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Computer science instructors frequently teach using slides displayed with a computer and a data projector. This has many advantages, e.g., ability to present prepared materials and ease of switching the display to a development environment during midpresentation. However, existing computer-based presentation systems severely limit flexibility in delivery, hindering instructors' extemporaneous adaptation of their presentations to match their audiences. One major limitation of computer-based systems is lack of support for high-quality handwriting over slides, as with overhead projectors and other manual presentation systems. We developed and deployed Classroom Presenter, a Tablet PC-based presentation system that (1) combines the advantages of existing computer-based and manual presentation systems and (2) builds on these systems, introducing novel affordances. Classroom Presenter has been used in 25 Computer Science courses at three universities. In this paper we describe the system, summarize results from its deployment, and detail several novel uses of the system by instructors in computer science courses.

Applying the systematic method discussed in previous papers, we derive the invariants and the groups of the time-dependent Schrödinger equations for the rigid rotator and the symmetric top. The groups for these systems are found to be SO(3,2) (rigid rotator) and SU(2,2) (symmetric top). For the case of the symmetric top, it is found that under the symmetry breaking I1 = I2 = I3 → I1 = I2 ≠ I3, where I1, I2, and I3 are the moments of inertia of the top, two of the time-independent constants of the motion become time-dependent constants of the motion.

A superposition rule is obtained for the matrix Riccati equation (MRE) Ẇ=A+WB+CW+WDW [where W(t), A(t), B(t), C(t), and D(t) are real n×n matrices], expressing the general solution in terms of five known solutions for all n≥2. The symplectic MRE (W=WT, A=AT, D=DT, C=BT) is treated separately, and a superposition rule is derived involving only four known solutions. For the ‘‘unitary’’ and GL(n,R) subcases (with D=A and C=BT, or D=−A and C=BT, respectively), superposition rules are obtained involving only two solutions. The derivation of these results is based upon an interpretation of the MRE in terms of the action of the groups SL(2n,R), SP(2n,R), U(n), and GL(n,R) on the Grassman manifold Gn(R2n).

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