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3.2: Variables in M-file Environments

Difficulty Level: At Grade Created by: CK-12
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A variable is a named storage location that can be set to a particular value which can be used in subsequent computations. For example, we store a value of \begin{align*}5\end{align*} in the variable


with the statement



This value remains in


until we store a different value (for example, using the command


) or we clear


using the command

clear a


Once a variable is set to a particular value, we can get this value by using the variable name in an expression (e.g.



Example 3

Suppose we wish to compute the circumference of a circle of diameter 5 units using the formula \begin{align*}c = \pi d\end{align*}. We could first set the variable


to a value of 5 using the following input to the m-file environment. In the following,


is the prompt displayed by the m-file environment:

>> d = 5
d =

Then we could compute the circumference and assign its value to the variable



>> c = pi*d
c =

In this command, the product of the value of


(which is known because we earlier set it to 5) and the value of \begin{align*}pi\end{align*} (which is a pre-defined variable) is computed and the value of the product is stored in the variable



Variable names must begin with an upper- or lower-case letter. They may contain letters, digits, and underscores; they may not contain spaces or punctuation characters. Variable names are case sensitive, so




are different variables.

Exercise 1

Which of the following are valid variable names?

  1. a
  2. B
  3. ecky_ecky_ecky_ecky_ptang_zoo_boing
  4. ecky ecky ecky ecky ptang zoo boing
  5. 2nd
  6. John-Bigboote

There are several predefined variables. The most commonly used include

  • ans

    - the default variable in which computation results are stored.

  • pi

    - \begin{align*}\pi\end{align*}.

  • i



    - \begin{align*}\sqrt{-1}\end{align*}.

Once assigned, variable names remain until they are reassigned or eliminated by the



Variables can contain several types of numerical values. These types include the following:

  • Scalar - a scalar is a single value (i.e. a number).



    in the example above are scalar variables.

  • Vector - a vector is an ordered series of numbers.
  • Matrices - a matrix is a rectangular array of numbers. The ability to do computations on vectors and matrices gives MATLAB its name (MATrix LABoratory).
  • strings - variables may also contain strings of characters.

Exercise 2

Figure 1 shows a Sharp GP2D12 infrared distance sensor (http://www.acroname.com/robotics/info/articles/sharp/sharp.html) and a BasicX-24 microprocessor (http://www.basicx.com/).

The infrared distance sensor and microprocessor.

The infrared distance sensor and microprocessor.

The distance sensor uses a beam of infrared light to measure the distance from the sensor to an object; the sensor provides an output voltage that has a fairly complicated relationship to this distance. The BasicX processor converts the voltage from the sensor into a number between zero and one. Let us denote this number as \begin{align*}x\end{align*}, and the distance (measured in inches) between the sensor and object as \begin{align*}d\end{align*}. The relationship between \begin{align*}x\end{align*} and \begin{align*}d\end{align*} is

\begin{align*}d=\tfrac{\tfrac{34.63}{x} - {5.162}}{2.54}\end{align*}

Compute the value of \begin{align*}d\end{align*} for the following values of \begin{align*}x\end{align*}:

  • \begin{align*}x = 0.10\end{align*}
  • \begin{align*}x = 0.15\end{align*}
  • \begin{align*}x = 0.20\end{align*}

Exercise 3

The terminal velocity reached by a sky diver depends on many factors, including their weight, their body position as they fall, and the density of the air through which they fall. The terminal velocity is given by (http://en.wikipedia.org/wiki/Terminal_velocity)

\begin{align*}V_t = \sqrt{\tfrac{2mg}{rAC_d}}\end{align*}


  • \begin{align*}m\end{align*} is the sky diver's mass
  • \begin{align*}g\end{align*} is Earth's gravitational constant
  • \begin{align*}r\end{align*} is the atmospheric density
  • \begin{align*}A\end{align*} is the sky diver's effective area
  • \begin{align*}C_d\end{align*} is the sky diver's coefficient of drag

Compute the terminal velocity of the sky diver for each of the following values of \begin{align*}m\end{align*}:

  • \begin{align*}m = 40\;\mathrm{kg}\end{align*}
  • \begin{align*}m = 80\;\mathrm{kg}\end{align*}
  • \begin{align*}m = 120\;\mathrm{kg}\end{align*}

Use the following values for the other variables:

  • \begin{align*}g = 9.8\end{align*}
  • \begin{align*}r = 1.2\end{align*}
  • \begin{align*}A = 0.5\end{align*}
  • \begin{align*}C_d = 1\end{align*}

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