Coarse refers to an object composed of large parts or particles of inferior quality/appearance with a rough, blunt surface.
"His teacher described his character as coarse and unrefined."
Course could mean the flow or rush of blood or any other liquid. It also means a treatment plan or learning program in a school.
A. "I can feel your blood coursing through your veins."
B. "Gareth is offering only four courses this semester."