For each numerical value of v, one can calculate a pair of numerical values of g − f 0( T) and p, and ultimately construct a graph of g versus p, such as shown in Figure 9–7a. This can be done by assigning a fixed value to T and then allowing v to range through a set of numerical values. ( 9.30) and ( 9.2) to be a parametric representation 3 of g( T, p), with v as a parameter. A much more useful procedure is to regard Eqs.

This would result in unwieldy expressions for g whose functional behavior would not be easy to analyze. ( 9.3), one would have to write analytical expressions for its three roots by using the cubic formula and then substitute into Eq. Equation ( 9.2) for p could be solved for v( p). Equation ( 9.30) gives g as a function of T and v, but this is not very useful information because the equilibrium criterion for g is that it be a minimum for given values of T and p.

Writing first ∣ z 2 - 1 ∣ 2 = ( z 2 - 1 ) ( z ∗ 2 - 1 ) = s 2 and inserting z = x + iy, we reach Numsol = NDSolve Ī more involved example is to plot the curves identifying the values of x and y that satisfy the equation ∣ z 2 - 1 ∣ = s, where s is a positive-valued parameter.

Plots of solutions of Van der Pol's equation for various values of μ.

Parametricplot mathematica