For a modern undergraduate math major not to have ever had a course in complex analysis seems to me to be shocking. As an electrical engineering major, 50 years ago, I took complex analysis up through contour integration (from Stanford’s math department) at the start of my junior year using R.V. Churchill’s famous book Complex Variables and Applications. (I still have my beat-up, coffee-stained copy.) I think contour integration is just too beautiful and powerful to be left out of this book but, recognizing that my assumed reader may not have prior knowledge of complex analysis, all the integrals done in this book by contour integration are gathered together in their own chapter at the end of the book. Further, in that chapter I’ve included a ‘crash mini-course’ in the theoretical complex analysis required to understand the technique (assuming only that the reader has already encountered complex numbers and their manipulation).