# Why aren't integral equations often taught "back to back" with differential equations?

In single variable calculus, integral calculus is taught "back to back" with differential calculus. This is generally true, although to a lesser extent, with multivariable calculus.

Yet I don't see the teaching of integral equations accompanying that of (ordinary) differential equations; instead, differential equations are often paired with linear algebra or partial differential equations. For instance, on this site, there was a tag for differential equations but not for integral equations (until I created one).

Why is that?

• Just a wild guess (which doesn't address the issue of tags in Stack Exchange), but I wonder if it's because after the 1930s or so integral equations became subsumed under functional analysis? Commented Apr 7, 2018 at 12:11
• We probably should be teaching more integral equations with PDEs. I just have a token week or two in my intro to DEqns class , so getting to Green's functions is a bit much for my course. In retrospect, it ought to have played a larger role in the PDE course I took as an undergrad. I think you have a point here to some extent. But, maturity and difficulty of the topic makes it formidable for many audiences. That explains the direction that Dave Renfro points out. Commented Apr 7, 2018 at 18:08
• I never encountered them in science or engineering, but saw ODEs and PDEs all over the place. [Note for pedants, I am not saying there is not a single journal article in science or engineering that with an integral equation. I am saying it is not a common part of undergrad physics or engineering, including the harder classes junior and senior year.] Commented Apr 7, 2018 at 23:24
• @guest at the graduate level, even introductory, it becomes important. Particularly, the interplay between the method of images and Green's functions in the graduate electricity and magnetism course (ala Jackson). For a nice undergrad book which makes a good case for the importance of Green's functions I think Haberman's text is helpful. See books.google.com/books/about/… Commented Apr 11, 2018 at 4:00
• OK, Green's function is part of pde books. what does that have to do with a full topic on integral equations, kernels, etc.? I mean the Laplace transform has an integral in it also and that is part of regular sophomore ODE course. Commented Apr 11, 2018 at 11:55