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MATLAB An Introduction to MATLAB (Matrix Laboratory) 1
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MATLAB Windows 2
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Command Window – Heart of MATLAB – Access most commands and functions Workspace window – Shows created variables during present session – Variables remain only for present session Current Directory Window – Contains options for locating, opening, editing, and saving files Command History Window – Keeps a history of commands used and executed in the Command Window – Does not show results of your commands 3
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Document Window (Double-click on any Variable in the Workspace window automatically launches a document window ) 4 Document Window
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Figure Window When Figures are created a new window opens 5
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Edit Window 6 Save and Run
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Order of Operation 1.Exponentiation 2.Multiplication / division 3.Parentheses first 4.Addition / subtraction 7
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Parentheses Use only ( ) { } and [ ] mean something different MATLAB does not assume operators 8 5 * (3+4) not 5(3+4)
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Basic Math Functions Built into MATLAB – Addition (+) – Subtraction (-) – Multiplication (*) – Division (/) – Exponentiation (^) 9
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Saving a MATLAB Session Only values of the variables are saved in the workspace Window ( Caution: Do not program in the Command Window. Program in the Editor Window) 10
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Saving a MATLAB Session ( Caution: Use Editor Window to program.) 11
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Saving a Program as a M-file 1.Save your work by creating an m-file 2.File->New->m-file 3.Type your commands in the edit window that opens 4.Save as XXX.m 5.The file is saved into the current directory 6.It runs in the command window 12
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Comments (%) Be sure to comment your code – Add your name – Date – Section # – Assignment # – Descriptions of what you are doing and why 13
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Comments (%) 14
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Elementary Math Functions abs(x)absolute value sign(x)plus or minus exp(x)e x log(x) natural log log10(x)log base 10 15
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Rounding Functions round(x) fix(x) floor(x) ceil(x) 16
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Rounding Functions 17
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Discrete Mathematics 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) 18
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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 19
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Data Analysis max(x) min(x) mean(x) median(x) sum(x) prod(x) sort(x) 20
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Data Analysis 21 When x is a matrix, the max is found for each column
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Data Analysis 22
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Data Analysis 23
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Data Analysis 24
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Determining Matrix Size size(x)number of rows and columns length(x) biggest dimension 25
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Determining Matrix Size 26
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Variance and Standard Deviation 27
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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 28
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Random Numbers 29
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Matrices Group of numbers arranged into rows and columns Single Value (Scalar) – Matrix with one row and one column Vector (One dimensional matrix) – One row or one column Matrix (Two dimensional) 30
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Scalar Calculations You can use MATLAB like you’d use a calculator 31
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Scalar Calculations 32
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Variables MATLAB allows you to assign a value to a variable A=3 Should be read as A is assigned a value of 3 Use the variables in subsequent calculations 33
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Predefined MATLAB Functions 34 Functions consist of – Name – Input argument(s) – Output Sqrt (x) = results Sqrt (4) = 2
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Functions accept either scalar or matrix input 35 X=1:10 is one row matrix 1 to 10
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d - Matrix 36
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Array Operations 37 To create a row vector, enclose a list of values in brackets
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Array Operations 38 You may use either a space or a comma as a “delimiter” in a row vector
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Array Operations 39 Use a semicolon as a delimiter to create a new row
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Array Operations 40 Use a semicolon as a delimiter to create a new row
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Array Operations 41 Hint: It’s easier to keep track of how many values you’ve entered into a matrix, if you enter each row on a separate line. The semicolons are optional
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Array Operations While a complicated matrix might have to be entered by hand, evenly spaced matrices can be entered much more readily. The command b= 1:5 or the command b = [1:5] both return a row matrix 42
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Array Operations 43 The default increment is 1, but if you want to use a different increment put it between the first and final values
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Array Operations Array multiplication.* Array division./ Array exponentiation.^ 44 In each case the size of the arrays must match
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Array Operations Repetitive Calculations assume you have a list of angles in degrees that you would like to convert to radians. 45
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Array Operations Repetitive Calculations 46
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Array Operations Transpose Operator 47
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Array Operations Transpose Operator 48
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Array Operations Transpose Operator 49
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Number Display Scientific Notation – Although you can enter any number in decimal notation, it isn’t always the best way to represent very large or very small numbers – In MATLAB, values in scientific notation are designated with an e between the decimal number and exponent. (Your calculator probably uses similar notation.) 50
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Number Display 51
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To calculate spacing between elements use linspace and logspace 52
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logspace 53 e = 10 100 1000
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Manipulating MATLAB Matrices 54
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