Compressible flow problems are characterized by highly nonlinear, implicit, and often transcendental governing equations. In undergraduate gas dynamics education, solving these equations traditionally relies on iterative numerical methods or extensive look-up tables, which can obscure the physical intuition of the solution space. This paper introduces a comprehensive framework using Deep Learning (DL) to generate high-fidelity surrogate models for five canonical problems: Rayleigh flow, Fanno flow, oblique shocks, convergent-divergent nozzles, and unsteady shock tubes. We detail the specific neural network architectures and physics-informed feature engineering strategies required for each problem, such as using logarithmic inputs for Fanno friction parameters or geometric anchors for oblique shocks. The resulting models achieve high accuracy (< 1% error) and enable instantaneous visualization of complex design spaces, such as thermodynamic T −s diagrams and unsteady x−t wave interactions. This approach demonstrates how modern data-driven techniques can be integrated into the physics curriculum to enhance conceptual understanding.