  The purpose of this paper is to explore how accretion discs manifest the
phenomenon of transient growth on a global scale. We investigate analytically
the time response of a thin accretion disc to particular axisymmetric
perturbations. To facilitate an analytical treatment we replace the energy
equation with a general polytropic assumption. The asymptotic expansion of
Klu\'zniak & Kita (2000), which extended the method of Regev (1983) to a full
steady polytropic disc (with $n=3/2$), is further developed and implemented for
both the steady (for any polytropic index) and time-dependent problems. The
spatial form and temporal behaviour of selected dynamical disturbances are
studied in detail. We identify the perturbation space which leads to transient
growth and provide analytical solutions which manifest this expected transient
growth behaviour. Three terms (physical causes) responsible for the appearance
of transient growth are identified. Two depend explicitly on the viscosity
while the third one is relevant also for inviscid discs. The main conclusion we
draw is that the phenomenon of transient growth exists in discs on a global
scale.
