MATH221 · Annotated SlidesChapter 3 — Divided Differences
Chapter 3 · Annotated slides

Divided Differences

Newton's divided differences, the divided-difference table, and Newton's forward- and backward-difference formulas.

Slide text Study notes Highlight: key words Tips, tricks & traps Seen again elsewhere How it can come up
Slide 1: Slide 1
Exam weight Low
    Slide 2: Divided Differences
    Exam weight High
    1. f[xᵢ, xᵢ₊₁] = (f[xᵢ₊₁] − f[xᵢ])/(xᵢ₊₁ − xᵢ), and so on. Pₙ(x) = f[x₀] + f[x₀, x₁](x − x₀) + f[x₀, x₁, x₂](x − x₀)(x − x₁) + …
    Memory trickAdding a new point only adds one new term: no need to start over (unlike Lagrange).
    🎯 How this can come up · 1 question
    MCQ

    With f(1) = 2, f(2) = 5, the first divided difference f[1, 2] is:

    Slide 3: Slide 3
    Exam weight Low
      Slide 4: Newton’s Forward Differences
      Exam weight Low
      1. Equally spaced nodes: forward differences Δ and the binomial-coefficient form.
      Slide 5: Slide 5
      Exam weight Low
        Slide 6: Slide 6
        Exam weight Low
          Slide 7: Slide 7
          Exam weight Low
            Slide 8: Slide 8
            Exam weight Low