Question

An Integral formula - change of variables

score 32 · Answer 1 · 2023-12-17 06:54:55

32

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An Integral formula - change of variables

Published on 17 Dec 2023 - 6:54

score 76 · Answer 2 · 2023-12-17 23:56:22

76

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How bad is the error in the volume of a transformed region, when the transformation is approximated as linear?

Published on 17 Dec 2023 - 23:56

score 54 · Answer 3 · 2023-12-18 10:00:59

54

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$F(u,v)$ is a rational function. If $\pi$ is a period of $F(\cos x,\sin x)$, then $F(u,v)=F(-u,-v)$. "Introduction to Analysis" by Teiji Takagi.

Published on 18 Dec 2023 - 10:00

score 52 · Answer 4 · 2023-12-19 14:52:58

52

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What is the area of the domain corresponding to small change in the function?

Published on 19 Dec 2023 - 14:52

score 69 · Answer 5 · 2023-12-26 11:15:56

69

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Exercise 6 from "Measure Theory and Integration" Micheal E.Taylor, a maximal inequality.

Published on 26 Dec 2023 - 11:15

score 103 · Answer 6 · 2026-03-25 23:58:42

103

Views

Find the density of random variable $X+Y$ for $f(x,y) = 6(x-y)$ if $0 \leq y \leq x \leq 1$

Published on 25 Mar 2026 - 23:58

score 69 · Answer 7 · 2024-01-07 21:16:29

69

Views

Convolution of random variables - confusion about change of variables

Published on 07 Jan 2024 - 21:16

score 36 · Answer 8 · 2024-01-09 21:15:36

36

Views

How to show $\int_{h(g(A))} f=\int_{g(A)} (f\circ h)|\det h'|$ holds when $\int_{h(B)} f=\int_{B} (f\circ h)|\det h'|$ Calculus on Manifolds Spivak.

Published on 09 Jan 2024 - 21:15

score 65 · Answer 9 · 2024-01-10 01:40:28

65

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I wonder why we need (2) to prove the change of variable theorem for the case $n=1$. ("Calculus on Manifolds" by Michael Spivak.)

Published on 10 Jan 2024 - 1:40

score 32 · Answer 10 · 2024-01-10 12:52:08

32

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Why did the author calculate $D_n(g^n\circ h^{-1})(h(a))$ to conclude $k'(h(a))=I$? ("Calculus on Manifolds" by Michael Spivak.)

Published on 10 Jan 2024 - 12:52

score 53 · Answer 11 · 2026-03-27 16:27:36

53

Views

How to determine a change of variable that makes the Hessian matrix diagonal?

Published on 27 Mar 2026 - 16:27

score 27 · Answer 12 · 2024-01-10 18:28:42

27

Views

$h(D\times\{x^n\})\subset\mathbb{R}^n$ and the author wrote $\int_{h(D\times\{x^n\})} 1 dx^1\cdots dx^{n-1}$. Is this ok? Calculus on Manifolds Spivak

Published on 10 Jan 2024 - 18:28

score 50 · Answer 13 · 2024-01-11 04:23:58

50

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How to solve Problem 3-39 in "Calculus on Manifolds" by Michael Spivak? (Change of variable Theorem, Sard's Theorem)

Published on 11 Jan 2024 - 4:23

score 64 · Answer 14 · 2024-01-12 00:13:20

64

Views

Solve PDE with condition

Published on 12 Jan 2024 - 0:13

score 96 · Answer 15 · 2026-03-27 07:49:44

96

Views

What does $\int_{B_r} h$ mean? Problem 3-41 in "Calculus on Manifolds" by Michael Spivak. $\int_{-\infty}^{\infty}e^{-x^2}dx=\sqrt{\pi}$.

Published on 27 Mar 2026 - 7:49

List Question

An Integral formula - change of variables

How bad is the error in the volume of a transformed region, when the transformation is approximated as linear?

$F(u,v)$ is a rational function. If $\pi$ is a period of $F(\cos x,\sin x)$, then $F(u,v)=F(-u,-v)$. "Introduction to Analysis" by Teiji Takagi.

What is the area of the domain corresponding to small change in the function?

Exercise 6 from "Measure Theory and Integration" Micheal E.Taylor, a maximal inequality.

Find the density of random variable $X+Y$ for $f(x,y) = 6(x-y)$ if $0 \leq y \leq x \leq 1$

Convolution of random variables - confusion about change of variables

How to show $\int_{h(g(A))} f=\int_{g(A)} (f\circ h)|\det h'|$ holds when $\int_{h(B)} f=\int_{B} (f\circ h)|\det h'|$ Calculus on Manifolds Spivak.

I wonder why we need (2) to prove the change of variable theorem for the case $n=1$. ("Calculus on Manifolds" by Michael Spivak.)

Why did the author calculate $D_n(g^n\circ h^{-1})(h(a))$ to conclude $k'(h(a))=I$? ("Calculus on Manifolds" by Michael Spivak.)

How to determine a change of variable that makes the Hessian matrix diagonal?

$h(D\times\{x^n\})\subset\mathbb{R}^n$ and the author wrote $\int_{h(D\times\{x^n\})} 1 dx^1\cdots dx^{n-1}$. Is this ok? Calculus on Manifolds Spivak

How to solve Problem 3-39 in "Calculus on Manifolds" by Michael Spivak? (Change of variable Theorem, Sard's Theorem)

Solve PDE with condition

What does $\int_{B_r} h$ mean? Problem 3-41 in "Calculus on Manifolds" by Michael Spivak. $\int_{-\infty}^{\infty}e^{-x^2}dx=\sqrt{\pi}$.

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