Manifolds Questions and Answers

Manifolds

$60.00

accepted

Characterizing the Tangent and Normal Bundles - Submanifolds in Banach Spaces and Their Classifications $60.00 accepted Let $M\subset\mathbb{R}^n$ of class $C^k$ and dimension $m$. Show that the set $TM=\{(p,v)\in\mathbb{R}^n\times\mathbb{R}^n;p\in M, v\in T_pM\}$ is a submanifold of class $C^{k-1}$ and dimension $2m$...

Elviegem

$50.00

answered

Complex Variables $50.00 answered Exercise 4.33 from Spivak's Calculus on Manifolds. (Attached).For the definitions and theorems: http://www.strangebeautiful.com/other-texts/spivak-calc-manifolds.pdfThe exercise is on page 118-119. Yo...

Matchmaticians Alumnus

$50.50

answered

Calculus on Submanifolds Challenge $50.50 answered Two multi-part questions about submanifolds given to my class as challenges based on the book Calculus on Manifolds by Spivak. The more detailed the better.

Matchmaticians Alumnus

$10.00

answered

Prove that $f$ is a diffeomorphism $C^∞$, that maps... (More inside) $10.00 answered Prove that $f:(x, y) ∈ R^2$ - {(0, 0)} → ($\frac{x}{x^2 +y^2} $ ; $\frac{y}{x^2+y^2} $) ∈ $R^2$ - {(0, 0)} is a diffeomorphism $C^∞$, that maps each circle of radius $r > 0$ centered in the origin...

Matchmaticians Alumnus

$20.00

answered

Let $f:U\subset\mathbb{R} ^3\rightarrow \mathbb{R} ^2$  given by $f(x,y,z)=(sin(x+z)+log(yz^2) ; e^{x+z} +yz)$  where $U = { (x, y, z) ∈ R^3| y, z > 0 }.$  Questions Inside.  $20.00 answered 1. Prove that $f$ is class $C^{∞} $  and calculate the Jacobian Matrix in $(0,1,1)$.2. Considering $R^3 = R^2×R$, calculate the partial derivatives $D_{i}f(0, 1, 1)$ with $(i = 1, 2)$.3. Using the The...

Matchmaticians Alumnus

$50.00

answered

Exercise 4.33 from Spivak's Calculus on Manifolds. $50.00 answered Exercise 4.33 from Spivak's Calculus on Manifolds. (Attached).For the definitions and theorems: http://www.strangebeautiful.com/other-texts/spivak-calc-manifolds.pdfThe exercise is on page 118-119. Yo...

Savionf