Functions & Inverses Course for Calculus

WHAT STUDENT STILL DONT GET, YET?!

• What are functions? Its easy and obvious, right?... Its just f(x), right? NO! xD... Most student know how to work the basics with functions but are clueless about the concept involved, even college student! In this course we'll give different points of view such as relations, procedures.

• Functions viewed as labelers (what the HECK??!...you'll see..) will motivate the notions of 1-1, onto or bijective properties.

• What operations can be made with functions? (you all know that... but lets review it in a mature manner, OK?.. ) Sum, multiplication, division, composition, restriction. We'll see these in detail. These are very simples, but they contain many important concepts in mathematics, we will find them... illuminating... like a Christmas tree! :)

• Use composition of functions as a means to understand change of variables (you most probably did not expect that...), moreover when combined with image of sets, allow us to better understand function transformations (yes...yes... now this is a new idea, a good idea indeed! :O). This is one of the subjects that students have more difficulties, both high-school and college. It is now that you'll make sense of them, finally...phew

• What is the inverse function? This is intimately connected with bijective functions, wow! And what about those, nasty.... that are not bijective, what should we do? (I'm sooo psyched for this episode!)  We'll discuss in detail examples of both.

• Yes, I want more now!... This is part 1, more soon... this takes a lot of work to put together :)

With this lecture videos you'll find a pdf file. The videos complement the sections of the pdf, which also has the exercises with solutions. On the title of each video you find the corresponding section of the pdf.