 2 3 4 5 7 10 14 19 25];
y = [0 -1 -3 -2 -4 -3 -6 -4 -10 -20];
figure;
grid on; hold on;
p4 = polyfit(x, y, 4);
p5 = polyfit(x, y, 5);
p6 = polyfit(x, y, 6);
p7 = polyfit(x, y, 7);
k = 1:0.1:25;
P4 = polyval(p4, k);
P5 = polyval(p5, k);
P6 = polyval(p6, k);
P7 = polyval(p7, k);

plot(x, y);
plot(k, P4);
plot(k, P5);
plot(k, P6);
plot(k, P7);
legend('func','eval4','eval5','eval6','eval7');
%% Задание 6

x = [0.1 0.2 0.3 0.4 0.6 0.7 1.0 1.3 1.6 2.2];
y = [-3 -4 -3 -2 -1 0 1.5 4 6.5 12];
%% Задание 7

f = @(x) cos(x)-x.*sin(x)+x.*(sin(x.^2)-cos(x.^4));
int = integral(f,-1,0.9)
%% Задание 8

x = 0:.05:2;
y = (-2:.1:2)';
z = sin(x).*cos(y).*(x+y).*(x-y);
surf(x,y,z);
view(39,39);
fun = @(x,y) sin(x).*cos(y).*(x+y).*(x-y);
q = integral3(fun,0,2,-2,2,0,4)

%% Задание 10

syms x
f = sin(x)*cos(x);
t = taylor(f)
pretty(f)