A dark-mode interactive Shiny app built from recurring concepts in six ENGI-3022 final exams (2020-2025).

The app includes:

• Laplace transform explorer, property lab, and engineering applications
• Differential-equation characteristic-root and phase-portrait labs
• Linear-system lab and a concept-first eigenvalue pattern decoder with transformed-circle and camera-controlled 3D sphere simulations, stable eigen-directions, live matrices/equations, presets, and prediction checks
• A frontier-inspired rocket stability lab that connects eigenvalues to low-gravity propellant slosh, control lag, orbital refueling, and a live five-state disturbance simulation
• A three-mission Rocket Balancer mini game with a live one-tick pattern coach, ASCII concept diagrams, fully disclosed rules/scoring, named player runs, mastery scoring, and a persistent top-10 leaderboard
• Widescreen learning cockpits that align related plots side by side while automatically stacking them on tablets and phones
• Friendly shareable URLs for every main page and important subpage, with browser Back/Forward restoration
• Exam coverage map with matrix-size frequencies, difficulty proxies, efficiency stop rules, a study-time allocator, and a practice generator
• Five 50-mark mock finals with verified answers, displayed algebra, and tutorial matches
• A community feedback board with handles, ratings, comment history, and a live-session count

install.packages(c("shiny", "plotly"))
shiny::runApp()

The app uses base R plotting for most labs and Plotly for the interactive eigenvalue and rocket-stability cockpits.

Append a friendly query route to the deployed app URL. Examples:

• ?page=exam-practice&section=mock-exam
• ?page=linear-algebra&section=eigenvalues
• ?page=linear-algebra&section=rocket-balancer
• ?page=laplace&section=engineering&example=chemical-mixing
• ?page=formula-library&section=method-selector

The address bar updates as the user changes pages, and browser Back/Forward restores the matching main page, subpage, and engineering example.

The community board stores comments in community-data/comments.rds when the host permits file writes. Rocket Balancer stores its scores beside it in community-data/rocket_scores.rds. Set FINALPREP_COMMENT_DIR to a persistent writable directory in production. If persistent storage is unavailable, the app falls back safely and explains that community data may reset after a restart or redeploy.