What people have posted below is all true. You need to crawl before you can run. This is what you're being told. From a practical standpoint, you will use numerical analysis way more than real analysis. In fact, you will probably never directly use real analysis on the job. This is because numerical analysis concerns implementing various numerical algorithms (root-finding, DE solving, etc.) and studying their efficiencies. Obviously, if you're a quant, you'll be doing a whole lot of this. What you need to understand is that math isn't just about jumping in naked. In order to meaningfully understand numerical analysis (which is ultimately what you really want), you need to first have a solid grasp of real analysis. (FYI: You use real analysis in numerical analysis to understand how quickly/efficiently numerical algorithms converge/work - this is a BIG part of numerical analysis.) You would be doing yourself a disservice to take numerical analysis without first knowing a good deal about real analysis, linear algebra, ODEs, PDEs, and basic programming. You should first solidify your foundation in these areas, and only then should you start taking numerical analysis courses.
