Recent content by unintuit

Homework Statement Find the value of the 2-form dxdy+3dxdz on the oriented triangle with (0,0,0) (1,2,3) (1,4,0) in that order. Homework EquationsThe Attempt at a Solution I have tried various subtraction of these coordinates and applying them to the formula but the answer is in the back of...

I want to apply the knowledge of Spivak's 'Calculus on Manifolds' to physics. However, I am still a math major. Physics is just an interesting aside.

I do not know multivariable calculus. I have studied out of Apostol Vol.1. I do not want to learn the material from Apostol Vol. II. Therefore I want to know If it would be worthwhile to go through Hubbard and Hubbard's 'Vector Calculus, Linear Algebra, and Differential Forms' after going...

Nevermind, I figured out my mistake. I was thinking about it in the wrong way. It was starting with k=1 and ki∈ℕ with k1<k2. Thank you for your help.

Yes to your first question. I was also interested in how one would determine the limit of the expression Σ[k2-(k-1)2]=Σ(2k-1). How would one know if it were to approach 0 vs. 1. I assumed that it went to zero because i. (k+1)2=k2+2k+1=(k+1)2-k2=2k+1 then summing over n we have...

1+3+5+...+(2n-1)=∑(2k-1) but (2k-1)=k2-(k-1)2 summing we use the telescoping property and deduce that ∑(2k-1)=n2-02=n2 This seems accurate to me. Now my question is this a proper use of the telescoping property. In the least it reveals the proper answer, which can then be proved by induction.

Does Ross's book teach and/or use Epsilon-delta proof techniques?

I have one question about Spivak's Calculus on Manifolds book. I have not learned directional derivatives and understand that these are left as exercises in his book, which would make one think these are not that important whereas he focuses on total derivatives or what you may name them...

I am currently having some issue understanding, what you may find trivial, epsilon-delta proofs. I have worked through Apostol Vol.1 and ran through Spivak and I found Apostol just uses neighborhoods in proofs instead of the epsilon-delta approach, while nesting neighborhoods is 'acceptable' I...

Homework Statement For every real x>0 and every n>0 there is one and only one positive real y s.t. yn=x Homework Equations 0<y1<y2 ⇒ y1n<y2n E is the set consisting of all positive real numbers t s.t. tn<x t=[x/(x+1)]⇒ 0≤t<1. Therefore tn≤t<x. Thus t∈E and E is non-empty. t>1+x ⇒ tn≥t>x, s.t...