What about the 'nuts and bolts' of integration, differentiation, etc. Why is linear algebra covered but no calculus? Even if calculus is covered in real analysis, I think calc needs its own course, and is the most important one by far as a building block before you dive into the other stuff. Otherwise, you will be stuck and not knowing any of the notation. No mention of partial differential equations either, which is also very important. You need to learn how to master change of variables and substitution--those come up constantly in advanced concepts.