Lecture 22

Recap

Sum and Product FunctionsMatrix Size FunctionVariance and Standard DeviationRandom NumbersComplex 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 functionslogarithmic functionsroots

Rounding functionsFunctions used in discrete mathematics, such as

factoring functionsprime-number functions

Trigonometric functions, includingstandard trigonometric functionsinverse trigonometric functionshyperbolic trigonometric functionstrigonometric functions that use degrees instead of radians

Continued….Data analysis functions, such as

maxima and minimaaverages (mean and median)sums and productssortingstandard deviation and variance

Random-number generation for bothuniform distributionsGaussian (normal) distributions

Functions used with complex numbers

Chapter 5Plotting

Two-Dimensional PlotsThe most useful plot for engineers is the x–y plotA 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 calculatedGenerally, 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 plotsSuppose a set of time versus distance data were obtained

through measurementWe 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 GridsGood engineering practice requires that we include axis

labels and a title in our plotThe 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 PlotsIf 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 figureCreate a second figure, using the figure function

Continued….The pause command stops the program execution until

any key is pressedIf 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 plottingExecuting 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