MATLAB Learning Note (iii): Symbolic calculation (integral + derivative)

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) ^ (1)-2*atan ((1/x + 1) ^ () *i) *i
 
 
s =
 
- ()-2*atan ((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)
 
ans =
 
[(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