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h_t+(|h|^nh_(xxx))_x=0, where h(x,t) is the height of a film at position x and time t and n is a parameter characteristic of the surface forces.

∡A_2MA_3=∡A_2A_1A_3+∡P_2P_1P_3, where ∡ is a directed angle.

The system of partial differential equations U_t = [V,W] (1) V_t = [W,U] (2) W_t = [U,V], (3) where [A,B] denotes the commutator.

The simple first-order difference equation y_(t+1)-Ay_t=B, (1) where A = -(m_s)/(m_d) (2) B = (b_d-b_s)/(m_d) (3) and D_t = -m_dp_t+b_d (4) S_(t+1) = m_sp_t+b_s (5) are the ...

The twistor equation states that del _(A^')^((A)phi^(B...E))=0, where the parentheses denote symmetrization, in a Lorentz transformation, primed spinors transform under the ...

In toroidal coordinates, Laplace's equation becomes (1) Attempt separation of variables by plugging in the trial solution f(u,v,phi)=sqrt(coshu-cosv)U(u)V(v)Psi(psi), (2) ...

The Fredholm integral equation of the second kind f(x)=1+1/piint_(-1)^1(f(t))/((x-t)^2+1)dt that arises in electrostatics (Love 1949, Fox and Goodwin 1953, and Abbott 2002).

The so-called Malthusian equation is an antiquated term for the equation N(t)=N_0e^(lambdat) describing exponential growth. The constant lambda is sometimes called the ...

The Euler-Lagrange differential equation is the fundamental equation of calculus of variations. It states that if J is defined by an integral of the form J=intf(t,y,y^.)dt, ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...