This document is a chapter on using MATLAB for problem solving. It discusses MATLAB's capabilities for simple calculations using variables and functions, working with matrices and vectors, plotting and visualization, and solving systems of linear equations. The chapter provides examples of MATLAB code for these tasks and concludes with a practice problem asking the reader to solve a system of equations using MATLAB.

1. Chapter 01
COURSE CODE: CEB 40403
USE OF MATLAB IN PROBLEM SOLVING
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2. Learning
outcomes
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Simple calculations through MATLAB
Use of variables and functions
Matrices and Vectors
Plotting and visualization in MATLAB
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3. Introduction
High level language for technical computing
Stands for MATrix LABoratory
Everything is a matrix - easy to do linear algebra
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4. Menu and toolbar
Workspace
History
Command
Saved files
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5. Simple calculations
a= b+c
If b=4, c=7
Then a=11
Similarly, a= z+b(c+d)
If z=-2, b=3, c=2 and d=6
Then, a=-2+3(2+6)=16
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6. Use of Variables and
functions
f(x)=a.x+b
Where x=independent variable and ‘a’
and ‘b’ are constants, and f(x) is
dependent variable.
If, a=2, and b=3, and x=-1, 0, 1
Then f(x)=1, 2, and 5
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7. Variable names
MATLAB legal names consist of any combination of letters and digits,
starting with a letter. Eg. NetCost, Left2Pay, X3, x3 Z25c5 etc.
These are not allowed as variable names in MATLAB eg., Net-Cost,
2Pay, %x, @sign, sin cos, tan etc.
Special names: you should avoid using eps, pi, I, j (both represents
imaginary number
1
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8. Functions
Trigonometric functions: those known to MATLAB are sin, cos, tan and
their arguments should be in radians. E.g 30o=pi/6 radians
The inverse trigonometric functions are called as: asin, acos, atan etc.
the results are in radian.
Other functions: sqrt, exp, log, log10.
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9. Vectors
Vectors are classified as in two types:
Row vector: they are list of numbers separated by either commas or
spaces. The number of entries is known as the length of the vector and
the entries are often referred as “elements” or “components” of the
vector.
>>v=[1 3, sqrt(5)]
Column vector: to create a column vector type the left square bracket[
and then enter the element with a semicolon between them.
>>cv=[1; 2; 3; 4]
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10. Matrices and Vectors
Linear systems of algebraic equations:
11 1 12 2 13 3 1 1
21 1 22 2 23 3 2 2
1 1 2 2 23
...............
................ a
..
..
..
.................
N N
N N
N N NN N N
a x a x a x a x b
a x a x a x x b
a x a x a x a x b
   
   
   
is the constant coefficients (assume) real that multiply with independent Variable,
in above equation is the constant for right hand side of eq.
ija
jx ib
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11. Consider a system:
It is common to write linear equations in matrix form as:
1 2 3
1 2 3
1 2 3
4
2 3 7
3 6 2
x x x
x x x
x x x
  
  
  
11 12 13 1 1
21 22 23 2 2
31 32 33 3 3
a a a x b
a a a x b
a a a x b

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12. 1
2
3
,
1 1 1 4
2 1 3 7
3 1 6 2
Ax b
where
x
A b x x
x

  
19
7
8
x  

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13. Plotting and visualization
MATLAB used plot command to create two dimensional plots.
The instruction can be written in following way: plot(x,y)
The arguments x and y are each a vector (one-dimensional array). The
two vectors must have the same number of elements.
The x-values on the abscissa (horizontal axis) and the y-values on the
ordinate (vertical axis)
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14. Some specific commands for
plot
Notes about using the specifiers:
The specifiers are typed inside the plot command as strings.
Within the string the specifiers can be typed in any order.
The specifiers are optional. This means that none, one, two, or all three types can be
included in a command.
Some examples:
plot(x,y) A blue solid line connects the points with no markers (default).
plot(x,y,‘r’) A red solid line connects the points.
plot(x,y,‘--y’) A yellow dashed line connects the points.
plot(x,y,‘*’) The points are marked with * (no line between the points).
plot(x,y,‘g:d’) A green dotted line connects the points that are marked with diamond
markers.
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15. Example plot
Year 1988 1989 1990 1991 1992 1993 1994
Sales
(millions)
8 12 20 22 18 24 27
To plot this data, the list of years is assigned to one vector (namely yr),
and the corresponding sales data is assigned to a second vector (named sle). The
command window where the vectors are created and the plot command is used is
shown below:
>> yr=[1988:1:1994];
>> sle=[8 12 20 22 18 24 27];
>> plot(yr,sle,'--r*','linewidth',2,'markersize',12)
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16. Practice question
Solve the following equations using MATLAB:
2 3 1
5 7 3
x y
x y
 
 
2 3 1
5 7 3
2
1
x
y
x
y
     
     
     
   
      
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17. Summary of topic
Simple calculation using MATLAB
Difference between function and variable, Row vector and column
vector, vector and matrices.
Formation of matrices from linear equations
Use MATLAB in plot and visualization.
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18. End of slides for
chapter one
Dr. Mohammed Danish
Sr. Lecturer, Malaysian Institute of Chemical and
bioengineering Technology (MICET)-Universiti
Kuala Lumpur, Alor Gajah, Melaka, Malaysia
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