MATH221 · Chapter 3 · Annotated SlidesDivided Differences
Original
Overview

Divided Differences

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

How to read this page

Every original slide is shown unchanged. Yellow marks on a slide point to a numbered note: hover or tap a mark to jump to its note, and hover a note to see its marks. Questions tagged Past exam appeared on a real paper; Prediction questions are likely angles, not confirmed. Pick an answer to each question: a wrong pick tells you why it is wrong, so you can try again.

All 8 slides
  1. 1 Slide 1
  2. 2 Divided Differences
  3. 3 Slide 3
  4. 4 Newton’s Forward Differences
  5. 5 Solve Q1 & 2 using Divided Difference Rule
  6. 6 Slide 6
  7. 7 Slide 7
  8. 8 Slide 8
Slide 1 / 8

Slide 1

Slide 1: Slide 1
Slide 2 / 8

Divided Differences

Slide 2: Divided Differences

Notes

  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) + …

  2. Memory trick Adding a new point only adds one new term: no need to start over (unlike Lagrange).

Exam angle

PredictionQ1

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

Slide 3 / 8

Slide 3

Slide 3: Slide 3
Slide 4 / 8

Newton’s Forward Differences

Slide 4: Newton’s Forward Differences

Notes

  1. Equally spaced nodes: forward differences Δ and the binomial-coefficient form.

Slide 5 / 8

Solve Q1 & 2 using Divided Difference Rule

Slide 5: Solve Q1 & 2 using Divided Difference Rule
Slide 6 / 8

Slide 6

Slide 6: Slide 6
Slide 7 / 8

Slide 7

Slide 7: Slide 7
Slide 8 / 8

Slide 8

Slide 8: Slide 8