As mentioned here, it is my strong belief that part of the purpose of a university education is to teach one to think. This requires being faced with difficult material. Thus I would suggest that Goursat's book's not being the kind of thing most of you are used to reading, far from being a reason for eschewing its use, actually argues in favour of it, and that the extra effort it might take to understand it will prove its worth in multiple ways. (There is a specific point here which is worthy of attention. While I believe the major notations in Goursat are quite similar to modern ones, there might be a few points where they differ. Several years ago, while a Master's student at Utah State University, I attended a talk about undergraduate physics pedagogy in which the speaker described an experiment they had done in upper-division physics classes which necessitated -- among other things -- students' simultaneously referencing different books with different notations. Prior to beginning this program students were asked to describe barriers to their study, and mentioned -- among other things -- differing notations. Coming out of it, though, they said they had begun to understand what it meant to be a physicist and solve physics problems. While consistency in notation most definitely has its place -- particularly locally, say within a single chapter or a single book -- it can also disguise a lack of actual understanding. If one really understands what is going on, the exact notation used is less important.)

When I taught partial differential equations in the summer of 2019, one of my goals was to make sure that my students learned to actually solve hard problems. This informed my choice of textbook -- though I am not certain the textbook was ultimately as useful as I might have hoped -- and in particular my decision not to use the textbook ordinarily used in that course, which I consider too 'soft'. While I have not had sufficient exposure to all of the different textbooks in complex analysis now available to be sure that this is an accurate sentiment when referred to particular area, my general feeling is that textbooks in many areas of mathematics have steadily become less demanding on their readers over the years. This is not a trend I view positively, and with this current course as with my course in partial differential equations just mentioned, one goal is that all of you as my students learn to solve hard problems. Conceptual understanding, as I have emphasised both here and elsewhere, is also important, but cannot replace the ability to actually solve problems. In fact I would argue that in some ways the ability to solve hard problems is rather the foundation of conceptual understanding.

(To some extent the sentiments in the previous paragraph touch on the debate between Hilbert and Brouwer regarding the foundations of mathematics which occurred during the first part of the twentieth century. For those who are interested, the Wikipedia page on Errett Bishop provides some information and links on the matter. The hyper-abstraction apparent in many -- if not all -- fields of modern pure mathematics, and the too-oft-encountered lack of any concern for the actual content or meaning of the results obtained, is something which distresses the current author considerably.)

Another reason suggests itself from the author's own experience. Some time ago he was studying some problem related to space physics; perhaps it was the problem of using electromagnetic fields to put limits on the extent of a subsurface ocean on the Jovian moon Europa. (This is a fascinating problem which still interests him greatly; some information is in the Wikipedia page.) At any rate, the problem required knowledge of a collection of special functions known as spherical harmonics (which those of you who have taken classes in quantum mechanics or electromagnetics have probably seen in some form already). Some of the most thorough references on these functions are texts from the first part of the twentieth century, which were nigh impenetrable when he first attempted their study. He cannot beileve but what this is also the case in other areas of applied mathematics as well. Thus those of you whose ultimate purpose in studying mathematics is more towards application than pursuing research in mathematical theory are well-served by exposure to texts from past years.

For all of the foregoing reasons, I do sincerely hope that you will make an honest effort to follow through the indicated sections of Goursat's text. I know that there are many other useful texts as well, and you are more than welcome to reference whatever text you like. But the main text we will be using is Goursat's and his only.