The calculus tag has no wiki summary.
0
votes
0answers
52 views
Contour Integrals and Residues [closed]
I'm trying to figure out what it is all about, but my mind is blowing up. First of all, I have turned back and looked at the general definitions of integrals. Then I have looked to line integrals. ...
7
votes
1answer
429 views
I reached a result concerning displacement with quantized time intervals. Am I on to something?
A few days ago, I realized a similarity between distance with constant acceleration, $d = v_i t + 1/2 a t^2$, and the sum of integers up to n, $(n^2 + n)/2$. This came up again today when I decided to ...
-1
votes
1answer
31 views
Can someone help with this hydrostatic force question? [closed]
A gate is in the form of a trapezoid 8 ft wide at the top, 5 ft wide at the bottom and is 3 ft high. If water reaches the top of the gate, what is the total hydrostatic force on the face of the gate?
...
0
votes
0answers
62 views
Small oscillations [closed]
I am asked to consider a fixed homogeneous rod of length $2L$ and mass density $\rho$ It is centered around $O$. A particle with mass M is moving in the same plane. The attractive force between the ...
32
votes
2answers
797 views
What is the meaning of the third derivative printed on this T-shirt?
Don't be a $\frac{d^3x}{dt^3}$
What does it all mean?
1
vote
1answer
122 views
$\nabla({\bf u}^2)=2({\bf u}\cdot \nabla){\bf u} - 2(\nabla \times {\bf u}) \times {\bf u}$
Please see the next link: http://www3.kis.uni-freiburg.de/~peter/teach/hydro/hydro02.pdf
In (2.13), he used:
$$\nabla({\bf u}^2)=2({\bf u}\cdot \nabla){\bf u} - 2(\nabla \times {\bf u}) \times {\bf ...
2
votes
1answer
63 views
Partial derivative potential energy of 'free' vibration
I have this rather mathematical question about the calculation of the partial derivative of a potential energy function given by:
$$U(x_i)=\frac{1}{2}\sum_{i,j}\frac{\partial^2U(0)}{\partial ...
1
vote
0answers
189 views
Apostol or Spivak for mathematical physics? [closed]
I came across many recommendations for both of these books, but I'm not sure which one should I use to study calculus...
I know most of the methods used in calculus and I use them frequently, but I'm ...
0
votes
2answers
298 views
Level of calculus required for physics [closed]
First time for me here so kindly let me know if I violate the rules - especially if this is a duplicate.
After reading the page how to become a good theoretical phycist, I started a serious revision ...
0
votes
0answers
87 views
Nicholas Kollerstrom article on the history of Calculus
Today, Newton´s birthday, I read an article posted in the arXiv by Nicholas Kollerstrom
http://www.arxiv.org/abs/1212.2666
That basically claims that Newton did not invent Calculus. The article does ...
1
vote
1answer
302 views
Derivation of the self gravitational potential energy of a sphere
I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 ...
0
votes
1answer
934 views
Calculating Moment Of Inertia
The problem I am working on is:
A uniform, thin, solid door has height 2.10 m, width 0.835 m, and mass 24.0 kg.
(a) Find its moment of inertia for rotation on its hinges.
(b) Is any ...
0
votes
1answer
279 views
Divergence of cross product of transverse component
If I define the vector as $V_i=V^T_i+V^L_i$ and the transverse part is defined by $$V^T_i=\Big(\delta_{ij}-\frac{\partial_i\partial_j}{\partial^2}\Big)V_j$$ then is is obvious that $\nabla.V^T=0$ as ...
2
votes
3answers
212 views
How to get an integral formula for the flux time derivative
$$\frac{d}{dt}\int \limits_{A} \mathbf B d \mathbf A = \int \limits_{A} \left( \frac{\partial \mathbf B}{\partial t} + \mathbf v (\nabla \cdot \mathbf B ) + [\nabla \times [\mathbf v \times \mathbf B ...
0
votes
0answers
482 views
Create general equation of racing cars with head start [closed]
Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance $d_A$ beyond the starting line at $t=0$. The starting line is at ...
4
votes
3answers
261 views
Is it safe to ignore derivatives of velocity w.r.t. position and vice versa?
In a certain textbook a function is given as:
$$f=f(x(t))$$
And then this is differentiated w.r.t. $t$ to get:
$$f_t=\dot{x}f_x$$
(Where the notation $f_u=df/du$, $f_{uu}=d^2f/du^2$, etc.)
This ...
4
votes
3answers
170 views
How empty of fuel are spacecraft booster rockets typically?
A recent XKCD What-if article mentions the situation where each additional kilogram of cargo to LEO requires an additional 1. 3 kilograms of fuel, which in turn requires fuel to carry ...
0
votes
1answer
84 views
Showing $ \textbf{F} \cdot d\textbf{s} = -dV$ is equivalent to $ F_s = -\frac{\partial V}{\partial s}$
Can someone please explain how the following
$$ \textbf{F} \cdot d\textbf{s} = -dV$$
is equivalent to
$$ F_s = -\frac{\partial V}{\partial s}$$
using some intermediate steps. I don't follow this ...
0
votes
2answers
101 views
Showing $ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$
Can someone please explain how this equation is valid, using intermediate steps if available?
$$ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$$
...
1
vote
1answer
113 views
Determine the flow and amplitude equation for thermal energy (with Del operator)
It is a question vector calculus and Maxwell's laws. I put it this way. Let's say, we are working in a $3$-Dimensional space ( e.g $x\cdot y\cdot z = 4\cdot3\cdot2$, a certain room/class of that size ...
0
votes
0answers
22 views
Calculus Practice Book for Physicists [duplicate]
Possible Duplicate:
Best books for mathematical background?
I am a college senior looking to apply to graduate school in hopes of becoming a theoretical physicist. One of the things my ...
1
vote
1answer
107 views
Confused about the physical meaning of velocity variation
I am reading a paper and saw the author wrote something like,
Because of no-slip wall assumption, so velocity vector $\vec{v}$ is $0$ on the wall, and also the variation of this velocity on the wall ...
1
vote
1answer
128 views
How to decompose a divergence operator
I am reading a paper, and see someone decompose a divergence operator as follows, could someone judge and see if it is correct?
$$\nabla \cdot {\bf{v}} = \left( {{\bf{n}} \cdot \nabla } \right){v_n} ...
2
votes
2answers
364 views
Galilean transformation of wave equation
I have this general wave equation:
\begin{equation}
\dfrac{\partial^2 \psi}{\partial x^2}+\dfrac{\partial^2 \psi}{\partial y^2}-\dfrac{1}{c^2}\dfrac{\partial^2 \psi}{\partial t^2}=0
\end{equation}
...
1
vote
4answers
357 views
How can/does calculus describe the movement of a particle?
I was talking to Roger Penrose about calculus in the appendix in his book Cycles Of Time and he said I'd need a good understanding of calculus if I wanted to read his book in great depth. He said I ...
