# Tagged Questions

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### A question in application of derivatives and vectors

Consider a skier who is sliding without friction on the hill ${y = h(x)}$ in a two dimensional world. The skier is subject to two forces. One is gravity. The other acts perpendicularly to the hill. ...
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### looking for asymmetric probability distribution

In physics, quantities are sometimes measured with both an upper and lower error. For example, I might say that an object's mass is $m = 10^{+0.1}_{-0.2} \text{ kg}$. In my case, these arise from ...
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### Mathematical interpretation of pressure (gradient)

I'm having some problem with the following. Usually, the pressure of some mass on an area A is defined by $$P=\frac{F}{A}$$ where $F$ is the force of the mass exerted due to gravity. However, here ...
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### Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )

Good day people of math.stackexchange.com This is a pet project that I plan to use to convince my Prof that I would rather try something similar to this than to do the prescribed project. Edit : ...
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### Modeling with First Order Equations [closed]

A ball with mass 015kg is thrown upward with initial velocity 20m/s from the roof of a building 30m high. There is air resistance of magnitude v^2/1325 directed opposite to the velocity , where the ...
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### Nondimensionalize an equation with logs

I have an equation with logs in it. Specifically the equation takes the form: $log(Y)=\alpha+\beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3$ Where $X_1$ through $X_3$ are variables. The trouble is that Y ...
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### Calculating Humidity, Wet Bulb Temp and Dew Point [closed]

I have been trying to simulate a climate system, but I have hit a wall. I am trying to calculate Humidity. But to calculate Humidity you need the Wet Bulb Temperature, but to calculate the Wet Bulb ...
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### Can the differentiating and squaring process in the cochlea explain a reported dichotic stimulation experiment?

On this math.stackexchange on url What is Octave Equivalence? in an answer on the related ( octave equivalence ) question is stated: Mathematically, this signifies that the mammalian cochlea ...
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### Cat Dog problem using integration

Consider this equation : $$\sqrt{\left( \frac{dy\cdot u\,dt}{L}\right)^2+(dy)^2}=v\,dt,$$ where $t$ varies from $0$ to $T$ , and $y$ varies from $0$ to $L$. Now how to proceed ? This equation ...
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### Check my solution - Modelling of a spring with Differential Equation

I am doing some work with differential equations. I have solved the following problem but am uncertain if I'm doing it correctly. Could someone look over it for me and check if I'm doing something ...
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### Practical physics problem about distance between lines.

I am a software engineer and I’m developing a soccer game. I have a solution for this problem based on Newton law and I’m using Newton method to solve the equation I got. I’m here because I think ...
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### Heat Equation Derivation and Mean Value Theorem

Farlow book PDEs for Scientists and Engineers pg. 27 shows derivation for Heat Equation. It starts by stating Net change of heat inside $[x,x+\Delta x]$ = Net flux of heat across boundaries + Total ...
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### NDSolve simple matrix problem in mathematica

I have a problem with command NDSolve in mathematica. If we have simple second order differential equation, it is easy to write code in mathematica. But if we have matrix problem (for example 4 ...
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### How to make simple iteration in Mathematica

How to make simple iteration in Mathematica for this three equations and save $q$ for each step. If we define $q'=dq/dx$, $q''=dq'/dx$ we have two equations (1) ...
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### How to make iteration for Newmark method in Mathematica 8

How to make iteration method for solving differential equations by Newmark method? There are just three equations which describe the Newmark method. I need q for time step for example 0.01. Also, for ...
Snell's law from geometrical optics states that the ratio of the angles of incidence $\theta_1$ and of the angle of refraction $\theta_2$ as shown in figure1, is the same as the opposite ratio of the ...
### why does $\frac{b\partial a}{a \partial b} = \frac{\partial \log a}{\partial \log b}$?
I am doing some background research on sensitivity and elasticity analysis, and I came across the following definitions of elasticity: e_{ij}=\frac{a_{ij}\partial \lambda}{\lambda \partial ...