Interdisciplinary Connections
The master bridge map. /process-lecture-notes cross-references student-noticed connections against this list and adds new ones. Hermes names these bridges in session when they appear. The Aristotle app surfaces them after every completed problem.
Bridges
Derivatives → instantaneous velocity
MATH 1A03 ↔ PHYSICS 1C03 — is the limit definition made physical. If limit-definition feels abstract, kinematics-with-calculus is its meaning.
Integration → work-energy theorem
MATH 1A03 ↔ PHYSICS 1C03 — . The definite integral as accumulated effect. antiderivatives ↔ work-energy-theorem.
Exponential functions → radioactive decay, rate laws
MATH 1A03 ↔ CHEM 1AA3 ↔ PHYSICS 1CC3 — one function, three costumes: , , attenuation (and MEDPHYS makes it four). All solutions of . nuclear-decay · reaction-kinetics · separable-odes.
Wave equations → atomic orbitals
PHYSICS 1C03 ↔ PHYSICS 1CC3 ↔ CHEM 1AA3 — standing waves on a string quantise frequencies; standing electron waves quantise energies. wave-properties → schrodinger-equation → orbital shapes behind chemical-bonding-vsepr.
Planck’s constant → photoelectric effect → periodic table trends
PHYSICS 1CC3 ↔ CHEM 1A03 — photon energy quantisation explains ionisation energies and why the periodic table has its shape. photoelectric-effect ↔ atomic-structure.
Boltzmann distribution → thermodynamic equilibrium → reaction rates
PHYSICS 1C03 ↔ CHEM 1AA3 — governs both: which states are occupied (thermodynamics) and which collisions clear the activation barrier (Arrhenius, reaction-kinetics).
Fourier analysis → spectroscopy
MATH 1AA3 ↔ CHEM 1AA3 ↔ PHYSICS 1CC3 — decomposing signals into frequencies is how instruments read molecular structure. taylor-series is the gateway; FT-IR and NMR are the payoff.
Differential equations → decay, circuits, oscillators
MATH 1AA3 ↔ PHYSICS 1C03 ↔ PHYSICS 1CC3 — and cover half of first-year physics. separable-odes · oscillations · nuclear-decay-physics.
Lorentz factor → nuclear binding energy
PHYSICS 1CC3 ↔ MEDPHYS 1A03 — is why mass defect equals binding energy, which is why radiation therapy works. mass-energy-equivalence ↔ radiation-therapy.
Inverse square law → gravity, electrostatics, radiation intensity
PHYSICS 1C03 ↔ MEDPHYS 1A03 ↔ ASTRON 1F03 — same geometry, three fields: , , (radiation safety, stellar brightness, distance-measurement).
Student-Noticed Bridges
Added by /process-lecture-notes from the “Connections I noticed” section of lecture captures.