An exact expression is obtained for the acoustic-gravity layer matrix for an atmospheric layer having a linear temperature variation. Expressions are also derived for the layer derivative matrices needed to calculate group velocity and mode excitation. The method requires the evaluation of confluent hypergeometric functions, whose series representations are rapidly convergent for layers, such as the lower thermosphere, which have large temperature gradients. The procedure allows rapid accurate calculations in studies of acoustic gravity wave propagation. The new procedure is used to calculate phase and group velocities for the GR_o mode at periods between 5 and 12 min and gives a change in these velocities of 0.3 per cent as compared with Press and Harkrider's results
