# Boundary Value Problems/Lesson 1

## Title: Conservation of mass and flux modeling.

### Objectives

1. Develop the student's ability to create qualitative elemental model of mass flow process that will allow extrapolation to heat flow process.

### Methods

1. Reading material on development of flux model based on conservatio of mass.
1. Consider modeling the movement of a small quantity of material ${\displaystyle \delta M}$ through a incremental surface,${\displaystyle \delta \Omega }$ within a unit of time.
2. Have student(s) post elemental models using online simulation package.
3. Provide examples of modeling heat flow.

### Assessment

1. Provide feedback on a student's mode: critique by "experts", comments by other students, providing student with a document that shows them how to determine the validity of their model, a self grading checklist.
2. Multipe choice or short answer Quizzes

Our goal is to understand Partial Derivatives and equations that are composed of terms that include PD's. Such equations are called Partial Differential Equations or PDEs. More specifically, our interest is to solve PDEs , that is find a function ${\displaystyle f(x,y)}$ such that
${\displaystyle a_{1}(x,y){\frac {\partial ^{2}f}{\partial x^{2}}}+a_{2}(x,y){\frac {\partial ^{2}f}{\partial x\partial y}}+a_{3}(x,y){\frac {\partial ^{2}f}{\partial y^{2}}}+a_{4}(x,y){\frac {\partial f}{\partial x}}+a_{5}(x,y){\frac {\partial f}{\partial y}}+a_{6}(x,y)f+a_{7}(x,y)=0}$