Recent content by jppike

So the argument is not pointless if I don't announce an opinion outright? Sorry this just doesn't seem to make sense to me, the point of debate is to discuss a topic from various points of view, how do my deep and true feelings of the matter change that? I'm taking a specific side either way...

I will answer your question assuming that you meant 4 to be 4*E, where E is the identity matrix of GL(4,R) (i.e x=E). To solve the system you are given you simply reduce it to a simple equation in each entry. So if we denote by Xij, Yij, Zij, Eij the entry in the ith row, jth column of X,Y,Z,E...

Before I begin my response I should mention that I am honestly not one of the advocates that infinitesimal calculus should be one's first introduction to the calculus. Indeed, I don't believe I have a sound enough understanding of Non Standard Analysis yet to really make such a decision. I'm...

I'm sorry? There has been a mathematically rigorous definition of infinitesimals that has been accepted by the mathematical community...

This isn't true. In the 1960's a logician named Abraham Robinson proved the mathematical validity of infinitesimals by constructing the Hyperreal Number System, an ordered field which strictly contains the Real Numbers, but also includes numbers which are smaller than every real number (and...

It will perhaps become more clear if you switch your notation slightly. How about we denote dy/dx instead by ω. Okay, so ω is a function, and what we are looking for is dω/dx. We will apply the chain rule: dω/dx=dω/dt * dt/dx=d/dt(ω)*dt/dx Now we simply put back dy/dx for ω to get...

t is a parameter that you would parametrize your curve with, usually thought of as time. However, there is a natural parameter, s, which in some sense measures the 'distance travelled' as you said. For more on the difference between an arbitrary parameter t and the natural parameter s, refer...

I think you are a bit confused about what it means for something to be tangent. A tangent vector is NOT a normal vector, it should not be perpendicular to the path; it should be "parallel". Recall that a tangent line to a point t=x on the path β(t) is a line that passes through the point...

Actually, there is no need for Non Standard Analysis here at all. The differential df of a function f is well defined without it; if you study differential geometry you will learn what the symbols dp, dV, dT in your equation actually mean. They are 1-forms, which are linear functions on...

So next fall I will be taking the Mathematics subject GRE, and I've been looking over the website, here is a description of the Calculus which will make up the majority of the examination: Material learned in the usual sequence of elementary calculus courses — differential and integral...

Vector Calculus by Susan Jane Colley is what my school is using for our vector calculus course intended for mathematics majors. To be honest I didn't even purchase the book for that course, but from other students who had a bit of trouble with calculus I've heard it's quite good :)

I am currently a mathematics major in my third year of study, and I recently changed my minor from economics to physics, so I am taking physics courses at the second year level, including classical mechanics, e&m, etc, which are all going fine, and an introductory course in modern physics. This...