It could be said that mathematics is the language of physics. That is another way of better understanding what is physics. Numerical values, units of measurement, and similar concepts are all mathematical in nature, and are used to describe physical quantities in the most accurate and precise manner.
In brief: Cough headache. There are a couple of possibilities. Coughing can raise the pressure inside your head, which can cause pain sometimes. There is also a poorly-understood entity called the primary cough headache,  that is associated with coughing, straining, laughing, crying, etc.
Pain in Abdominal wall- Abdominal pain when coughing can arise due to pain or conditions in the abdominal wall. Abdominal wall pain usually results from muscle diseases, muscle trauma or strain and or nerve involvement in diseases like diabetes or herpes. Sometimes, involvement of an abdominal organ too can cause referred pain.