CALCULUS-BASED PHYSICS / 120 WORKED CHAPTERS
Start with an observable event, choose the smallest model that could explain it, derive the equation, and test its prediction against units, limits, and numbers.
THE THROUGH-LINE
Velocity is the derivative of position; acceleration is the derivative of velocity; force is the momentum change that produces acceleration. The same discipline scales up: fluid pressure gradients and viscous stresses enter a momentum balance, and the Navier–Stokes equation is what remains after the terms are named. Each chapter makes one such move, calculates a number, and asks where the approximation breaks.
Describe motion cleanly before explaining it.
Explain motion through interaction.
Find conservation laws that survive complicated motion.
Open course brief →Move from particles to bodies with shape.
Understand repeating motion and transported patterns.
Make temperature, heat, and irreversibility quantitative.
Add fields, circuits, and electromagnetic energy.
Acquire the language that fields and fluids require.
Treat matter as a field of material points.
Close the loop with flowing matter.
THE WORKING HABIT
A force on a cart, a pressure on a pipe section, and an energy transfer across a pump boundary are different statements. Draw the boundary before writing symbols.
For example, v = √(2gH) comes from trading gravitational potential energy for kinetic energy after pressure and loss terms are removed; it is not a universal nozzle law.
Check units, zero and extreme limits, and one measured scale. A result that cannot survive those tests is not yet physics, however elegant the algebra.