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First Differences(Example of it, imagine in a table format):

X.....Y .......First Differences

So basically, in a real question, you would know your x variable and y and then, what you do to find a first difference is subtract. First you find all the numbers on the 'y' side and subtract by subtracting the bottom number below the first number in the 'y' column. By doing this, you will find what is called first difference. As you continue to do this, if the numbers are constantly staying the same, the pattern or equation will be a linear but if not, it will be a non-linear. I honestly hope this helps if it doesn't, feel free to correct me by posting a comment below with the correct answer.

Q: Definition for a mathematical first difference?

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