function analysis. the understanding of spatial and time relationships through the study of their changes

there are many books you can read which will teach you calculus. they will start with limits, then move to derivatives, then integrals. this course will not do that. our goal is to truly understand a function. who are they? how do they grow? what can they tell us? what are their strengths and weaknesses? in order to achieve this, we must define verbiage to describe functions and compare them to one another. this leads to a toolbox of tools we can use on functions to pry valuable information out of them. then, of course, we must be able to perform these actions on functions in all dimensions and of any strange body they take on. this course assumes the reader has an intimate understanding of linear algebra, but no "calculus" skills, so to speak. also, please be kind about the title- this is "function" analysis not functional analysis, which is a more advanced topic of study!

first, we begin with a question: how do we study functions? what does divination look like? then, we accrue the tools of the trade required to carry out these practices. At last, we finally study the methodology and practice of function analysis, and all of its moving pieces (the brunt of the course)

chapters

ii.i the limit

ii.ii parameterization

ii.iii multiple variables

iii. the future

iii.i how do we see the future?

iii.ii the one form

iii.iii the exterior derivative and the partial derivative

iii.iv recursion

iv. the past

iv.i how do we see the past?

iv.ii the determinant

iv.iii change of variables (basis)

iv.iv stokes

iv.v the integral

v. selected applications and cases

v.i frenet frames

v.ii the physicists

v.iii geodesics (not coming anytime soon LOL at least until fall '25)