Introduction to MATLAB

1
Introduction to MATLAB

• MATLAB is a mathematics program that works by
  either typing in commands or by writing programs
• Typing x5sqrt(83)/(53exp(.2)) will result in
  x .3609
• MATLAB handles matrix mathematics and complex
  number arithmetic with ease

2
Matlabs Workspace

• Each command or each program creates a set of
  variables with values in the workspace
• Values are kept until you no longer need them
• Use clear to wipe the workspace clean
• Use clear x to eliminate the variable x
• Use clear variables to clear all variables
• Clear the screen of text by using clc on the
  command line or choosing Clear Session under Edit
  in the menu. This does not clear the variables.

3
Matlabs Workspace

• You can check your variables at any time
• who generates a listing of all variables
• whos generates a listing of all variables plus
  the size, bytes and class of the variables
• Choosing Show Workspace under the File menu
  brings up a window showing the same information
  as whos)
• Type help who for more detailed information
• Type the variable to see its value(s)

4
Matlab Built-In Functions

• Matlab commands and functions are broken down
  into many categories
• Type help elfun
• trigonometric functions
• exponential functions
• complex number functions
• rounding/remainder functions

5
Common Math Functions

• Trigonometric cos, sin, tan, atan
• Be sure to use radians in the argument
• Square root sqrt(2) yields 1.414
• Natural Log log(3) yields 1.0986
• Base 10 Log log10(4) yields .6021
• Base 2 Log log2(4) yields 2
• Exponential exp(2) yields e2 7.3891

6
Complex Number Functions

• Enter in rectangular form
• x43j or x43i or xcomplex(4,3)
• Magnitude abs(x) yields 5
• Phase angle angle(x) yields .6435 radians
• Complex conjugate conj(x) yields 4-3j
• Real part real(x) yields 4
• Imaginary part imag(x) yields 3

7
Matlab Matrix Math

• Matrices are rectangular arrays of numbers
• Matlab uses matrix math to simplify many
  calculations
• Each element in a matrix can be accessed using
  its row and column m(row,column)
• An entire row or column can be accessed to form a
  vector m( ,column) or m(row, )

8
Generating a Vector

• Generate a vector by listing its values
• Rowvector1 2 3 4 5 6 7 8 9
• Columnvector123456789 the semicolon
  starts a new row
• Create a row vector with a constant interval
• Tstart value increment end value
• T0 2 10 gives T0 2 4 6 8 10
• Tlinspace(start value, end value, number wanted)
• Tlinspace(0,10,5) gives T0 2.5 5 7.5 10

9
Generating a Vector

• You can create a row vector with logarithmic
  spacing
• Tlogspace(starting power of 10, ending power of
  10, number of values wanted)
• Tlogspace(0,2,4) gives
• T1 4.6416 21.5443 100

10
Generating a Matrix

• You can create a matrix by entering each row with
  semicolons between each row
• A 3 4 7 5 7 3 2 0 6
• 3 4 -7
• A 5 7 3
• 2 0 6

11
Matrices and Sets of Equations

• Matrices can be used to represent a system of
  equations and solve it
• 3x4y-7z10
• 5x-7y3z-6
• 2x-6z6
• The matrix equation implements the above system
• 3 4 -7 x 10
• 5 7 3 . y -6 or A S C
• 2 0 6 z 6

12
Matlab Solution of ASC

• A3 4 7 5 7 3 2 0 6
• C10 -6 6
• Premultiply both sides by the inverse of A
• inv(A) A S inv(A) C
• Which simplifies to S inv(A) C
• 0.3140 or x
  .3140
• Results in S 0.6977 or y .6977
• -0.8953 or z
  -.8953

13
Running Matlab Programs

• Under file, select open
• Find the M-file that you want to run
• The M-file should appear in the editor window
• Modify the M-file as needed
• Under debug, choose run
• Results should be displayed in the main window
• Plots should be displayed in new figure windows