Matlab for Engineers 100 200 300 400 500 100 200 300 400 500 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 R ate ofC hange tim e, hour Rate of tem perature change, degrees/hour Built-in Matlab Functions Chapter 3 0 200 400 600 800 1000 0 20 40 60 80 100 TestS cores S tudentN um ber Score 0 20 40 60 80 100 0 20 40 60 80 100 120 D istribution ofTestS cores S core # ofstudents 0 200 400 600 800 1000 0 20 40 60 80 100 S tudentN um ber Score 0 20 40 60 80 100 0 20 40 60 80 100 120 S core # ofstudents A verage = 50 A verage = 50 A verage = 50 A verage = 50
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Matlab for Engineers
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Built-in Matlab Functions
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In this chapter we’ll cover
• 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
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Matlab uses function names consistent
with most major programming languages
For example• sqrt• sin• cos• log
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Function Input can be either scalars or matrices
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Function Input can be either scalars or matrices
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Using Predefined Functions
• Functions consist of• Name• Input argument(s)• Output
sqrt (x)= result
In MATLAB
sqrt(4)
ans = 2
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Some functions require multiple inputs
• Remainder function returns the remainder in a division problem
• For example the remainder of 10/3, is 1
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Some functions return multiple results
• size function determines the number of rows and columns
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You can assign names to the output
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Nesting Functions
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There are functions for almost anything you want to do
• 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
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From the Help Menu
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Elementary Math Functions
• abs(x) absolute value
• sign(x) plus or minus
• exp(x) ex
• log(x) natural log
• log10(x) log base 10
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Rounding Functions
• round(x)
• fix(x)
• floor(x)
• ceil(x)
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Discrete Mathmatics
• factor(x)• gcd(x,y) greatest common denominator
• lcm(x) lowest common multiple
• rats(x) represent x as a fraction
• factorial(x)• primes(x)• isprime(x)
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Trigonometric Functions
• sin(x) sine• cos(x) cosine• tan(x) tangent• asin(x) inverse sine• sinh(x) hyperbolic sine• asinh(x) inverse hyperbolic sine• sind(x) sine with degree input• asind(x) inverse sin with degree
output
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Data Analysis
• max(x)
• min(x)
• mean(x)
• median(x)
• sum(x)
• prod(x)
• sort(x)
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When x is a matrix, the max is found for each column
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max value
element number where the max value occurs
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Vector of row numbers
Vector of maximums
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Determining Matrix Size
• size(x) number of rows and columns
• length(x) biggest dimension
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Variance and Standard Deviation
• std(x)• var(x)
11
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Standard Deviation
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Random Numbers
• rand(x)• Returns an x by x matrix of random
numbers between 0 and 1
• rand(n,m)• Returns an n by m matrix of random
numbers
• These random numbers are evenly distributed
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Gaussian Random numbers
• randn(n)
• Also called a normal distribution
• Generates numbers with a mean of 0 and a standard deviation of 1
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To generate random numbers between other
bounds…
arabx a and b are the upper and lower bounds
r is the array of random numbers
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Average = 50
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More about Manipulating Matrices
• M(:)• Converts a two dimensional matrix
to a single column
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Complex Numbers
• complex(x,y)• real(A) used if A is a
complex number
• imag(A)• isreal(A)• conj(A)• abs(A)• angle(A)
real
imaginary
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Computational Limits
• Matlab’s computational range on most computers is:• 10-308
• 10308
• When you divide by 0, the computer returns Inf
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Check the limits on your computer with these commands
• realmax
• realmin
• intmax
• intmin
Matlab for Engineers
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-4.5
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-0.5
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Rate of Change
time, hour
Rat
e of
tem
pera
ture
cha
nge,
deg
rees
/hou
r
Matlab for Engineers
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100
200
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-5
-4.5
-4
-3.5
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-1
-0.5
0
Rate of Change
time, hour
Rat
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tem
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deg
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/hou
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When using very large or very small numbers the result may depend on
the order of operation
Matlab for Engineers
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100
200
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-0.5
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Special Values and Functions
• 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
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Summary
• MATLAB contains a wide array of predefined functions• Elementary Math Functions• Trigonometric Functions• Data Analysis Functions• Random Numbers• Complex Numbers
Matlab for Engineers
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Rate of Change
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Summary
• The colon operator allows you to manipulate matrices
Matlab for Engineers
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100
200
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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
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Summary
• Computational Limits
• Special Values and Functions
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