Differential Operators and the Elimination Method for Systems

Differential Operators and the Elimination Method for SystemsExpected Educational ResultsDifferential OperatorsProperties of Linear Differential OperatorsInvestigation 10Investigation 11AnnihilatorsDefinition: Annihilator, Forms of AnnihilatorsCC BY-NC-SA 4.0

Author: John J Weber III, PhD Corresponding Textbook Sections:

Expected Educational Results

Differential Operators

Properties of Linear Differential Operators

Let , , , be polynomial differential operators; and be sufficiently differentiable functions of ; and constants.

Investigation 10

Prove any property of linear differential operators.

Investigation 11

  1. Show is equivalent to .
  2. Show is equivalent to .
  3. Show is not equivalent to .

Annihilators

Definition: Annihilator,

A linear differential operator, is said to annihilate a function if for all .

Forms of Annihilators

Note: You do not to memorize all of the above . How can you succinctly remember the forms for each ?

CC BY-NC-SA 4.0

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

Last Modified: Monday, 19 October 2020 8:23 EDT