partI - Part I Matlab and Solving Equations c Copyright,...

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Part I Matlab and Solving Equations c c Copyright, Todd Young and Martin Mohlenkamp, Mathematics Department, Ohio University, 2007
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Lecture 1 Vectors, Functions, and Plots in Matlab In this book > will indicate commands to be entered in the command window. You do not actually type the command prompt > . Entering vectors In Matlab , the basic objects are matrices, i.e. arrays of numbers. Vectors can be thought of as special matrices. A row vector is recorded as a 1 × n matrix and a column vector is recorded as a m × 1 matrix. To enter a row vector in Matlab, type the following at the prompt ( > ) in the command window: > v = [0 1 2 3] and press enter. Matlab will print out the row vector. To enter a column vector type: > u = [9; 10; 11; 12; 13] You can access an entry in a vector with > u(2) and change the value of that entry with > u(2)=47 You can extract a slice out of a vector with > u(2:4) You can change a row vector into a column vector, and vice versa easily in Matlab using: > w = v’ (This is called transposing the vector and we call the transpose operator.) There are also useful shortcuts to make vectors such as: > x = -1:.1:1 and > y = linspace(0,1,11) Plotting Data Consider the following table, obtained from experiments on the viscosity of a liquid. 1 We can enter T (C ) 5 20 30 50 55 μ 0.08 0.015 0.009 0.006 0.0055 this data into Matlab with the following commands entered in the command window: > x = [ 5 20 30 50 55 ] 1 Adapted from Ayyup & McCuen 1996, p.174. 2
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3 > y = [ 0.08 0.015 0.009 0.006 0.0055] Entering the name of the variable retrieves its current values. For instance: > x > y We can plot data in the form of vectors using the plot command: > plot(x,y) This will produce a graph with the data points connected by lines. If you would prefer that the data points be represented by symbols you can do so. For instance: > plot(x,y,’*’) > plot(x,y,’o’) > plot(x,y,’.’) Data as a Representation of a Function A major theme in this course is that often we are interested in a certain function y = f ( x ), but the only information we have about this function is a discrete set of data { ( x i , y i ) } . Plotting the data, as we did above, can be thought of envisioning the function using just the data. We will ±nd later that we can also do other things with the function, like di²erentiating and integrating, just using the available data. Numerical methods, the topic of this course, means doing mathematics by computer. Since a computer can only store a ±nite amount of information, we will almost always be working with a ±nite, discrete set of values of the function (data), rather than a formula for the function. Built-in Functions If we wish to deal with formulas for functions, Matlab contains a number of built-in functions, including all the usual functions, such as sin( ) , exp( ) , etc. . The meaning of most of these is clear. The dependent variable (input) always goes in parentheses in Matlab . For instance: > sin(pi) should return the value of sin π , which is of course 0 and > exp(0) will return e 0 which is 1. More importantly, the built-in functions can operate not only on single numbers but on vectors. For example: > x = linspace(0,2*pi,40) > y = sin(x) > plot(x,y)
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This note was uploaded on 02/09/2012 for the course MATH 344 taught by Professor Young,t during the Fall '08 term at Ohio University- Athens.

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partI - Part I Matlab and Solving Equations c Copyright,...

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