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If you're interested in applications of differential equations in the biological/medical area, I suggest looking at Clifford Taubes, "Modeling differential equations in biology" http://books.google.ca/ …

Actually this is less obvious than it looks. GE's stock split several times, most recently a 3-for-1 split on May 8, 2000. There was a time on June 22, 2000 when the stock price was approximately \$ …

Automobile suspensions. What happens when you drive over a speed bump?

Functions in the modern sense of the word are much more general than the expressions that you seem to think of as "functions". In particular, most functions (in the sense of cardinality) cannot be s …

$f(x) = -x^3$ is strictly decreasing and has an inflection at $x=0$.

Whenever you use a numerical method to approximate something, you'd like to know that your numerical answer will be close to the actual value. A common situation is that the numerical approximation i …

It very often happens in applications that a model produces equations that are extremely difficult or impossible to solve. However, some of the factors are more important than others. …

Whenever $f(t)$ represents a rate of change of something, $\int_a^b f(t)\ dt$ represents the total change from $t=a$ to $t=b$. If $f(x)$ represents a density of something, $\int_a^b f(x)\ dx$ repres …

PRuler is an iPhone app that lets you measure objects using a credit card and your iPhone camera. I'm told it uses a Singular Value Decomposition (which is very closely related to eigenvalues and eig …

With $G$ higher-dimensional you don't want to think of its action as representing translations in time, but rather translations in space.

One thing you might try is breaking a modern tortoise shell under as close to similar conditions as possible and seeing how the dimensions change. Hopefully the proportions will be preserved.

Much of the theory of probability can be considered as a branch of functional analysis (although some probabilists might object to this statement). For example, the Strong Law of Large Numbers can be …

The equation appears rather bizarre, and I would be surprised to see a "physical meaning" in any reasonable sense of the word "physical". You might note, though, that if $A$ has nonzero eigenvalues $ …

For the Manhattan distance, you can think of this an an Assignment problem: assigning a member of the $m$ to each index of your vector $n$, where the cost for assigning $m_j$ to index $i$ is $|m_j - n …

The coronavirus picture that you see everywhere does not look to me like a regular tiling. I don't know how accurate it is, though.