Gah, I’m bloody worthless: I know so much that I use so little, I might just as well know nothing at all. But…

Aside from the usual geometric identities, here are the fun ones.

Euler’s Identity:

**e[sup]***j*θ[/sup]= *j*sin θ + cos θ

and the special, beautiful case of:

**e[sup]***j*π[/sup] + 1 = 0

Exponental series:

*e*[sup]x[/sup] = 1 + x/1! + x[sup]2[/sup]/2! + x[sup]2[/sup]/3! + . . .

Maclaurin Expansion:

**f(x) = f(0) + x f’(0)/1! + x[sup]2[/sup] f’’(0)/2! + x[sup]3[/sup] f’’’(x)/3! + . . .**

The sine and cosine series[sup]1[/sup]:

**sin x = x - x[sup]3[/sup]/3! + x[sup]5[/sup]/5! - x[sup]7[/sup]/7! + . . .**

and

**cos x = 1 - x[sup]2[/sup]/2! + x[sup]4[/sup]/4! - x[sup]6[/sup]/6! + . . .**

ODE for 1D linear damped vibrations:

**d[sup]2[/sup]y/dx[sup]2[/sup] + 2b dy/dx + a[sup]2[/sup]y = 0 **

and its associated solutions. (Like I’ll ever use that again, but after three courses of linear systems/vibrations/classical controls it won’t go away. :rolleyes: )

The Laplace Integral:

**L[f(t)] = int(0, inf) e[sup]-st[/sup]f(t) dt** (too lazy to figure out the coding for the integral sign, and vCode doesn’t like the infinity symbol, I guess.)

and more mundane,

Moment of Inertia for a rectangle:

**I[sub]x[/sub] = ab[sup]3[/sup]/12**

The Parallel Axis Theorem:

**I[sub]x[/sub] = I[sub]0[/sub] + x[sub]0[/sub][sup]2[/sup]m**

Stress Due to Bending (Outer Fiber):

**σ[sub]x[/sub] = M[sub]x[/sub]b/I[sub]x[/sub]**

Period of a Simple Pendulum:

**τ = 2π √(l/g)**

Bernoulli’s Equation:

**p[sub]1[/sub]/γ + V[sub]1[/sub][sup]2[/sup]/2g + z[sub]1[/sub] = p[sub]2[/sub]/γ + V[sub]2[/sub][sup]2[/sup]/2g + z[sub]2[/sub]**

and the always useful Ideal Gas Equation:

**PV = nRT**

I’d slap down Maxwell’s equations and the Lorentz transformations too, but…meh. Enough intellectual boasting for one day. It doesn’t bring in the chicks.

Sadly, except for the rectangular moment of inertia formula and bending/shear stress, this is the only place I’ve ever had to use any of these equations in my post-collegate career. Why, exactly, did I leave school? :dubious:

Stranger

- Okay, I checked these to make sure I got them right…but I did.