Question

Why does a parametric curve need to be smooth for line integrals?

score 469 · Answer 1 · 2026-04-13 17:45:04

469

Views

Why does a parametric curve need to be smooth for line integrals?

Published on 13 Apr 2026 - 17:45

score 40 · Answer 2 · 2026-04-14 07:45:56

40

Views

Proof of: $ u_j\frac{\partial}{\partial x_i}u_j=\frac{1}{2}\frac{\partial}{\partial x_i}(u_j^2) $

Published on 14 Apr 2026 - 7:45

score 113 · Answer 3 · 2026-04-15 03:28:18

113

Views

Definition about convergence of a sequence in $\mathbb{R}^n$

Published on 15 Apr 2026 - 3:28

score 146 · Answer 4 · 2026-04-13 02:09:02

146

Views

Tensor Calculus Notation

Published on 13 Apr 2026 - 2:09

score 52 · Answer 5 · 2026-04-15 11:47:35

52

Views

Determine if the sequence $x_k \in \mathbb{R}^3$ is convergent when $x_k=(2, -k^{-1}, k^{-3})$

Published on 15 Apr 2026 - 11:47

score 264 · Answer 6 · 2026-04-10 17:05:25

264

Views

Level set corresponding to the value $0$ for $f(x,y,z)=y^3-z^3$ is a smooth surface?

Published on 10 Apr 2026 - 17:05

score 159 · Answer 7 · 2026-04-16 14:09:59

159

Views

Showing that $\nabla(\frac{1}{f})=-\frac{\nabla f}{f^2}$

Published on 16 Apr 2026 - 14:09

score 886 · Answer 8 · 2026-05-10 21:28:35

886

Views

Prove that the cone $S = \{(x,y,z) \in \Bbb R^3 ~|~x^2+y^2-z^2=0 \}$ is not a smooth surface

Published on 10 May 2026 - 21:28

score 269 · Answer 9 · 2026-04-14 14:41:24

269

Views

Use Stokes' theorem to show this integral relation.

Published on 14 Apr 2026 - 14:41

score 88 · Answer 10 · 2026-04-18 00:04:17

88

Views

show that $\partial_u(f \circ g)=f'(g(x))\partial_ug(x)= f'(g(x))(\nabla g(x) \cdot u)$

Published on 18 Apr 2026 - 0:04

score 97 · Answer 11 · 2026-04-15 16:36:37

97

Views

Finding the derivative of a linear map $Tx = x_1 -2x_2 + x_3$

Published on 15 Apr 2026 - 16:36

score 164 · Answer 12 · 2026-04-08 03:11:06

164

Views

Explaining Directional derivatives

Published on 08 Apr 2026 - 3:11

score 168 · Answer 13 · 2026-04-12 17:58:02

168

Views

Question on conservative fields.

Published on 12 Apr 2026 - 17:58

score 908 · Answer 14 · 2026-04-12 09:41:08

908

Views

Derivation of Snells Law using boundary conditions

Published on 12 Apr 2026 - 9:41

score 613 · Answer 15 · 2026-04-15 11:33:41

613

Views

Is a convervative and spherical symmetric vector field a radial vector field?

Published on 15 Apr 2026 - 11:33

List Question

Why does a parametric curve need to be smooth for line integrals?

Proof of: $ u_j\frac{\partial}{\partial x_i}u_j=\frac{1}{2}\frac{\partial}{\partial x_i}(u_j^2) $

Definition about convergence of a sequence in $\mathbb{R}^n$

Tensor Calculus Notation

Determine if the sequence $x_k \in \mathbb{R}^3$ is convergent when $x_k=(2, -k^{-1}, k^{-3})$

Level set corresponding to the value $0$ for $f(x,y,z)=y^3-z^3$ is a smooth surface?

Showing that $\nabla(\frac{1}{f})=-\frac{\nabla f}{f^2}$

Prove that the cone $S = \{(x,y,z) \in \Bbb R^3 ~|~x^2+y^2-z^2=0 \}$ is not a smooth surface

Use Stokes' theorem to show this integral relation.

show that $\partial_u(f \circ g)=f'(g(x))\partial_ug(x)= f'(g(x))(\nabla g(x) \cdot u)$

Finding the derivative of a linear map $Tx = x_1 -2x_2 + x_3$

Explaining Directional derivatives

Question on conservative fields.

Derivation of Snells Law using boundary conditions

Is a convervative and spherical symmetric vector field a radial vector field?

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