Derive the equation of the line through the points (α, a) and (β, b) in the τt plane that are shown in Fig. 37. Then use it to find the linear function φ(τ) which can be used in equation (9), Sec. 39, to transform representation (2) in that section into representation (10) there.
(9)
t = φ(Ï„ ) (α ‰¤ Ï„ ‰¤ β),
where φ is a real-valued function mapping an interval α ‰¤ Ï„ ‰¤ β onto the interval a ‰¤ t ‰¤ b in representation (2). (See Fig. 37.) We assume that φ is continuous with

a continuous derivative. We also assume that φ'(τ) > 0 for each τ; this ensures that t increases with τ. Representation (2) is then transformed by equation (9) into
(10)
z = Z(Ï„) (α ‰¤ Ï„ ‰¤ β),

Transcribed Image Text:

아-1(x, a) 이