I will give a hands-on tutorial (with some Octave coding) on numerical analysis, by walking through some inspiring examples from real analysis. I will focus on demonstrating some fundamental concepts in numerical analysis, from the perspective of real analysis. This talk is intended for any faculties and graduate students who are interested in gaining some first experience of computational mathematics, which has become increasingly useful in all fields of our modern society. No prior programming experience is required. In particular, Octave (compatible with Matlab) has a free online coding website http://octave-online.net/.