Chapter 3 -Built-in Matlab Functions
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The document discusses the various built-in functions available in MATLAB for engineers. It covers fundamental math functions, trigonometric functions, data analysis functions, and how to use the help feature. Examples of functions include sqrt(), sin(), max(), and help to find documentation on any function's usage.
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Chapter 3 -Built-in Matlab Functions
- 1. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Built-in Matlab Functions Chapter 3 0 200 400 600 800 1000 0 20 40 60 80 100 Test Scores Student Number Score 0 20 40 60 80 100 0 20 40 60 80 100 120 Distribution of Test Scores Score #ofstudents 0 200 400 600 800 1000 0 20 40 60 80 100 Student Number Score 0 20 40 60 80 100 0 20 40 60 80 100 120 Score #ofstudents Average = 50 Average = 50 Average = 50 Average = 50
- 2. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 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
- 3. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Matlab uses function names consistent with most major programming languages For example • sqrt • sin • cos • log
- 4. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Function Input can be either scalars or matrices
- 5. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Function Input can be either scalars or matrices
- 6. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Using Predefined Functions • Functions consist of • Name • Input argument(s) • Output sqrt (x)= result In MATLAB sqrt(4) ans = 2
- 7. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Some functions require multiple inputs • Remainder function returns the remainder in a division problem • For example the remainder of 10/3, is 1
- 8. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Some functions return multiple results • size function determines the number of rows and columns
- 9. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour You can assign names to the output
- 10. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Nesting Functions
- 11. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 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
- 12. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour From the Command Window
- 13. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour From the Help Menu
- 14. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 15. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 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. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Rounding Functions • round(x) • fix(x) • floor(x) • ceil(x)
- 17. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 18. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 19. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 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)
- 20. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 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
- 21. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Data Analysis • max(x) • min(x) • mean(x) • median(x) • sum(x) • prod(x) • sort(x)
- 22. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour When x is a matrix, the max is found for each column
- 23. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour max value element number where the max value occurs
- 24. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Vector of row numbers Vector of maximums
- 25. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Determining Matrix Size • size(x) number of rows and columns • length(x) biggest dimension
- 26. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 27. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Variance and Standard Deviation • std(x) • var(x) ( ) 1 1 2 2 − − = ∑= N x N k k µ σ 2 σ σ
- 28. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Standard Deviation
- 29. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 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
- 30. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 31. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 32. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 33. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Gaussian Random numbers • randn(n) • Also called a normal distribution • Generates numbers with a mean of 0 and a standard deviation of 1
- 34. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 35. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 36. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 37. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour To generate random numbers between other bounds… ( ) arabx +⋅−= a and b are the upper and lower bounds r is the array of random numbers
- 38. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 0 200 400 600 800 1000 0 20 40 60 80 100 Test Scores Student Number Score 0 20 40 60 80 100 0 20 40 60 80 100 120 Distribution of Test Scores Score #ofstudents 0 200 400 600 800 1000 0 20 40 60 80 100 Student Number Score 0 20 40 60 80 100 0 20 40 60 80 100 120 Score #ofstudents Average = 50 Average = 50 Average = 50 Average = 50
- 39. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour More about Manipulating Matrices • M(:) • Converts a two dimensional matrix to a single column
- 40. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 41. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 42. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 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
- 43. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Computational Limits • Matlab’s computational range on most computers is: • 10-308 • 10308 • When you divide by 0, the computer returns Inf
- 44. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Check the limits on your computer with these commands • realmax • realmin • intmax • intmin
- 45. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour
- 46. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour When using very large or very small numbers the result may depend on the order of operation
- 47. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour 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.
- 48. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Summary • MATLAB contains a wide array of predefined functions • Elementary Math Functions • Trigonometric Functions • Data Analysis Functions • Random Numbers • Complex Numbers
- 49. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Summary • The colon operator allows you to manipulate matrices
- 50. 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 Rate of Change time, hour Rateoftemperaturechange,degrees/hour Summary • Computational Limits • Special Values and Functions
Editor's Notes
- Welcome to Matlab for Engineers – Chapter Three. In this chapter we’ll explore a number of the functions built into Matlab.
- In particular we’ll cover using builit in functions and the help feature. We’ll look at…. and the computational limits that control our use of these functions.
- Sin and cos are also standard function names, as is l-o-g for natural logarithm.
- Let’s take a look at the square root function.
- Let’s take a look at the square root function.
- All functions consist of three basic parts
- Variance and standard deviation are statistical measures of variation in data. The definition of variance
- This is a representation of data that varies in what is called a normal distribution. It’s the bell curve, that’s often used by teachers to analyze student scores.
- Matlab can generate random numbers that are distrubuted using two schemes . The first is an even distribution and uses the rand function