mathwonk's latest activity

Welcome to PF. I recommend Michael Artin's book: Algebra, as a good guide to linear algebra and other topics in algebra. With your...

Courant, Differential and Integral Calculus, vol. 1, pp. 352-3.

(Apologies if some of this was already said while I was typing it out... had to leave and come back to it...) In most cases when a...

You flunked two semesters of community college? If I'm reading that right, that's not a good sign of potential success at this time...

If the z2- partial derivative of f at p is non -zero, then near p, on f=0, z2 is indeed a single valued function of z1; but if both...

I don't know if the argument for my statement is of interest, but it is nice and fairly short; namely, Riemann showed for analytic...

are z1, z2 complex variables? if so, the zeroes of an analytic function of 2 complex variables are never isolated.

It helps to have a definition of e. One definition is that e is the unique base such that the derivative of e^y at y=0 equals 1. Since...

short calc is a first course in calc, less than 300 pages, terse, no epsilonics. Undergrad analysis is a 3rd course in calc, very...

You already solved the differential equation here so it might be hard to tell what it was. The differential equation originates from...

f is clearly not continuous at 0 (sequential def makes it obvious with any sequence xₙ→0) but it's continuous everywhere else since...

@PeroK: I like your suggestion to use previously proved general theorems to deduce discontinuity of specific functions. One such...

I apologize for provoking sad faces by post #12. To be honest, most people will not need to give an actual proof of sequential...

midget dwarf, nice example, but there is a typo in your statement; likely you meant f(0) = 1, but f(x) = 0 for x ≠ 0.

Rule of thumb: If you want to prove that something is continuous, use Epsilon delta definition of limit. If you want to disprove...