Matlab reference

dslove,solve,ode45,simplify,
syms,inline

eval( Used to cycle ）
eval Function can also evaluate the value of a symbolic expression . Don't define f(x）
Direct definition f,x=2, eval（f） You can figure it out f(2) Value
rref： Reduce the matrix to Row trapezoidal matrix , By the way, linear equations can be solved
rref It can also simplify at the same time , By the way, we get the maximal unrelated group
rref Find the maximum independent group and pass for Loop printing
expand、factor( polynomial ）
vpa

MATLAB Knowledge system

Knowledge system of linear algebra

Symbolic function
syms f(x) —— Define two symbolic variables ,f and x, And there is a functional relationship between the two
When declaring symbolic functions , You can also use inline function ：
f = inline(“x ^ 3+5x”) perhaps ff = inline(’-xsin(x^2-x-1)’, ‘x’) If not quoted , Then its internal variables should be known .

Matrix operations

Matrix operations
1、 Some special matrices ,
ones(m,n)
zeros(M, N)
2、 Addition and subtraction of matrix
3、 Dot product of matrix 、 Point division
Matrix Point multiplication , Multiply the corresponding elements , You can also multiply each element of the matrix by a constant
4、 Left division of matrix \ Divide with right /
Simple memory Matlab Left division in () And right division (/)
be demoted : C = B\A That is to say BC =A
Divide right : C = B/A That is to say CA = B

AX=b, solve X matrix ,X = A\b

5、 The power of a matrix X^y

Solving differential equations

dsolve、ode A series of functions
D: Differential symbols ;D2 Second order differential ,D3 Represents a third-order differential , And so on .
Y = dsolve(‘eq1,eq2,…’ , ’cond1,cond2,…’ , ’Name’)

among ,‘eq1,eq2,…’: Represents a differential equation or system of differential equations ;

        ’cond1,cond2,…’: Indicates initial or boundary conditions ;

        ‘Name’: Said variable . When no variable is specified ,matlab The default variable is t;

About ode45 Use

Let's do another example
ode45 Numerical solutions for solving differential equations

matlab in desolve、solve The application of function
Second order differential equations , Turn up a few books

solve Detailed explanation ：1） equation ： single / Multivariable + linear / nonlinear ;2） inequality
Matlab in diff Use of functions