The transformation applied to the lower curve \(y = \\cos \\theta\) to obtain the upper curve involves both a vertical stretch and a horizontal stretch.

The vertical stretch is by a factor of 2, and the horizontal stretch is by a factor of 2, which affects the period of the cosine function. Additionally, there is a vertical translation upwards by 3 units.

Thus, the equation of the upper curve is:

\(y = 3 + 2 \cos \left( \frac{1}{2} \theta \right)\)