MATLAB

1. MATLAB An Introduction to MATLAB (Matrix Laboratory)

2. MATLAB Windows

3. MATLAB Windows • 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

4. Document Window(Double-click on any Variable in the Workspace window automatically launches a document window) Document Window

5. Figure Window When Figures are created a new window opens

6. Save and Run Edit Window

7. Order of Operation • Exponentiation • Multiplication / division • Parentheses first • Addition / subtraction

8. Parentheses • Use only ( ) • { } and [ ] mean something different • MATLAB does not assume operators 5 * (3+4) not 5(3+4)

9. Basic Math Functions • Built into MATLAB • Addition (+) • Subtraction (-) • Multiplication (*) • Division (/) • Exponentiation (^)

10. Saving a MATLAB SessionOnly values of the variables are saved in the workspace Window(Caution: Do not program in the Command Window.Program in the Editor Window)

11. Saving a MATLAB Session(Caution: Use Editor Window to program.)

12. Saving a Program as a M-file • Save your work by creating an m-file • File->New->m-file • Type your commands in the edit window that opens • Save as XXX.m • The file is saved into the current directory • It runs in the command window

13. Comments (%) • Be sure to comment your code • Add your name • Date • Section # • Assignment # • Descriptions of what you are doing and why

14. Comments (%)

15. Elementary Math Functions • abs(x) absolute value • sign(x) plus or minus • exp(x) ex • log(x) natural log • log10(x) log base 10

16. Rounding Functions • round(x) • fix(x) • floor(x) • ceil(x)

17. Rounding Functions

18. 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)

19. 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

20. Data Analysis • max(x) • min(x) • mean(x) • median(x) • sum(x) • prod(x) • sort(x)

21. Data Analysis When x is a matrix, the max is found for each column

22. Data Analysis

23. Data Analysis

24. Data Analysis

25. Determining Matrix Size • size(x) number of rows and columns • length(x) biggest dimension

26. Determining Matrix Size

27. Variance and Standard Deviation

28. 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

29. Random Numbers

30. 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)

31. Scalar Calculations • You can use MATLAB like you’d use a calculator

32. Scalar Calculations

33. 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

34. Predefined MATLAB Functions • Functions consist of • Name • Input argument(s) • Output • Sqrt (x) = results • Sqrt (4) = 2

35. Functions accept either scalar or matrix input X=1:10 is one row matrix 1 to 10

36. d - Matrix

37. Array Operations To create a row vector, enclose a list of values in brackets

38. Array Operations You may use either a space or a comma as a “delimiter” in a row vector

39. Array Operations Use a semicolon as a delimiter to create a new row

40. Array Operations Use a semicolon as a delimiter to create a new row

41. Array Operations 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

42. 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 

43. Array Operations The default increment is 1, but if you want to use a different increment put it between the first and final values

44. Array Operations • Array multiplication .* • Array division ./ • Array exponentiation .^ In each case the size of the arrays must match

45. Array OperationsRepetitive Calculations • assume you have a list of angles in degrees that you would like to convert to radians.

46. Array OperationsRepetitive Calculations

47. Array Operations Transpose Operator

48. Array Operations Transpose Operator

49. Array Operations Transpose Operator

50. 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.)