Matlab symbol limit, derivative and series summation

Author: Wang Flight, School of Transportation Engineering, Changsha University of Technology

1, the limit of the function

function:limit

function: The limit of the function to be obtained

Grammar:

Limit (f)

Limit (F,x,a)

Limit (f,x,a, ' right ')

Limit (F,x,a, ' left ')

Description: The first refers to the limit of the self-variable in the expression F to 0 , and the second refers to the limit of the independent variable x tending to a in the expression F, and the third refers to the right limit of the self-variable x in the expression F. The left limit of the expression F in the argument X tending to a .

Note: If Y=f (A,b,c,......) Ask A→n1,b→n2,c→n3 ... (N1,n2,n3 ... Represents a number) when the limit of Y is reached, the limit can be calculated in turn to obtain the final result. See Example 3

Example 1: Request

Syms N;    %SYMS declaration of the following variable is the symbolic variable y= (1+1/n) ^n; Limit (y,n,inf) ans =exp (1)

Example 2: Request

syms x; y=1/(x* (log (x)) ^2) -1/(x-1) ^2;  %log is lnlimit (y,x,1,'right')

The results can be as follows:

Ans =

1/12

Example 3:

>> syms x;>> syms y;>> z=x^2+1/y;>> z=limit (z,x,1);>> z=limit (z,y,2)

You can get the result

z =

3/2

2, the symbol summation of the series

The most common form of progression, as shown below.

S: Sum of series

I: independent variable, the range is [a, b]

F (i): For the function of the argument I

function:symsum

function: Sum of series symbols

Syntax:symsum (S)

Symsum (S,V)

Symsum (S,A,B)

Description: the function symsum (s) in S is a symbolic expression, S is relative to the ampersand variable K's and, K takes value from 0 to k-1. function Symsum (s,v) specifies s relative to the variable V and V from 0 to V-1. The function symsum (s,a,b) and Symsum (s,v,a,b) specify symbolic expressions to accumulate from v=a to v=b.

Cases:

Syms v fa = 1;b = 100;f = v^2; S = Symsum (f,v,a,b)

The result of the calculation is:

S = 338350

3, the derivation of the polynomial

function 1:polyder

function: derivation of polynomial or rational polynomial

Syntax:polyder (A)

Description: A is a polynomial matrix and a derivative of a.

Example: Derivation of f (x) =x4+2x3+3x2+1

A = [1,2,3,0,1]  % writes the polynomial matrix, the middle lacks the power to use 0 complete                         %, attention must be from the high write to the lower times, cannot miss the item P = Polyder (A)  % The result obtained here is also the polynomial matrix

function 2:fminsearch

function: starting from an initial value, find the minimum value of a scalar function

syntax:x= fminsearch (fun,x0)

Description: starting from x0, find the local minimum value of the function fun

Example: function Y=x2+4, when the x value is how large, Y has local minimum value

x0 = -2;a = Fminsearch (@ (x) (x^2+4), x0)

　　

　　

Matlab symbol limit, derivative and series summation