Feynman graphs arise in the asymptotic expansion of integrals of various types. We will look at the method of steepest descent and the stationary phase approximation. The Feynman diagram expansion of the partition function will then be derived in detail. The normalized partition function plays an important role in effective field theory. The data of an effective field theory is an action with values in R[[\hbar]] at every energy scale \lambda. We require that the effective actions at different energy scales satisfy a compatibility condition involving the normalized partition function of the higher energy effective action, which Costello calls the "renormalization group equation".