MATLAB Learning Note (iii): Symbolic calculation _-_2

2.3.1 Symbolic calculus

Find the Limit

Limit (F,x,a) for x in F (x) to approximate the limits of a

For example:

>> clear>> syms k x>> lim_t=limit ((1-1/x) ^ (k*x), x,inf) lim_t = 1/exp (k)

Derivative number

diff (F,x,n) to find n-derivative of f (x)

>> clear>> syms x>> dfdx=diff (x^3,x,1) DFDX = 3*x^2

Note that the Findsym acknowledgement is automatically called when X is default on the upper formula, and N defaults to the default N=1

There are also several functions:

Jacobian (f,v) The Jacobian matrix of the multivariate vector function f (v) (Advanced)

Taylor (F,n,x,a) expands f (x) into a power series (Taylor series) at X=a

Symbolic summation of 2.3.2 sequences/series

S=symsum (F,x,a,b) asks F (x) from A to B and

X Findsym is automatically confirmed by default, and a, B can default to [0,x-1]

When F is a matrix, the sum will be individually

>> clear>> syms t k>> f=[t,k^3];>> s=simple (Symsum (f)) s = [T^2/2-T/2, K^3*t]

2.3.3 Symbol integral

Int (f,x) to calculate indefinite integral of f (x) dx

int (f,x,a,b) definite integral from A to B

Similarly, x default findsym automatically confirms that a, B can be any value or symbol expression

>> clear>> syms x>> f=sqrt ((x+1)/x)/x;>> S=int (f,x), S=simple (s) s =-(1/x + 1) ^ (a)-2*atan (( 1/x + 1) ^ (*i) *i  s =-2*atan (1/x + 1) ^ ((1/x + 1) ^ () *i) *i

。。 The result is how the whole complex.

Matrix Quadrature

>> clear>> syms a b x>> f=[a*x,b*x^2;1/x,sin (x)];>> disp (' The ANS is '); the ANS is>> int (f) A NS = [(a*x^2)/2, (b*x^3)/3][    log (x),   -cos (x)] >> Pretty (int (f))   +-                 -+   |      2        3   |   |   A x      b x    |   |   ----,    ----   |   |    2        3     |   |                   |  | Log (x),-cos (x)  |   +-                 -+

Feel pretty () a bit uglier.

You can also ask for multiple integrals.

>> clear>> syms x y>> int (int (x*y,y,2,3), x,1,2) ans = 15/4

MATLAB Learning Note (iii): Symbolic calculation _-_2