Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems. The software can be used similarly to an engineering equation solver (EES) or it can be taken to the second level of jobs like Simulink. the software can do hard math and solve differential equations. Matlab software for math work is often used by mechanical engineers and mechanical engineering students for programming software for solving problems.
There are so many mathematical symbols that are important for students. To make it easier for you we’ve given here the mathematical symbols table with definitions and examples
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Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
There are so many mathematical symbols that are important for students. To make it easier for you we’ve given here the mathematical symbols table with definitions and examples
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Contact us via email: info@mathsassignmenthelp.com or reach out to us on
WhatsApp at +1(315)557-6473.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
The Internet of Things (IoT) is a revolutionary concept that connects everyday objects and devices to the internet, enabling them to communicate, collect, and exchange data. Imagine a world where your refrigerator notifies you when you’re running low on groceries, or streetlights adjust their brightness based on traffic patterns – that’s the power of IoT. In essence, IoT transforms ordinary objects into smart, interconnected devices, creating a network of endless possibilities.
Here is a blog on the role of electrical and electronics engineers in IOT. Let's dig in!!!!
For more such content visit: https://nttftrg.com/
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
2. 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
3. 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
4. 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 ]
5. 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
7. 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
8. 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 ] ;
9. 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
11. 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
12. 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
13. 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
14. 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
16. 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
17. 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
18. 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
19. 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
20. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
35. 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
36. 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
38. 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.
39. 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
40. 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.
41. 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'
42. 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+')
43. + 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)
44. 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 , '* - -' )
45. 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 ' )
46. 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 ')
47. 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
48. 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
49. 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')
50. 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 ) ;
52. 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--')
53. Function plot:
You can use:
fplot ( 'X' , [ A Z ] , 'r--+')
But will get warning
fplot ( 'sin' , [ 0 2*pi ] , 'm--')
54. Function plot:
Draw without period
fplot ( @X ,'r--+')
fplot ( 'X' ,'r--+')
fplot ( @exp , 'm')
fplot ( 'exp' , 'm')
58. 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
67. 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
68. 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
69. 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
70. 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
72. 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
73. 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
74. 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)
77. X=input(‘Enter the case number =n’);
switch X
case 1
disp (' one ');
case 2
disp (' two ');
otherwise
disp (' error ');
end
78. X=input('Enter the case letter =n','s');
switch X
case 'A'
disp (' a letter ');
case 'B'
disp (' B letter ');
otherwise
disp (‘ error ');
end
79. 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 );
80. 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
81. 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
82. 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
83. 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
84. 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
85. 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 )
86. 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
87. 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
88. 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))
90. 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 )
91. 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
92. 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 ] )
93. 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
94. 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 )
95. 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 )
96. 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 = [ ]
97. 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
98. 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 )