1
Department of Chemical Engineering
University of California, Santa Barbara
Ch. E. 152A
Fall, 2006
MATLAB Handout #1
The purpose of this MATLAB session is to introduce the basic functionality of
the software and to enable you to solve simple ordinary differential equation problems
(ODEs).
The basics of vector and matrix manipulations will be covered; then it will be
shown how simple linear equations can be solved using MATLAB.
The basics of
functions and scripts will be described next.
Finally, the use of the ODE integrator
function,
ode45
will be considered.
Next week’s lesson will introduce the graphical
modeling tool, SIMULINK.
.
In this report, boldface expressions denote MATLAB commands.
1.
Vectors
Square brackets denote vectors or matrices, and a semicolon at the end of a line
suppresses the output from being shown.
Elements in row vectors are separated by
spaces or commas.
v = [v
1
v
2
v
3
]
Elements in column vectors are separated by semicolons:
v = [v
1
; v
2
; v
3
]
2.
Matrices
Columns are separated by spaces or commas, rows are separated by semicolons.
M = [m
11
m
12
; m
21
m
22
]
The transpose of a matrix
M
is calculated using the command:
.
′
M
The inverse of a
matrix
M
is calculated as
inv(M)
.
For more functions and help on any Matlab operation,
type
help
.
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Consider the following matrices:
13
5
2
02
14
12
2
3
24
1
4
AB
CD
−
⎡
⎤⎡
⎤
==
⎢
⎥⎢
⎥
−
⎣
⎦⎣
⎦
⎡⎤
⎡
⎤
⎢⎥
⎢
⎥
−−
⎣⎦
⎣
⎦
Calculate the following:
a) AB
b) AB
T
c) A
1
d) DCD
T
e) C
1
f) (ADA
T
)
1
g) BC – D
1
Other matrix operations:
eigenvalues and eigenvectors:
eig(M)
singular value decomposition:
svd(M)
pseudoinverse:
pinv(M)
3.
Solution to algebraic linear equations
Using the functions considered above, simple linear algebraic equations can be easily
solved.
Solve the equation
Mx = b
for:
a) M = A, b=[1; 2]
b) M = B, b=[1; 2]
c) M = ADA
T
, b=[5 1]´.
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 Fall '08
 Seborg
 Chemical Engineering, matlab

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