Physics

Module 1: Mathematical Foundations  ·  Theory  ·  assumes Foundations 7 and 8 Adding up what changes continuously — and discovering that this is differentiation run backwards. Mahavakya To add up something that never holds still, cut it into pieces so small that on each one it does. On this page Slicing, and the Riemann sum … Read more

Module 1: Mathematical Foundations  ·  Theory  ·  assumes Foundations 3 and 7 Computing what Foundation 7 taught you to see — the exact rate of change at a single instant. Mahavakya A derivative is a rate measured over no interval at all. Nothing changes in an instant — and yet the change at that instant … Read more

Module 1: Mathematical Foundations  ·  Theory  ·  assumes Foundation 1 Learning to read a curve — before learning to compute on one. Mahavakya A graph is not a picture of a formula. It is the whole behaviour of a system, laid out where the eye can take it in at once. On this page What … Read more

Module 1: Mathematical Foundations  ·  Theory  ·  assumes Foundation 5 The second way to multiply two vectors — and the one that gives rotation something to point at. Mahavakya The cross product points somewhere no vector needs to point. We agree on which way — and physics works because we all agree. On this page … Read more

Module 1: Mathematical Foundations  ·  Theory  ·  assumes Foundation 4 The first way to multiply two vectors — and the one that turns geometry into energy. Mahavakya The dot product asks one question of two vectors: how much of one lies along the other? Everything else it does follows from that. On this page The … Read more

Module 1: Mathematical Foundations  ·  Theory  ·  assumes Foundation 3 Combining vectors, and taking them apart — from geometric construction to arithmetic you can trust under exam pressure. Mahavakya Vectors do not add like numbers, because direction is not a label attached to the quantity — it is part of the quantity itself. On this … Read more

Module 1: Mathematical Foundations  ·  Theory  ·  assumes Foundation 2 Mapping space into numbers — and why the grid you choose decides how hard the mathematics will be. Mahavakya A coordinate system is not part of the physical world; it is part of the physicist’s method of seeing it. Good representation does not change nature … Read more

Module 1: Mathematical Foundations  ·  Theory  ·  assumes Foundation 1 The building blocks of physical quantities — why some measurements need a direction and some do not. Mahavakya Every physical quantity carries either magnitude alone or magnitude with direction; this quiet distinction shapes the entire structure of mechanics. On this page The quiet distinction Scalars: … Read more

Module 1: Mathematical Foundations  ·  Orientation  ·  no prerequisites Why physics reaches for mathematics at all — and what an equation is actually doing when it describes the world. Mahavakya Nature behaves without mathematics; physics uses mathematics to represent the regularities we observe in nature. On this page Describing motion without mathematics Why mathematics becomes … Read more