IC3003
BASIC SCIENTIFIC
COMPUTING
Lecture 1
Monday 08:30-11:30
U204a
COURSE OUTLINE
 Assessment



30% Test – (30 Multiple Choice in 45 mins)
40% Assignment (8 Exercises)
30% Log sheet (Workshop Report) including
performance
 Lecture



Weighting
Notes & Reference Web site
http://edc.ic.polyu.edu.hk
http://www.ic.polyu.edu.hk
http://www.mathworks.com
 Using
POLYU webmail to submit assignments
2
OUTCOME – BASE LEARNING

After completed the course, the students should
be able to
1. Understand
the MATLAB can solve mathematical &
Scientific problem
2. Analyze the data by using 2D and 3D visualization plots
to enhance graphic presentation
3. Import and export data with other application
4. Use M-file programming to construct user defined math
functions
5. Construct programs with flow control functions
3
6. Construct graphic user interface
LECTURE 1
INTRODUCTION
INTRODUCTION








MATLAB stands for Matrix Laboratory
Basic Scientific Calculation (Linear Algebra,
Matrix )
Applied Pure Mathematics (Calculus, Partial
Fraction)
2D Plotting
3D Visualization
Curve Fitting
File Input / Output
Graphic User Interface, etc……
5
INTRODUCTION




MATLAB software version - MATLAB R2008a
The software icon in desktop
If you use previous version, it cannot open the
file
Another method:
 Use Notepad to save all file in the M-File
format (XXX.m)
 It cannot run in the Notepad, you just check
the solution in MATLAB
6
INTRODUCTION

MATLAB software interface
Current
Directory /
Workspace
Command
History
Command Window
7
INTRODUCTION

Current Directory / Workspace
Files in Current
Directory
8
INTRODUCTION

Current Directory / Workspace
Store the variables
The data is not saved after you exit MATLAB.
All data can be saved by :
1. Selecting “save Workspace As” from the
File menu
2. Using save function – This is used for
saving all data to MAT-File
9
INTRODUCTION

Command History
Display all previous
command
Double click the commands in
command history window will also
re-activate that command
10
INTRODUCTION

Command Window
Show the result
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INTRODUCTION

Command Window
Type the command
Show the result
MATLAB inserts a blank line to separate command lines.
You can eliminate it by using format compact
Pi or 
Remove blank line
3.14159265358979
3.1416
3.14
335/113
Command
Format compact
Format long (15 digits)
Format short (5 digits)
Format bank (2 decimal place)
Format rat (Ratio)
12
INTRODUCTION

M-File Programming
13
INTRODUCTION

M-File Programming
The new window
pump up
14
INTRODUCTION




M-File programming can be saved and
submitted the solution in a clear way
M-File programming has script or function file
(stand alone file)
Command windows is only to check the solution
directly
Note: When you do the exercise or assignment,
you should use M-File to run the solution and
you can see the answer and error in the
15
command window
INTRODUCTION

Simple Mathematics Functions










+, -, *, /, \,^
pi=
sin(pi)
cos(pi)
tan(pi)
sqrt(100)
factorial(5)
factor(100)
primes(100)
randperm(10)
16
INTRODUCTION

Round floating point numbers to integer

round

fix
>>round(10.5)
ans=
11
>>round(10.4)
ans=
10
>>fix(-10.5)
ans=
-10
>>fix(10.4)
ans=
10
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INTRODUCTION

Round floating point numbers to integer

ceil

floor
>>ceil(10.5)
ans=
11
>>ceil(-10.4)
ans=
-10
>>floor(10.5)
ans=
10
>>floor(-10.4)
ans=
-11
18
INTRODUCTION

It is convenience since it allows multiple
statements to be executed without printing the
intermediate results. You can suppress the
result by using “semicolon - ;” at the end of each
function,
>>pi/3;
>>sin(ans)/cos(ans);
>> ans-tan(pi/3);
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VARIABLE
 MATLAB
variables are created when they appear on
the left of an equal sign
>>variable = expression
 Variables include




Scalars
Vectors
Matrices
Strings

Variable names must begin with an alphanumeric
letter
Following that, any number of letters, digits and
underscores can be added, but only the first 19
characters are retained
20
MATLAB variable names are case sensitive so “x”
and “X” are different variables
 Characteristics


of MATLAB variables:
SCALARS
A
scalar is a variable with one row and one column
>>a=4;
>>b=5;
>>c=a+b;
 The
following statements demonstrate scalar
operation
Scalar Operation Statement
>>x=6;
>>y=3;
>>a=x+y;
>>s=x-y;
>>m=x*y;
>>d=x/y;
>>i=y\x;
>>p=x^y;
Addition
a=x+y
Subtraction
s=x-y
Multiplication
m=x*y
Division
d=x/y
Inverse
i=x\y
Power
p=x^y
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SCALARS
 Example:
Compute 5sin(2.53-pi)+1/75
>>5*sin(2.5^(3-pi))+1/75
ans=
3.8617
 Example:
Compute 1\3(cos3pi)
>>1\3*cos(3^pi)
ans=
2.9753
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VECTORS
A
vector is a matrix with either one row or one
column

Creating vector of the following statements
 Ones
To create a row vector of length 5 with single row
>>x=ones(1,5)
x=
1
1
1
1
1
 Zeros
To create a column vector of length 5 with single row
>>y=zeros(5,1)
The second one is
x=
no. of column
0
0
The first one is
0
no. of row
0
0
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VECTORS

Linspace
To create a linearly spaced element
>>x=linspace(1,5,5)
x=
1
2
3
4
5
 Logspace
To create a logarithmically spaced element
>>y=logspace(1,5,5)
y=
10 100 1000 10000 100000

The third argument of both linspace and logspace is
optional. The third argument is the number of elements
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to be used between the range specified with the first and
second arguments
VECTORS
 Addressing
vector elements
Location of vector can be address by using
>>x=linspace(11,15,3)
x=
11
13
15
>>x(2)
ans=
13
>>x(end)
ans=
15

25
VECTORS
 Increasing
the size of vector
We can also increase the size of vector by simply
assigning a value to an element
>>x=linspace(1,5,5)
x=
1
2
3
4
5
>>x(7)= -9
x=
1 2
3
4
5
0
-9


X(6) is assigned to zero
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VECTORS
 Colon
notation
The format of this command is shown as below:
>>x=xbegin:dx:xend
Or
>> x=xbegin:xend
 Where xbegin and xend are the range of values covered by
elements of the x vector and dx is the optional increment.
The default value of dx is (unit increment). The numbers
xbegin, dx and xend may not be integers.
>>x=1.1:5.1
x=
27
1.1 2.1
3.1 4.1 5.1

VECTORS
 Colon
notation
Location of vector can be address by using
>>x=1:10;
>>x(1:2:end)
ans=
1
3
5
7
9
 To create a column vector, append the transpose operator to the end
of the vector-creating expression
>>y=(1:5)'
y=
1
2
28
3
4
5

MATRICES
A
matrix is a variable with more than one row and
one column
Creating 2 by 2 matrix
>>A=[1 2; 3 4]
A=
1
2
3
4
 Creating 2 by 3 matrix
>>A=[1 2 3; 4 5 6]
A=
1
2
3
4
5
6

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MATRICES
 Addressing
matrix elements
>>A=[1 2 3; 4 5 6; 7 8 9]
A=
1
2
3
4
5
6
7
8
9
The second one is
>>A(2,3)
no. of column
ans=
6
>>A(3,2)=-5
A=
1
2
3
The first one is
4
5
6
no. of row
7
-5
9
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STRINGS
A
string is a word
>>a='test'
a=
test
 Converts to ASCII code for simple calculation
>>a+a
ans=
232
202 230 232
 Apply the string
>>[a a]
ans=
testtest
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MATHEMATICAL OPERATION
 Addition
>>A=[1 1 1; 1 2 3; 1 3 6];
>>B=[8 1 6; 3 5 7; 4 9 2];
>>X=A+B
X=
Addition & Subtraction require
9
2
7
both matrices to have same
4
7
10
dimension. If dimensions are
5
12
8
incompatible, an error will display
 Subtraction
>>Y=X-A
Y=
8
1
3
5
4
9
6
7
2
>>C=[1:3; 4:6];
>>X=A+C
32
??? Error using ==> plus
Matrix dimensions must agree.
MATHEMATICAL OPERATION
 Multiplication
>>u=[2 3 4];
>>v=[-2 0 2]';
>>x=u*v
x=
4
>>x=v*u
x=
-4
-6
0
0
4
6
u*v  v*u
-8
0
8
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MATHEMATICAL OPERATION
 Element
by Element Operations(.* or ./ or .^)
>>a=[1 2 3]; b=[2 5 8];
>>a+b
ans=
3
7
11
Let’s try to multiply
>>a*b
??? Error using ==> mtimes
Inner matrix dimensions must agree.
>>a*b'
It needs to transpose
the second vector
ans=
36
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MATHEMATICAL OPERATION
 Element
by Element Operations(.* or ./ or .^)
>>a=[1 2 3]; b=[2 5 8];
>>a.*b
ans=
2
10
24
It also needs to apply at .^
>>a.^2
ans=
1
4
9
If forget the period will lead to :
>>a^2
??? Error using ==> mpower
Matrix must be square.
35
MATHEMATICAL OPERATION
 Solving
Linear Equation
ax + by + cz = p
dx + ey + fz = q
gx + hy + iz = r
Set Matrices,
a
b
c
A= d
e
f ,
g
h
i
A B = C
B=A-1C
B=
x
p
y and C= q
z
r
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MATHEMATICAL OPERATION
 For
example,
x+y+z=0
x - 2y + 2z = 4
x + 2y - z = 2
Set Matrices,
1
1
1
A= 1
-2
2 , B=
1
2
-1
x
0
y and C= 4
z
2
>>A=[1 1 1;1 -2 2; 1 2 -1];
>>C=[0 4 2]';
>>B=inv(A)*C
Therefore the linear system has one solution:
B=
4.000 X=4, y=-2 and z=-2
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-2.000
-2.000