Recap Sum and Product Functions Matrix Size Function Variance and Standard Deviation Random Numbers Complex Numbers

Computational Limitations MATLAB includes functions to identify the largest real numbers and the largest integers the program can process

Special Values and Functions

Summary of Chapter General mathematical functions, such as exponential functions logarithmic functions roots Rounding functions Functions used in discrete mathematics, such as factoring functions prime-number functions Trigonometric functions, including standard trigonometric functions inverse trigonometric functions hyperbolic trigonometric functions trigonometric functions that use degrees instead of radians

Continued…. Data analysis functions, such as maxima and minima averages (mean and median) sums and products sorting standard deviation and variance Random-number generation for both uniform distributions Gaussian (normal) distributions Functions used with complex numbers

Chapter 5 Plotting

Two-Dimensional Plots The most useful plot for engineers is the x–y plot A set of ordered pairs is used to identify points on a two- dimensional graph; the points are then connected by straight lines The values of x and y may be measured or calculated Generally, the independent variable is given the name x and is plotted on the x -axis, and the dependent variable is given the name y and is plotted on the y -axis

Simple x-y Plots Once vectors of x -values and y -values have been defined, MATLAB makes it easy to create plots Suppose a set of time versus distance data were obtained through measurement We can store the time values in a vector called x and the distance values in a vector called y : x = [0:2:18]; y = [0, 0.33, 4.13, 6.29, 6.85, 11.19, 13.19, 13.96, 16.33, 18.17];

Continued…. To plot these points, use the plot command, with x and y as arguments: plot(x,y) A graphics window automatically opens, which MATLAB calls Figure 1

Titles, Labels and Grids Good engineering practice requires that we include axis labels and a title in our plot The following commands add a title, x - and y -axis labels, and a background grid: plot(x,y) xlabel('Time, sec') ylabel('Distance, ft') grid on

Continued…. As with any MATLAB commands, they could also be combined onto one or two lines, separated by commas: plot(x,y), title('Laboratory Experiment 1') xlabel('Time, sec' ), ylabel('Distance, ft'), grid

Multiple Plots If you are working in an M-file when you request a plot, and then you continue with more computations, MATLAB will generate and display the graphics window and then return immediately to execute the rest of the commands in the program If you request a second plot, the graph you created will be overwritten There are two possible solutions to this problem: Use the pause command to temporarily halt the execution of your M-file program so that you can examine the figure Create a second figure, using the figure function

Continued…. The pause command stops the program execution until any key is pressed If you want to pause for a specified number of seconds, use the pause(n) command, which will cause execution to pause for n seconds before continuing The figure command allows you to open a new figure window The next time you request a plot, it will be displayed in this new window

Continued…. For example: figure(2) opens a window named “Figure 2,” which then becomes the window used for subsequent plotting Executing figure without an input parameter causes a new window to open, numbered consecutively one up from the current window For example: if the current figure window is named “Figure 2,” executing figure will cause “Figure 3” to open