A.4. Table A.5: Predefined variables and math constants

ans Value of last variable (answer)

The variable ans in MATLAB stores the result of the last computed expression when you do not assign it a name. For example, if you calculate a value like 2 + 2 and don't assign it to a variable, MATLAB automatically saves this result in ans, allowing you to use or refer to it later without explicitly naming it.

Think of ans like your calculator's display that shows the last answer you obtained. If you use your calculator to add 5 and 3, it shows '8'. If you don’t note it down, you can simply use the last value again without needing to remember or write it down.

eps Floating-point relative accuracy

The variable eps represents the smallest difference between two distinct numbers in floating-point representation in MATLAB. It indicates the precision of the calculations in MATLAB. For example, it can help determine how close two floating-point numbers need to be for MATLAB to consider them equal.

Imagine you are measuring a piece of wood with a very precise ruler. Even if two pieces of wood look the same, if they are not identical to the smallest measurement on your ruler, they are considered different. Similarly, eps helps MATLAB know the limits of its precision.

i Imaginary unit of a complex number j Imaginary unit of a complex number

In MATLAB, both i and j are used to denote the imaginary unit, which is the square root of -1. This is crucial in complex number computations, allowing MATLAB to handle numbers that are not solely on the real number line. For instance, a complex number can be represented as 3 + 4i.

Think of complex numbers like a two-dimensional coordinate system, where the real part is mapped along one axis (like the x-axis) and the imaginary part is on another (the y-axis). Just like how you can have positions in both x and y directions, complex numbers combine both real and imaginary aspects.

Inf Infinity (∞)

The variable Inf represents an infinitely large value in MATLAB. This is typically used in computations that can result in an overflow or where a value exceeds finite limits. For instance, dividing a positive number by zero will yield Inf.

Imagine a very tall skyscraper that is so high, it feels like it touches the sky. In this analogy, Inf represents that height - it's not just tall, it surpasses any measurable or imaginable limit, just as infinity does in the mathematical sense.

NaN Not a number

The variable NaN stands for 'Not a Number' and is used in MATLAB to represent undefined or unrepresentable numerical results, such as the result of 0/0 or the square root of a negative number. It indicates a calculation that does not yield a valid number.

Think about a student trying to calculate how many apples they would receive when dividing zero apples among zero friends – it's an impossible scenario! Similarly, NaN signifies calculations that do not have a valid result.

pi The number π (3.14159...)

The variable pi in MATLAB represents the mathematical constant pi (π), which is approximately equal to 3.14159. It is widely recognized in geometry and trigonometry, particularly in calculations involving circles. For example, the circumference of a circle can be calculated as 2 * pi * radius.

Consider the process of baking a pie. To make a round pie, you need to understand how to calculate its area and perimeter, which involves pi. Just like the essential role of pi in cooking the perfect pie, it holds foundational importance in mathematics when dealing with circular shapes.

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