If the $1875 is already included in the $11,018, you don't normally need to think about it separately, unless it has restrictions.
There is a tax “loop hole” available to claim an education credit, for the parents of students on scholarship. The student reports all his scholarship, up to the amount needed to claim the American Opportunity Credit (AOC), as income on his return. That way, the parents (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the conditions of the grant are that it be used to pay for qualified expenses.
Using your numbers: Student has $11,018 in box 5 of the 1098-T and $10,991 in box 1. At first glance he/she has $27 of taxable income and nobody can claim the American opportunity credit. But if she reports $4027 as income on her return, the parents can claim $4000 of qualified expenses on their return.
Books and computers are also qualifying expenses for the AOC. So, extending the example, the student had another $1000 in expenses for those course materials, paid out of pocket. She would only need to report $3027 of taxable scholarship income, instead of $4027. The parents get a $2500 credit, and the student pays $0 to $666 in tax, depending on his other income.
The IRS actually encourages use of this technique. From the form 1040 instructions: “You may be able to increase an education credit if the student chooses to include all or part of a Pell grant or certain other scholarships or fellowships in income. For more information, see Pub. 970, the instructions for Form 1040 and IRS.gov/EdCredit". PUB 970 even has examples of how to do the “loop hole”.
