1 / 19

MAT 3724 Applied Analysis I

MAT 3724 Applied Analysis I. 2.1 Part I Cauchy Problem for the Heat Equation. http://myhome.spu.edu/lauw. Chapter 2. PDE on Unbounded Region In one dimension, it is the real line Easier to solve than bounded region. Preview. Initial Value Problem with the Heat equation

ona
Télécharger la présentation

MAT 3724 Applied Analysis I

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MAT 3724Applied Analysis I 2.1 Part ICauchy Problem for the Heat Equation http://myhome.spu.edu/lauw

  2. Chapter 2 • PDE on Unbounded Region • In one dimension, it is the real line • Easier to solve than bounded region

  3. Preview • Initial Value Problem with the Heat equation • Introduce Dimensional Analysis

  4. Cauchy Problem for the Heat Equation • Note the change of notations (u instead of q)

  5. Set Up Lateral side insulated Initially, the temp. distribution is given by ____

  6. Example 1

  7. Example 1:Thought Experiment Scenario 1Scenario 2

  8. Example 1:Thought Experiment What would happen to w(x,t) as the time moves on?

  9. Example 1: Simplification

  10. Example 1: Simplification

  11. Interpretations of HW 05 Problem 2 • The PDE model and inequality below appear in the last HW

  12. Interpretations of HW 05 Problem 2 • Even though the set ups are not exactly the same, some calculations with this example may help us to understand what the inequality means.

  13. Interpretations of HW 05 Problem 2

  14. Interpretations of HW 05 Problem 2

  15. Example 1 Solution Method: • Dimensional Analysis (units) • Guessing

  16. Inspirations

  17. Inspirations If we can find___________________, then we can recover_____________________.

  18. Example 1 If we can find_________________________, then we can recover_____________________.

  19. Notations Relaxation for Improper Integrals • Provided that you understand the correct concepts, you are allow to use less rigorous notations. Here is an illustration.

More Related