In this unit, you will explore the most common partial differential equations that arise in physics contexts. You will learn the separation of variables procedure to solve these equations.
Motivating Questions
- How are partial differential equations (PDEs) different from ordinary differential equations (ODEs)?
- What new kinds of physics can we learn from solving partial differential equations?
- What can we learn about physics and geometry from the separation of variables procedure?
Key Activities/Problems
Unit Learning Outcomes
At the end of this unit, you should be able to:
- Identify and classify several common PDEs.
- Identify the number and types of boundary and initial conditions that are appropriate to different PDEs.
- Identify the conditions where the separation of variables is appropriate and useful.
- Solve simple partial differential equations through the separation of variables procedure.