# Tagged Questions

21 views

### Definition of an integrand

General Question: Say we have integral $$\int f(z)\ dz$$ Is the integrand in this context (i) $f(z)$ or (ii) $f(z)\ dz$? In any case, is $f(z)\ dz$ a formally defined mathematical object in its ...
47 views

### Is $\omega = dU = sin(x+y)dx+cos(x+y)dy$ an exact form?

In my thermodynamics homework I should prove that $dU = sin(x+y)dx+cos(x+y)dy$ is a function of state. Which means it's integration over any path be constant or in other word $dU$ should be an exact ...
108 views

### What is the relation of $\int f dx^1\wedge dx^2\wedge …\wedge dx^n=\int f dx^1…dx^n$

In a book "calculus on manifolds" it is defined that $\int f dx^1\wedge dx^2\wedge ...\wedge dx^n=\int f dx^1...dx^n$ but how it is possible the relate the integrand of a multilinear function ...
180 views

### Concept of integration to differential form

How to integrate differential form actually. As far as I know, a differential form is a multilinear function mapping from a vector space to a real number. Let's take $\int_c fdx+gdy$ as an example. It ...
124 views

### Wedge product of differential and volume form

Let $f(x)$ be a $C^1$ function defined on $\mathbb{R}^n$ and $\nabla f(x) \neq 0$ for any $x \in \mathbb{R}^n$. If $d\sigma$ is the volume form on hypersurface $f(x)=c$ induced from $\mathbb{R}^n$ ...
259 views

### baby rudin, chapter 10, (differential forms) theorem 10.27

I'm having difficulties with the reasoning in the proof of theorem 10.27 (regarding integration over oriented simplexes). say ...
We can express every k-form in the form $\omega(x) = \sum_Id_Idx_I$ where $I$ is k-tuple and $d_I$ is just some scalar function of x. That's entirely understandable for me. But while reading ...