This article explains multiple ways to calculate AUC mathematically along with step by step implementation guide in Python, SAS and R.
ROC curves and Area Under the Curve explained (video)
Partial area under ROC curve
The Area Under an ROC Curve
ROC curve analysis
AUC - Insider's Guide to the Theory and Applications – Sin-Yi Chou – Data Science Enthusiast
A Layman's guide to ROC Curves And AUC - MLWhiz
Methods to determine area under curve
Receiver operating characteristic - Wikipedia
Calculating AUC: the area under a ROC Curve (Revolutions)
python - How to calculate a partial Area Under the Curve (AUC) - Stack Overflow
GraphPad Prism 10 Statistics Guide - Area under the curve