Matlab level 1.pptx

inf infinity
pi Ratio of circle
exp ( degree ) Exponential
sin (radian) cos (radian) tan (radian)
sind (degree) cosd(degree) tand (degree)
X = 3 + 4i
real ( X ) = 3
imag ( X ) = 4
abd ( X ) = 5
angle ( X ) = 0.9273 Angle in radian
conj ( X ) = 3.0000 - 4.0000i

asin (Value) Inverse sin
acos (Value) Inverse cos
atan (Value) Inverse tan
sec cosec cot sinh cosh tanh sech cosech coth
Can add ( d ) to use in degree or add ( a ) in first to get inverse
sqrt ( Value ) Root
log ( Value ) Ln
log10 ( Value )
factorial ( Value )
round ( Value ) Closest number for value

Format long increase accuracy of number
Format short decrease accuracy of number
round ( Value ) Round nearest integer  .5
fix ( Value ) Round toward zero
ceil ( Value ) Round toward infinity
floor ( Value ) Round toward minus infinity
rem ( X , Y ) Returns the remainder
sign ( X ) sign function. [ X>0 -> 1 , X<0 -> -1 , X=0 -> 0 ]

clc Clean command window
clear Delete all variable
clear all Delete all variable
clear A Delete variable A only
who Show all variables
& = and ( x , y ) And
~ = not( x ) Not
| = or( x , y ) Or
xor ( x, y ) Xor

Define Vector (horizontal matrix)

Vector = [ a(1) a(2) a(3) a(4) a(5) ] Define vector by elements
X = [ 12 8 2 34 0 ]
X = [ A : B : C ] Define vector by steps
A : first element B : steps of counter C : last element
X = [ 1 : 2 : 5 ]
X = 1 3 5
X = [ 1 : 5 ] Define with one step by default
X = 1 2 3 4 5

If you write X = [ 12 8 2 34 0 ] on command window without ; (semi Colom)
Matlab will print it .
X = [ 12 8 2 34 0 ]
X =
12 8 2 34 0
But if write X = [ 12 8 2 34 0 ] ; ( with semi Colom ) the matlab will not print
it.
X = [ 12 8 2 34 0 ] ;

Print vector
X = [ 0 1 2 3 4 ]
answer = X ( 1 ) print element a( 1 ) = 0
answer = X ( 1 : 4 ) print from elements from 0 to 3
answer = X ( 1 : end ) print from elements from 0 to 4
answer = X ( 1 : end - 1 ) print from elements from 0 to 3

X = [ 1 2 3 ] Y = [ 4 5 6 ]
prod ( X ) Product all elements of vector
Answer = prod ( X ) = 1 * 2 * 3 * 4 = 24
dot ( X , Y ) Dot product of two vectors
Answer = 1*4 + 2*5 + 3*6 = 32
cross ( X , Y ) Cross product of two vectors
Answer = -3 6 -3
Sum (X) To sum all elements in matrix
Answer = 6

linspace ( A , B , C ) generates C points between A and B
A : first element B : last element C : number of elements
X = linspace ( 0 , 1 , 5 )
= 0 0.2500 0.5000 0.7500 1.0000
X = linspace ( 0 , 1 , 6 )
= 0 0.2000 0.4000 0.6000 0.8000 1.0000

Define matrix
X = [ A B C ; D E F ] or X = [ A , B , C ; D , E , F ]
X = A B C Semi Colom to make new row
D E F
X = [ 1 : 0.5 : 2 ; 2 : -0.5 : 1 ] Different way to define
X = 1 1.5 2
2 1.5 1

Print matrix
X = [ 1 2 5 ; 0 1 7 ; 2 3 4 ]
X (1 , 3) = X ( A ( 1 ) , B ( 3 ) )
= 5
X (end - 1 , end - 2 ) = X ( A ( 2 ) , B ( 1 ) )
= 0
X (end , end) = X ( A ( 3 ) , B ( 3 ) )
= 4

X = [ 1 2 5 ; 0 1 7 ; 2 3 4 ]
X (1 , 1 : 3 ) = X (1 , : )
= 1 2 5
X (1 , [ 1 3 ] ) = X ( A( 1 ) , B( 1 ) X ( A( 1 ) , B( 3 ) )
= 1 5
X ([ 1 3 ] , [ 1 3 ] ) = 1 5
2 4

Delete Elements
Define by index number for row or column then equal with []
X = [ 1 2 5 8 ; 0 1 7 2 ; 6 2 3 4 ]
X = X (1 , : ) =[] Delete first row
= 0 1 7 2
6 2 3 4
X ( : , [ 1 3 ] ) = [] Delete first and third column
= 2 8
1 2
2 4

Add Elements
Define by index number for row or column then equal with elements
X = [ 1 2 5 ; 0 1 7 ; 6 2 3 ]
X = X ( 4 , : ) = [ 0 0 0 ] Adding row in last
= 1 2 5
0 1 7
6 2 3
0 0 0

Operations on matrix
X = [ 1 2 : 3 4 ] Addition on matrix
Answer = X + 5
Answer = 6 7
8 9
rand ( A , B ) Make matrix with random values
A : Number of rows B : Number of columns
X = prod ( 2 , 3 )
0.8147 0.1270 0.6324
0.9058 0.9134 0.0975

E–notation
E – 1 = 0.1
E – 2 = 0.01
9E - 1 = .9
4E - 2 = .04
X = [ 5E-1 7E-2 9e-4]
= 0.5000 0.0700 0.0009
It can be e or E

Complex Numbers
•Both i and j are allowed
•Don’t write I nor J
•Write 3i and don’t write i3
•You can write 3*i or i*3
X = [ 1 + 3i ; 5 - 1i ; 4 + 3j ]
1.0000 + 3.0000i
5.0000 - 1.0000i
4.0000 + 3.0000i

zeros ( Raw , Column ) Elements of matrix are zeros only
X= zeros ( 2 , 3 )
= 0 0 0
0 0 0
ones ( Raw , Column ) Elements of matrix are ones only
X= ones ( 1 , 4 )
= 1 1 1 1

eye( N ) Square matrix ( Identity matrix )
X= eye ( 3 )
= 1 0 0
0 1 0
0 0 1
inv ( X ) = X^-1 Inverse the matrix X=[ 1 2 ; 1 6 ]
answer= inv ( X )
= 1.5000 -0.5000
-0.2500 0.2500

magic ( N ) Make square matrix with random values
X= magic ( 2 ) N : number of raw or column
= 1 3
4 2
reshape ( A , B , C ) Reshape the size of matrix
A : Name of matrix B : Row of new matrix C : Column of new matrix
answer= reshape ( X , 2 ,3 ) // X = [ 1 2 ; 3 4 ; 5 6 ]
= 1 5 4
3 2 6

X = [ 1 2 3 ; 4 5 6 ]
max ( X ) Maximum element in matrix
= 6
min ( X ) Minimum element in matrix
= 1
size ( X ) Size of matrix
= 2 3 2 is raw , 3 is column
length ( X ) Number of columns in matrix
= 3

X = [ 1 2 3 ; 4 5 6 ]
fliplr ( X ) Replace columns from left to right
= 3 2 1
6 5 4
flipud ( X ) Replace rows from up to down
= 4 5 6
1 2 3

X = [ 1 2 3 ; 4 5 6 ]
transpose ( X ) = X ' Make rows to columns
= 1 4
2 5
3 6
rot90 ( X ) Rotate matrix 90 degree anti-clockwise
= 3 6
2 5
1 4

X = [ 1 2 ; 4 5 ] Y = [ 6 7 ; 8 9 ]
Product matrix element by element (square element)
Answer = X . * Y
= 6 1 4
3 2 4 5
Division in matrix element by element
Answer = X . / Y
= 0.1667 0.2857
0.5000 0.5556

X = [ 1 2 ; 4 5 ]
Product and matrix ( cross product )
X*X = X^2
= 7 1 0
1 5 2 2
Product matrix by number
Answer = X * 2
= 2 4
6 8

X = [ 1 2 ; 4 5 ]
Division in matrix by number (using / )
Answer = X / 2
= 0.5000 1.0000
1.5000 2.0000
Division in matrix to solve equations (using )
By invers matrix ( power -1 )
x + y = 2
x - y = 0

A ^ - 1 * B = inv( A ) * B = A B is up of enter key
B * A ^ - 1 = B * inv( A ) = B A
A X B
A = [ 1 1 ; 1 -1 ] B = [ 2 ; 0 ]
X = A B = inv (A) * B
answer = 1 x=1 y=1
1

X = [ 1 2 3 ; 4 5 6 ]
Power in matrix power elements
Answer = X.^2
= 1 4 9
16 25 36
Power to product in matrix ( cross product )
Answer = X^2 = X*X Must dimension allow
= Error

A = [ 1 2 ; 3 4 ] B = [ 1 -1 ; 2 -2 ]
Power in matrix by matrix
Answer = A.^B
= 1.0000 0.5000
9.0000 0.0625
The determinant in matrix ( | ‫المحددة‬ | )
det (A) = -2
det (B) = 0

A = [ 1 2 ; 3 4 ] Matrix
B = [ 10 -1 2 -2 ] Vector
sum ( Matrix ) Sum elements in each column
sum ( A ) = 4 6
But in vector the sum for row
sum ( B ) = 9

A = [ 1 2 5 ; 0 1 7 ; 2 3 4 ]
rank ( Matrix ) provides an estimate of the number of linearly independent
rows or columns of matrix.
rank ( A ) = 3
trace ( Matrix ) Sum of the diagonal elements
trace ( A ) = 6

pascal ( N ) Make random square matrix like magic (N)
N : number of row or column
pascal (3) = 1 1 1
1 2 3
1 3 6
diag ( A ) It is main diagonal elements of matrix
A = [ 1 2 5 ; 0 1 7 ; 6 2 3 ]
diag ( A ) = 1
1
3
Remember trace ( A ) get the sum of diag ( A ) = 5

GRAPHICS FUNDAMENTALS
(2D PLOTTING)

X = [ 0 pi/4 pi/2 pi ] Y = sin ( X )
plot ( A , B ) Drawing F(A) horizontal axis and F (B) Vertical axis
plot ( X , Y )
The problem is low
number of data points
no figure .
X vector is 4 points only.
So on Y function.

The solution by increase input data points in X vector by :
X = [ 0 : 0.01 : pi ] ; Y = sin ( X ) ;
plot ( X , Y )
In X vector increase point .Start form 1
to pi using steps 0.01 that data points
( increase accuracy ).
You can put ; after X and Y to don't
print the vector again

X = [ 0 : 1 : 360 ] ; Y = cosd ( X ) ;
plot ( X , Y )
Print sin function start from 0 degree
To 360 degree using 1 degree step.
plot ( X , Y ) = plot ( X , Y ) ;
If you put ; after plot ( X ,Y ) or
don't put the same.

X = [ 0 : 1 : 360 ] ; Y = cosd ( X ) ;
To change color of figure
plot ( X , Y , 'r')
Black ‘k'
Yellow ‘y'
Magenta ‘m'
Cyan ‘c'
Red 'r'
Green ‘g'
Blue ‘b'

X = [ 0 : 1 : 360 ] ; Y = cosd ( X ) ;
To draw grid on figure:
grid on
To turn of the grid:
grid off
Line marking:
Change line to be . + * o >
Put after color in the ‘ '
plot ( X , Y , 'r+')

+ plus sign
o circle
* asterisk
. Point
x cross
s square
d diamond
^ upward pointing triangle
v downward pointing triangle
> right pointing triangle
< left pointing triangle
p five-pointed star (pentagram)
h six-pointed star (hexagram)

Line Styles:
- solid line (default)
-- dashed line
: dotted line
-. dash-dot line
plot ( X , Y , '- - ' )
You can use line style or line mark
without color and can use them together
plot ( X , Y , '* - -' )

Multiple plot:
To plot multiple plots on the same
figure use the command:
hold on
X = [ 0 : . 01 : 10 ] ;
Y = X . ^ 2;
A = 3 * X ;
plot ( X , Y , 'r - -' )
hold on
plot ( X , A , 'c ' )

Multiple plot:
To plot multiple plots on the same
figure use the command:
plot (X,Y,A ,B)
grid on
X = [ 0 : . 01 : 10 ] ;
Y = X . ^ 2 ;
A = 3 * X ;
plot ( X , Y, 'b', X ,A , 'k ')

Adding Titles and Axes Labels :
title xlabel ylabel
grid on
A = [ 0 : . 01 : 10 ] ;
B = A . ^ 3;
plot ( A , B, 'c ')
title (' Two functions ')
xlabel (' A axis ' )
ylabel (' B axis ' )
Don't forget ' ' around text

Legend:
Legend is used when dealing
with multiple plots.
A = [ 0 : . 01 : 10 ] ;
B = A . ^ 2;
C = sqrt ( A ) ;
plot(A ,B, 'r ',A , C , 'g --') ;
legend ( 'square', 'root') ;
Square : first plot < A , B >
Root : second plot < A , C >
legend

subplot ( A , B , C ):
Divide the MATLAB plot window into sub-plot windows
A : number of rows.
B : number of columns.
C : wanted plot to drawing.
X = [ 0:0.01: 2*pi];
Y = sin (X );
s u bplot(1 , 2,1)
p l ot( X ,Y, 'r')
Z = X .^ 3;
s u bplot(1 , 2,2)
p l ot( X ,Z, 'k')

linewidth:
Change line style or line mark line size by :
plot(x,y,'linewidth',2)
plot(X,Y,'g-','linewidth',3)
fontsize:
Change title , xlabel or ylabel font size by :
title ( ' Sample Plot ' ,'fontsize', 14 ) ;
xlabel ( ' X values ' , ' fontsize ' , 14 ) ;
ylabel ( ' Y values ' , ' fontsize ' , 14 ) ;

Function plot:
fplot ( @X , [ A Z ] , 'r--+')
X : standard function to drawing
( sin exp sind acos sqrt log )
A : start substitution
Z : end substitution
fplot ( @sin , [ 0 2*pi ] , 'm--')

Function plot:
You can use:
fplot ( 'X' , [ A Z ] , 'r--+')
But will get warning
fplot ( 'sin' , [ 0 2*pi ] , 'm--')

Function plot:
Draw without period
fplot ( @X ,'r--+')
fplot ( 'X' ,'r--+')
fplot ( @exp , 'm')
fplot ( 'exp' , 'm')

Multi-Function plot:
fplot ( @(X)f(X)+g(X) ,[A Z],'r --+')
fplot ( 'f(X)+g(X)' ,[A Z],'r--+')
fplot (@(x)exp(x)-x-2,[-3 3])
fplot ('exp(x)-x-2',[-3 3])

fplot ( @(X)f(X).*g(X) ,[A Z],'r --+')
fplot ( '(X)f(X)*g(X)' ,[A Z],'r--+')
fplot (@(x)exp(-x).*sin(x),[0 pi])
fplot ('exp(-x)*sin(x)',[0 pi])

fplot ( @(X)f(X).*g(X) ,[A Z],'r --+')
fplot ( '(X)f(X)*g(X)' ,[A Z],'r--+')
fplot ( @(X)X^+2*X+1 ,[0 20],'r--')

figure : This command make new figure to draw new plot.
X=[ 0 : 1 : 360 ];
Y = sind (X);
Z = cosd (X);
plot(X,Y)
grid on
figure
plot(X,Z)
grid on
Figure 1 Figure 2

(3D PLOTTING)

plot3 (A,B,C,'r--')
t = 0 : .01 : 1;
x = t + 2 ;
y = t - 2 ;
z = t ;
plot3 (x,y,z,'r--')

Plot 3D :
t = -pi:0.01:pi;
X = ones ( length (t) );
Y =5*cos(t);
Z =5*sin(t);
plot3 (X,Y,Z, 'r.')
grid on

Plot 3D :
t= 0 : 0.01 : 10*pi ;
X = cos (t) ;
Y = sin (t) ;
Z = t ;
plot3 (X,Y,Z, 'g','linewidth',3)
grid on

Plot 3D :
X = 0:0.01:3*pi ;
Y1 = zeros (size(X));
Y2 = ones (size(X));
Z1 = sin(X) ;
Z2 = cos(X) ;
plot3 ( X, Y1 , Z1 , 'r' , X ,Y2 , Z2 , 'g' )
grid on

(MESH - SURFACE)

meshgrid ( A , B )
A = -10 : .01 : 10;
B = -10 : .01 : 10;
[ X , Y ] =meshgrid (A ,B);
C = X.^2 + Y.^2;
mesh ( X , Y , C )
grid on

To make m-file press N + ctrl or select New then script .
First rule in programming end every command with ;
X = input (' Text ') ; To receive value form user
X = input (' Text ' , 's') ; To receive text form user
X : The variable that the input will be saved in it.
Text : Told user what to enter.
X = input (' Enter the temperature ') ; Enter 2023
X = input (' Enter your name ' , 's') ; Enter Ahmed

Print text or print variable:
disp ( X ); Print the saved value in variable X
disp ( 'X' ); Print X letter
Area = 2 * pi * 10;
disp ( area ); Print 62.831853
disp ( 'area' ); Print area
You can not print variable and text together

Commands:
%
Any thing will be writhen after % called comment and will not read from matlab
% Matlab is big program
n Get new line (should put it every display command)
disp ( 'area n of circle' ); Print area
of circle

Area = 62.831853 length= 20
If you print integer number use %d else if float number use %f
fprintf ('the area of circle = %f - %d n' , Area, length);
the area of circle = 62.831853 , 20
fprintf ('% 12.3 f ' , Area);
12 Present on space in printing
.3 Present number of fractions after . In float numbers
fprintf ('the area of circle = %0.2f n' , Area);
the area of circle = 62.83

If statement:
if condition
Statement;
elseif condition
Statement;
else
Statement;
end
Result

Price=input('Enter the price=n');
if Price == 2000
Discount = .5;
elseif Price >1000
Discount = .3;
else
Discount = .1;
end
Price = Price – Price * Discount;
price == 2000 used to check equal

for statement:
for variable = condition
Statement;
end
condition : initial value : increment : end value
Result = 1; Factorial command
for X = 1 : 5
Result = Result * X;
end

i =input('Enter number of rows=n');
j =input('Enter number of columns=n');
for A = 1 : i
for B = 1 : j
X( A , B )=input('Enter the value =n');
end
end
disp(X)

while statement:
while condition
Statement;
end
N=input('Enter the number =n'); Result = 1; Factorial command
while N > 1
Result = Result *N;
N=N-1;
end
disp ( Result ) -> 120 if N = 5

switch statement:
switch condition
case 1
Statement;
case 2
Statement;
otherwise
Statement;
end

X=input(‘Enter the case number =n’);
switch X
case 1
disp (' one ');
case 2
disp (' two ');
otherwise
disp (' error ');
end

X=input('Enter the case letter =n','s');
switch X
case 'A'
disp (' a letter ');
case 'B'
disp (' B letter ');
otherwise
disp (‘ error ');
end

Break:
Use break to exit the loop ( for , while ).
for i = 1 : 360
X = sind(i);
if(X==1)
break;
end
end
fprintf (' X = %d n Angle = %d degree n', X , i );

To make function-file select New then function.
function [outputArg1,outputArg2] = untitled (inputArg1,inputArg2)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
outputArg1 = inputArg1;
outputArg2 = inputArg2;
end
First look when open function file
untitled title of function
outputArg1,outputArg2 Outputs
inputArg1,inputArg2 Inputs

function [Area_of_circle] = Area(Diameter)
%UNTITLED3 Summary of this function goes here
% Detailed explanation goes here
format long
Area_of_circle = (Diameter^2)*.25 * pi;
end
Function called Area calculate area of circle by one input Diameter and one output
Area_of_circle
Area (10) Calling in command
ans = 78.539816339744831

function [Area , Distance] = Circle(Diameter)
% Area of circle Function calculate Area and Circumference
% Distance : Circumference of circle
Area = (Diameter ^ 2 )*.25*pi;
Distance = Diameter*pi;
end
Use next expression when have two or more outputs
[ Area Distance ] = Circle (10)
Area =
78.5398
Distance =
31.4159

Symbols in matlab:
syms X Y Z T Define symbols
A = X^2 – 2*X +1
B = X^2 - 16
C = X^3 + X^2 + 2*X +1
solve ( Equation == 0 ) Solving equations for all degrees
But must define symbols at first syms X
solve ( X - 1 == 0) >>> X = 1
solve (X^2 - 10*X + 16 == 0) >>> X= 2 8

Solving equations together:
Define symbols then put the unknown symbols in [ ] then equal it to
solve (equations in one side equal to zero )
Solve A = X - Y = 6 , B = X + Y = -2
syms X Y
[ X Y ] = solve ( X - Y - 6 , X + Y + 2 )
X = 2 Y = - 4

Differentiation:
Define symbols then diff ( Equation )
syms x
Y = x^3 + x^2 + 2*x +1
diff ( Y )
Answer = 3*x^2 + 2*x + 2
By default matlab differentiate for x ( small letter )

Differentiation for any symbol and more than one:
syms X
Y = X^3 + X^2 + 2*X +1
diff ( Y , X ) Differentiate for X symbol
Answer = 3*X^2 + 2*X + 2
diff ( Y , 2 ) or diff ( diff ( Y ) ) Differentiate twice
Answer = 6*X + 2

Substitution in Differentiation:
subs ( Answer , [ A B X ] , [ 1 2 3] )
syms X A B
Y = A*X^3 + B*X^2 + 2*X +1
Answer = diff ( Y , X )
Answer = 3*A*X^2 + 2*B*X + 2
subs ( Answer , [ A B X ] , [ 1 2 3] )
ans = 41

Simple in Differentiation:
simplify ( Answer ) Simple the answer of differentiation
syms X
Y = X^3 * exp ( - X^2) * sin ( X )
Answer = diff ( Y , X )
Answer = X^3*exp (-X^2)*cos(X) + 3*X^2*exp (-X^2)*sin(X) - 2*X^4*exp(-
X^2)*sin(X)
simplify ( Answer )
ans = X^2*exp(-X^2)*(3*sin(X) + X*cos (X) - 2*X^2*sin(X))

Expand in Differentiation:
expand ( Answer ) Expand the answer of differentiation
Answer = X^2*exp(-X^2)*(3*sin(X) + X*cos (X) - 2*X^2*sin(X))
expand ( Answer )
Answer = X^3*exp (-X^2)*cos(X) + 3*X^2*exp (-X^2)*sin(X) - 2*X^4*exp(-
X^2)*sin(X)

Integration:
Define symbols then int ( Equation )
syms x
Y = x^3 + x^2 + 2*x +1
int ( Y )
Answer = x^4/4 + x^3/3 + x^2 + x
By default matlab integrate for x ( small letter )

Integration for any variable :
int ( Equation , Integration for )
syms X Y
F = Y*X^3 + + Y^2+X^2 + 2*Y^3*X +1
int ( F , Y )
Answer = (X*Y^4)/2 + Y^3/3 + Y*(X^2 + 1) + (X^3*Y^2)/2
For integration more than one time:
int ( int ( F ) )
Answer = (X^5*Y)/20 + X^2*(Y^2/2 + 1/2) + X^4/12 + (X^3*Y^3)/3

Substitution in integration :
int ( Equation , Integration for , Star , End )
syms X
Y = 3*X^2 + 2*X + 1
int ( Y , X , 0 , 1 )
Answer = 3
You can use command subs ( ) :
subs ( Answer , [ X ] , [ 1 ] ) - subs ( Answer , [ X ] , [ 0 ] )

Integration for X then for Y and substitution:
syms X Y
F = Y*X^3 + Y^2 + X^2 + 2*Y^3*X +1
int ( int ( F , X , 0 , 1 ) , Y , 0 , 2 )
Answer = 59/6
Wil integrate F for X and substitution form 0 to 1 then integrate answer for Y
and substitution form 0 to 2

Limits:
Define symbols then limit ( Equation , limit by , limit to )
syms X
Y = sin ( X ) / X
limit ( Y , X , 0 )
Answer = 1
By default matlab do limits without define ( limit by ) if there are one symbol
in equation only ( Equation has X or Y not X and Y )
limit ( Y , 0 )

Partial fraction for numerical:
[ C , D , E ] = residue ( A , B )
A = [ - 4 8 ];
B = [ 1 6 8 ];
[ C D E ] = residue ( A , B )
C = - 12 8 D = - 4 - 2 E = []
You can change A,B,C,D and E with any symbols but the arrangement
required the first is numerator and the second is maqam.
[ r p k ] = residue ( b , a ) == [ C D E ] = residue ( A , B )

When define A and B must arrange power and if power missed equal zero
Y = (x^2+5)/(x^3+2*x)
A = [ 1 0 1 ] ;
B = [ 1 0 2 0 ] ;
[C D E] = residue ( A , B )
C = 0.2500 0.2500 0.5000
D = 0.0000 + 1.4142i 0.0000 - 1.4142i 0.0000 + 0.0000i
E = [ ]

The unification of the stations:
[ A , B ] = residue ( C , D , E )
Must C and D vertical matrix (one column))
C = [ - 12 ; 8 ];
D = [ - 4 ; - 2 ];
E = [];
[ A B ] = residue (C , D , E )
A = - 4 8 B = 1 6 8

Partial fraction for symbols:
syms X
A = - 4*X+8 ;
B = X^2+6*X+8 ;
diff ( int ( A / B ) )
Answer = 8/(X + 2) - 12/(X + 4)
More better diff ( int ( A / B , X ) , X )

Differential equation:
dsolve ('equation')
y’’ + 5* y’ + 8* y =10
D2y+6*Dy+8*y=10
dsolve ('D2y+6*Dy+8*y=10')
Answer = C2*exp(-2*t) + C1*exp (-4*t) + 5/4

Substitution in differential equation:
dsolve (' Equation ','y(0)=0')
y’’ + 5* y’ + 8* y =10
D2y+6*Dy+8*y=10
dsolve ('D2y+6*Dy+8*y=10',‘y(0)=0',‘y(1)=1')
Answer = 5/4 - (exp(-4*t)*(5*exp(2) - exp(4)))/(4*(exp(2) - 1)) - (exp(-
2*t)*(exp(4) - 5))/(4*(exp(2) - 1))

Matlab level 1.pptx

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