Use this tag for questions about differential and integral calculus with more than one independent variable. Some related tags are (differential-geometry), (real-analysis), and (differential-equations).
1
vote
2answers
40 views
Triple integral problem involving a sphere
Let $R = \{(x,y,z)\in \textbf{R}^3 :x^2+y^2+z^2\le\pi^2\}$
How do I integrate this triple integral
$$\int\int\int_R \cos x\, dxdydz,$$ where $R$ is a sphere of radius $\pi$?
I have trouble ...
1
vote
2answers
33 views
How do you evaluate this line integral, where C is the given curve (Please help)?
Evaluate the line integral $$\int_C (x+2y)dx + x^2dy,$$ where $C$ consists of line segments from $(0,0)$ to $(2,1)$ and from $(2,1)$ to $(3,0)$.
How do you solve this by using the following ...
0
votes
2answers
43 views
Vector Derivatives
I know that
$\nabla_x [\mathbf{a}^T\mathbf{x}] = \mathbf{a}$
$\nabla_x [\mathbf{x}^T\mathbf{a}] = \mathbf{a}$
but what about $\nabla_x [\mathbf{y}\mathbf{x}^T\mathbf{a}]$ where $y \in ...
0
votes
2answers
45 views
Whats the connection between formss and vector fields?
I heard someone talking about how vector fields are the kernels of forms. Can someone give me a detailed explanation about how this works? Thanks.
0
votes
0answers
14 views
Subgradient of matrix $l1$-norm
Let $X$ be a square matrix, what is the sub-gradient of $f(X) = ||AX-XB ||_{l1}$?
$A$ and $B$ are both constant matrix.
I am very confuse about the chain rule on matrix derivatives.
-1
votes
0answers
18 views
Estimating error of radius given the errors of volume and hight. [closed]
The volume of a right circular cone $V= \frac{\pi}{3} r^2 h$. Use differentials to approximate the relative error calculating the radius of the cone given measurements for volume and height with ...
-1
votes
0answers
33 views
Chain Rule Problem [closed]
Newton's Law of Gravitation asserts that the magnitude of force between objects of masses $M$ and $m$ is $F = GMm/r^2$ where $r$ is the distance between them and $G$ is a universal constant. Let an ...
8
votes
0answers
55 views
Find all functions $F(x,y)$ such as $\frac{\sqrt{3}}{2}\frac{\partial{f}}{\partial{x}}+\frac{1}{2}\frac{\partial{f}}{\partial{y}}=0$
How to find all possible functions $f(x,y)$ such as:
$$ \frac{\sqrt{3}}{2}f_x+\frac{1}{2}f_y=0$$
(with $f_x = \frac{\partial{f}}{\partial{x}}$ )
Here's everything I tried:
1) I can guess the ...
1
vote
3answers
43 views
surface area of a sphere above a cylinder
I need to find the surface area of the sphere $x^2+y^2+z^2=4$ above the cone $z = \sqrt{x^2+y^2}$, but I'm not sure how. I know that the surface area of a surface can be calculated with the equation ...
3
votes
1answer
61 views
Derive the solution to the Lagrangian $ \mathcal L= y(x)\sqrt{1+y'(x)^2}$
I am supposed to derive the solution to the Lagrangian $$ \mathcal L= y(x)\sqrt{1+y'(x)^2}$$
Unfortunately I am unable to solve both, the Euler Lagrange equation or the Beltrami equation. It may be ...
0
votes
1answer
22 views
Changing from rectangular coordinates to spherical coordinates (integration)
I am taking calculus 3 and I have problems understanding how to change from rectangular coordinates to spherial ones (integration).
For example, I have this problem:
Find the volume of the solid $T$ ...
0
votes
1answer
41 views
Integration in $\mathbb{R}^n$ region
If its all parameterized usually I can solve it, but I have a problem with integration in vagues regions, usually I dont know the right procedure to solve them.
The problem I need to solve is: given ...
1
vote
2answers
34 views
Can a Covariance matrix have negative elements?
I have a $N \times N$ covariance matrix $C$ of a multivariate Normal distribution. Can any of the elements of the Covariance matrix $C$ be negative for a real-valued distributions ?
-5
votes
0answers
56 views
Can someone please help me prove this using the chain rule?
∇∙F= r'∙(d F)/dr
r=x i+y j+z k .........................................................................................................
r=|r|=sqrt(x^2+y^2+z^2) ...
1
vote
1answer
26 views
Show that product of x, y, and z intercents of tangent plane to surface xyz=1 is a constant
I am studying for my math final and I just wrote the practice final. Unfortunately there are no solutions and I am completely lost on how to do this problem. If anyone could help I would really ...
