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formula-sheets's Issues

MECH 360: Neutral Axis

Need a formula for retrieving the neutral axis of a cross-section of a beam composed of rectangular shapes.

You can find the formula in the lecture from Oct 9.

MATH 217 spacing

In the section about the second derivative test, a space is missing between "fxx < 0" and "or" (line 171 in tex source).

image

PHYS 350: Typo in E-L Equation and Energy Expression

In the formula sheet, there are total derivatives in the Euler-Lagrangian Equation for d/dq_dot and d/dq. These should be partials.

The expression for calculating energy under Conservation of Energy should be q_dot (dL/dq_dot) - L rather than q (dL/dq) - L.

PHYS 401 Law of Reflection

Hi, I think the law of refraction on the PHYS 401 sheet page 1 should actually be the law of reflection.

Typo in ELEC 221 - Z-Transform Properties

Under "Time Shifting (acausal)" (Line 299), a negative sign is missing before the first ^N.

Should be: Time Shifting (acausal) & $x[n-N]$ & $z^-NX(z) + x[-1]z^{-N + 1}$\\

PHYS 301: Dipole Moment

In the equation for dipole moment of a charge distribution, the $d\tau$ should be $d\tau'$.

PHYS 301: Multipole Expansion

Need the following formulas (especially after the midterm):

  • Equation of a electric dipole (summation)
  • Voltage of an electric monopole
  • Voltage of an physical electric dipole
  • Binomial theorem

PHYS 301: Vector Potential

For the magnetic vector potential equation, the assumption should be $\mathbf J\to\mathbf 0$ instead of $\mathbf A\to\mathbf 0$ at infinity.

In the equation written beneath that, $d\tau$ should be $d\tau'$.

PHYS 301: Poisson's Equation

In the PHYS 301 formula sheet, Poisson's equation is missing a negative sign.

image

The right hand side should be $-\rho/\epsilon_0$.

PHYS 301: Magnetic Dipole Moment

In the equation for magnetic dipole moment, the integral should be $\displaystyle\int d\mathbf a$ instead of $\displaystyle\int d\mathbf A$.

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