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A quantity a is said to be less than b if a is smaller than b, written a<b. If a is less than or equal to b, the relationship is written a<=b. In the Wolfram Language, this ...

A level set in three dimensions.

The ordinary differential equation y^('')+(1-|y|)y^'+y=0.

The second-order ordinary differential equation y^('')+f(x)y^'+y=0.

Let suma_k and sumb_k be two series with positive terms and suppose lim_(k->infty)(a_k)/(b_k)=rho. If rho is finite and rho>0, then the two series both converge or diverge.

A linear approximation to a function f(x) at a point x_0 can be computed by taking the first term in the Taylor series f(x_0+Deltax)=f(x_0)+f^'(x_0)Deltax+....

product_(i)dp_idq_i, where p_i and q_i are momenta and positions of particles.

Let F be a differential field with constant field K. For f in F, suppose that the equation g^'=f (i.e., g=intf) has a solution g in G, where G is an elementary extension of F ...

A function f(x) satisfies the Lipschitz condition of order beta at x=0 if |f(h)-f(0)|<=B|h|^beta for all |h|<epsilon, where B and beta are independent of h, beta>0, and alpha ...

A function f such that |f(x)-f(y)|<=C|x-y| for all x and y, where C is a constant independent of x and y, is called a Lipschitz function. For example, any function with a ...