These short films connect numerical formulas with the areas, lines, and decisions they represent. Each viewing page includes a question to consider before playing, the key mathematics, and links to the lecture and full reading.
Choose a method, pause at a decision, and explain the next step before continuing. These are review resources, not an additional assignment.
Block 2 · Quadrature¶
| Animation | What to follow |
|---|---|
| Left rectangles | Accumulate areas; derive first-order composite error. |
| Trapezoids | Integrate endpoint chords; compare Taylor coefficients. |
| Simpson’s rule | Integrate quadratic pairs; use symmetry to explain fourth order. |
| Adaptive Simpson quadrature | Split error budgets; combine accepted contributions. |
Block 3 · Root Finding¶
| Animation | What to follow |
|---|---|
| Bisection | Retain a bracket; connect width to root error. |
| Newton’s method | Find a tangent zero; rebuild the tangent on the curve. |
| The secant method | Reuse two values; track which point is replaced. |
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