# Boundary Value Problems/Lesson 5.2

1. Title: One 1D heat equation with several boundary conditions
2. Objectives: Specifically what is to be retained by the learner.
1. Setup of heat equation
2. Solution of heat equation with homogeneous/nonhomogeneous Dirichlet, Neumann and mixed boudary conditions.
3. Activities: Content directed at the learner to achieve learning objectives.
1. Solve specific homework prooblems.
4. Assessment: Determine lesson effectiveness in achieving the learning Objectives.
1. Homework and quizzes

## Background

### The derivation of the Heat Equation

Heat Flow: Fourier's Law

What is heat? Heat is a form of energy that is measured in units of degree Celsius .

For a gas this measure is the average kinetic energy  $m|v|^{2}/2$ of the molecules in the gas.

For a solid heat is associated with vibrational energy of the crystalline structure.
Heat is measured by us in units of degrees, these are related to calories by the definition, one calorie is the amount of heat required to increase the temperature of one gram of water(at one atmosphere of pressure) by one degree Celsius.