MAT 3724 Applied Analysis I 1.2 Part I Conservation Laws

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Presentation transcript:

MAT 3724 Applied Analysis I 1.2 Part I Conservation Laws

HW Download HW 02 HW 02 may not have direct relation with section1.2 part I Review today’s lecture after class!

Preview Fundamental Conservation Law

A Source of PDE Many PDE come from a basic balance law/conservation law. We are going to look at a very simple case.

General Idea Quantity of something … e.g

Review: Riemann Sum i th subinterval sample point

Review: Riemann Sum

One Dimension Conservation Law: Set Up

Total Quantity from x=a to x=b

Rate In and Rate Out

Rate Created / Destroyed

Fundamental Conservation Law

PDE model

Challenge

Review: Fundamental Theorem of Calculus Need this for the HW. Example and Expectations