Matlab numerical calculus

1, polyval ()% polynomial constructors, parameters vector vectors, vector independent variables

f=[9,-5,3,7];   X=-2:0.01:5; The range of%x is 2 to 5

Y=polyval (F,X); %x is an argument range and F is a polynomial coefficient

Plot (x, y, ' linewidth ', 2);

Xlabel (' x '); Ylabel (' Y ');

Set (GCA, ' fontsize ', 14);

2, Polyder ()% derivative

P=[5 0-2 1]; %5x^4-2x^2+x

Polyder (P); % result is 20 0-4 0

3, when x=7, the guide value

P=[5 0-2 1]; %5x^4-2x^2+x

Polyval (Polyder (P), 7);

4, Conv ()% is used to denote multiple 20x^3+7x^2 of f (x) = (x^3+4x)

Product of

Y1=[20 7 0 0]; Y2=[1 0 4 0];

F=conv (Y1,Y2);

5, Polyint ()% gives indefinite integral a definite constant term k, ...

F (x) =x+4; 1/2x^2+4x+k the integral to it.

P=[5 0-2 0 1]; %f (x)

Polyint (p,3); % constant term k is 3 after given integral

Polyval (Polyint (p,3), 7); % calculates the integral of F (7)

6, diff ()% vector difference of neighboring elements, used to calculate slope

X=[1 2];  Y=[5 7]; %X1,X2 Y1,y2

Slope=diff (Y)./diff (x); % calculates the slope of the point (1,5) (2,7)

7. Calculate the derivative within the entire defined field

h=0.5; X=0:h:2*pi;

Y=sin (x);        M=diff (y)./diff (x); % Compute sin ' (x)

8. Calculate two differential, three differential

X=-2:0.005:2; y=x.^3;

M=diff (y)./diff (x); % First-order guide

M2=diff (M)./diff (x (1:end-1)); The dimensions of the%m are 1 less than x, and the second-order guide

Plot (X,y,x (1:end-1), M,x (1:end-2), m2);

Legend (' F (x) ', ' F ' (x) ', ' F ' (x) '); % do image callout

9, calculate the definite integral, calculate the integral of 4x^3 in interval [0,2] by using differential rectangle summation

h=0.05; X=0:h:2;

Midpoint= (x (1:end-1) +x (2:end))./2; % calculates the midpoint of each rectangle (xmid)

y=4*midpoint.^3; % result is 15.99

S=sum (H*y); % of all trapezoidal bottom multiply high sum

10, Trapz () Calculate the definite integral, use trapezoid accumulation

h=0.05; X=0:h:2;        y=4*x.^3; The%h is a trapezoidal high

S=h*trapz (y); % result is 16.01

11, Integral2 double integral integral3 triple integral

[Email protected]   (x, Y) y.*sin (×) +8.*cos (y); % of functions to be integral

Integral2 (F,PI,2*PI,0,PI); The% parameters are: function, first level integration interval, second level integration interval

Integral3 (f,0,pi,0,1,-1,1);

Matlab numerical calculus