Download Chapter 3 - Built-In Matlab Functions

Built-in Matlab
Functions
Rate of Change
Rate of temperature change, degrees/hour
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time, hour
Test Scores
Distribution of Test Scores
100
120
100
Chapter 3
100
200
Average = 50
Average = 50
60
# of students
Score
80
40
20
0
80
60
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Student Number
800
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1000
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Score
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120
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# of students
500
Score
80
Average = 50
60
40
20
0
Average = 50
80
60
40
20
0
200
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600
Student Number
800
1000
0
0
20
Matlab for Engineers
40
60
Score
80
100
In this chapter we’ll cover
Rate of Change
Rate of temperature change, degrees/hour
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-4.5
-4
-3.5
-3
-2.5
-2
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•
•
•
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Using Built in Functions
Using the Help Feature
Elementary Math Functions
Trigonometric Functions
Data Analysis Functions
Random Number Functions
Complex Number Functions
Computational Limits
Special Values and Miscellaneous Functions
Matlab for Engineers
Matlab uses function names consistent
with most major programming languages
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
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time, hour
For example
•
•
•
•
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500
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sqrt
sin
cos
log
500
Matlab for Engineers
Function Input can be either
scalars or matrices
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
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time, hour
100
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500
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500
Matlab for Engineers
Function Input can be either
scalars or matrices
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
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time, hour
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Matlab for Engineers
Using Predefined
Functions
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-3.5
-3
-2.5
-2
-1.5
-1
-0.5
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• Functions consist of
• Name
• Input argument(s)
• Output
In MATLAB
100
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sqrt (x)= result
300
400
500
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sqrt(4)
500
ans = 2
Matlab for Engineers
Some functions require
multiple inputs
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
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100
• Remainder function returns the
remainder in a division problem
• For example the remainder of
10/3, is 1
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500
100
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300
400
500
Matlab for Engineers
Some functions return
multiple results
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-2.5
-2
-1.5
-1
-0.5
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time, hour
• size function determines the
number of rows and columns
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500
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Matlab for Engineers
You can assign names to the
output
Rate of Change
Rate of temperature change, degrees/hour
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time, hour
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Matlab for Engineers
Nesting Functions
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-3.5
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-2.5
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-1.5
-1
-0.5
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time, hour
100
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Matlab for Engineers
There are functions for almost
anything you want to do
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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time, hour
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• Use the help feature to find out
what they are and how to use
them
• From the command window
• From the help selection on the
menu bar
Matlab for Engineers
From the Command Window
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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2
2.5
3
3.5
4
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5
time, hour
100
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500
100
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500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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1.5
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time, hour
100
200
From the Help Menu
300
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500
100
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300
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Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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4
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time, hour
100
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500
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Matlab for Engineers
Elementary Math
Functions
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-3.5
-3
-2.5
-2
-1.5
-1
-0.5
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time, hour
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•
•
•
•
•
abs(x)
sign(x)
exp(x)
log(x)
log10(x)
absolute value
plus or minus
ex
natural log
log base 10
Matlab for Engineers
Rounding Functions
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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time, hour
100
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•
•
•
•
round(x)
fix(x)
floor(x)
ceil(x)
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
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2
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4
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time, hour
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Matlab for Engineers
Discrete Mathmatics
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-3.5
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-1.5
-1
-0.5
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time, hour
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•
•
•
•
•
•
•
factor(x)
gcd(x,y)
lcm(x)
rats(x)
factorial(x)
primes(x)
isprime(x)
greatest common denominator
lowest common multiple
represent x as a fraction
Matlab for Engineers
Trigonometric Functions
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
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time, hour
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•
•
•
•
•
•
•
•
sin(x)
cos(x)
tan(x)
asin(x)
sinh(x)
asinh(x)
sind(x)
asind(x)
sine
cosine
tangent
inverse sine
hyperbolic sine
inverse hyperbolic sine
sine with degree input
inverse sin with degree
output
Matlab for Engineers
Data Analysis
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
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-1.5
-1
-0.5
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time, hour
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•
•
•
•
•
•
•
max(x)
min(x)
mean(x)
median(x)
sum(x)
prod(x)
sort(x)
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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time, hour
100
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500
100
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When x is a matrix,
the max is found for
each column
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
max value
-4.5
-4
-3.5
-3
-2.5
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-1.5
-1
-0.5
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time, hour
element number
where the max
value occurs
100
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500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
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time, hour
Vector of maximums
100
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500
100
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Vector of row numbers
Matlab for Engineers
Determining Matrix Size
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-3.5
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-2.5
-2
-1.5
-1
-0.5
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time, hour
• size(x)
• length(x)
number of rows and
columns
biggest dimension
100
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500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
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time, hour
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Matlab for Engineers
Variance and Standard
Deviation
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5

2
-2
-1.5
-1
-0.5
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time, hour
• std(x)
• var(x)
N
100
200
300
 
2
400
500
100
200
300
400
500
 x
k 1
 
2
k
N 1
Matlab for Engineers
Standard Deviation
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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time, hour
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Matlab for Engineers
Random Numbers
Rate of Change
Rate of temperature change, degrees/hour
-5
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-2.5
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-1.5
-1
-0.5
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• rand(x)
• Returns an x by x matrix of random
numbers between 0 and 1
• rand(n,m)
100
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500
100
200
300
400
500
• Returns an n by m matrix of random
numbers
• These random numbers are
evenly distributed
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Gaussian Random
numbers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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2.5
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5
time, hour
100
200
• randn(n)
• Also called a normal distribution
• Generates numbers with a mean
of 0 and a standard deviation of 1
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
To generate random
numbers between other
bounds…
x  b  a  r  a
100
200
300
400
500
100
200
300
400
500
a and b are the upper and lower
bounds
r is the array of random numbers
Matlab for Engineers
Test Scores
Distribution of Test Scores
100
120
Rate of Change
100
80
Average = 50
-4
-3.5
-2
-1.5
-1
Average = 50
60
# of students
-3
-2.5
Score
Rate of temperature change, degrees/hour
-5
-4.5
40
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
80
60
40
5
time, hour
20
0
20
0
200
400
600
Student Number
800
0
1000
0
20
40
60
80
100
Score
100
120
100
80
Score
200
300
# of students
100
Average = 50
60
40
400
500
100
200
300
400
500
20
0
Average = 50
80
60
40
20
0
200
400
600
Student Number
800
1000
0
0
20
40
60
Score
Matlab for Engineers
80
100
More about Manipulating
Matrices
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
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-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
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time, hour
• M(:)
• Converts a two dimensional matrix
to a single column
100
200
300
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500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Complex Numbers
Rate of Change
Rate of temperature change, degrees/hour
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-4.5
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-3
-2.5
-2
-1.5
-1
-0.5
0
0
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5
time, hour
100
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500
100
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500
• complex(x,y)
• real(A)
•
•
•
•
•
imag(A)
isreal(A)
conj(A)
abs(A)
angle(A)
used if A is a
complex number
imaginary
real
Matlab for Engineers
Computational Limits
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
• Matlab’s computational range on
most computers is:
• 10-308
• 10308
100
200
300
400
500
100
200
300
400
500
• When you divide by 0, the
computer returns Inf
Matlab for Engineers
Check the limits on your
computer with these commands
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
•
•
•
•
realmax
realmin
intmax
intmin
300
400
500
100
200
300
400
500
Matlab for Engineers
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
When using very large or very small
numbers the result may depend on
the order of operation
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Special Values and
Functions
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
•
•
•
•
•
•
•
•
pi
i,j
Inf
NaN
clock
date
eps
ans
Hint: The function i is the
most common of these
functions to be
unintentionally renamed
by Matlab users.
Matlab for Engineers
Summary
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
100
200
300
400
500
100
200
300
400
500
• MATLAB contains a wide array of
predefined functions
•
•
•
•
•
Elementary Math Functions
Trigonometric Functions
Data Analysis Functions
Random Numbers
Complex Numbers
Matlab for Engineers
Summary
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
• The colon operator allows you to
manipulate matrices
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers
Summary
Rate of Change
Rate of temperature change, degrees/hour
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
time, hour
• Computational Limits
• Special Values and Functions
100
200
300
400
500
100
200
300
400
500
Matlab for Engineers