The science of Aerothermodynamics covers what happens during a spacecraft's fiery flight through a planetary atmosphere as it sheds speed, converting kinetic energy into thermal energy. This represents a complex interaction between fluid mechanics, thermal radiation and chemistry.
The engineering required to shield hardware against this intense heating is an equally complex multi disciplinary art.

If you want to learn the math then this course offered an excellent overview:
https://tfaws.nasa.gov/TFAWS12/Procee...

Background music:
"Ever Mindful" Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/b...