MATH221 · Chapter 4 · Annotated SlidesNumerical Differentiation
Original
Overview

Numerical Differentiation

Numerical differentiation: forward/backward differences, three- and five-point endpoint and midpoint formulas, and the second-derivative midpoint formula.

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 15 slides
  1. 1 Slide 1
  2. 2 Slide 2
  3. 3 Three-Point Endpoint Formula
  4. 4 Three-Point Midpoint Formula
  5. 5 Slide 5
  6. 6 Five-Point Midpoint Formula
  7. 7 Five-Point Endpoint Formula
  8. 8 Second Derivative Midpoint Formula
  9. 9 Slide 9
  10. 10 Slide 10
  11. 11 Exercise Set 4.1
  12. 12 Slide 12
  13. 13 Exercise Set 4.1
  14. 14 Exercise Set 4.1
  15. 15 Slide 15
Slide 1 / 15

Slide 1

Slide 1: Slide 1
Slide 2 / 15

Slide 2

Slide 2: Slide 2
Slide 3 / 15

Three-Point Endpoint Formula

Slide 3: Three-Point Endpoint Formula
Slide 4 / 15

Three-Point Midpoint Formula

Slide 4: Three-Point Midpoint Formula

Notes

  1. Three-point midpoint: f′(x₀) ≈ (f(x₀ + h) − f(x₀ − h))/(2h), error O(h²).

Exam angle

PredictionQ1

The three-point midpoint formula for f′(x₀) is:

Slide 5 / 15

Slide 5

Slide 5: Slide 5
Slide 6 / 15

Five-Point Midpoint Formula

Slide 6: Five-Point Midpoint Formula
Slide 7 / 15

Five-Point Endpoint Formula

Slide 7: Five-Point Endpoint Formula
Slide 8 / 15

Second Derivative Midpoint Formula

Slide 8: Second Derivative Midpoint Formula
Slide 9 / 15

Slide 9

Slide 9: Slide 9
Slide 10 / 15

Slide 10

Slide 10: Slide 10
Slide 11 / 15

Exercise Set 4.1

Slide 11: Exercise Set 4.1
Slide 12 / 15

Slide 12

Slide 12: Slide 12
Slide 13 / 15

Exercise Set 4.1

Slide 13: Exercise Set 4.1
Slide 14 / 15

Exercise Set 4.1

Slide 14: Exercise Set 4.1
Slide 15 / 15

Slide 15

Slide 15: Slide 15