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(Note: This is NOT a homework question; it's just a query.)

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- Thread starter Benjamin113
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(Note: This is NOT a homework question; it's just a query.)

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But the world involves functions that depend on several variables. For example the pressure of a gas depends on density and temperature. The speed of sound (squared), it turns out, in a nebula in space (which is very nearly at constant temperature due to radiative transport) is the partial derivative of the pressure with respect to density keeping temperature fixed.

Your happiness H depends on how much money, m, you make and the number of hours, h, you spend with your family. H = H(m, h). But how much money you make also depends on how much on how much time you spend with your family. The more time you spend with them the less money you will make. So m = m(h) and we must write

H = H(m(h), h)

Now, we want to know how many hours "h" to work to maximize happiness so we take the _total_ derivative of H with respect to h and set it equal to zero:

dH/dh = (partial H/partial m)*(partial m/partial h) + (partial H/partial h) = 0.

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Okay, cool. :D

Thanks for the response.

(Also, I like your analogy)

Thanks for the response.

(Also, I like your analogy)

- #4

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(1) Maxwell's equations of electromagnetism

(2) Einstein's general relativity equation for the curvature of space-time given mass-energy-momentum.

(3) The equation for heat conduction (Fourier)

(4) The equation for the gravitational potential of a blob of mass (Newton-Laplace)

(5) The equations of motion of a fluid (gas or liquid) (Euler-Navier-Stokes)

(6) The Schrodinger equation of quantum mechanics

(7) The Dirac equation of quantum mechanics

(8) The Yang-Mills equation

(9) The Liouville equation of statistical mechanics

So you see PDEs are fundamental.

Cheers

- #5

symbolipoint

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Every trading day, traders on Wall-Street solve some version of the Black-Scholes equation for the value V(S, t) of an option as a function of the price S of the underlying stock and time "t".

The Black-Scholes equation and its different versions are partial differential equations.

See this wikipedia article: http://en.wikipedia.org/wiki/Black-Scholes" [Broken]

The Black-Scholes equation and its different versions are partial differential equations.

See this wikipedia article: http://en.wikipedia.org/wiki/Black-Scholes" [Broken]

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hotvette

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I use them occasionally in the study of CFD (Computational Fluid Dynamics) simulations.

Thanks

Matt

Thanks

Matt

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