1. 2.2 Cauchy Problem for the Wave Equation
MAT 3724 Applied Analysis I
2.2 Cauchy Problem for the Wave Equation

2. Wave Equation: Set Up
Assumptions:

3. Cauchy Problem

4. Thought Experiment
What would you expect to happen?

5. Thought Experiment

6. Thought Experiment

7. Modeling Wave Propagation in a String

8. Modeling Wave Propagation in a String

9. Compare with Advection
What are the differences?
What are the similarities?
What thing do you think we can mimic from the advection equation when solving the wave equation?

10. Solve the Wave Equation…
…without the initial conditions

11. Solve the Wave Equation…
…without the initial conditions

12. Solution: d’Alembert’s Formula

13. Classwork Verify d’Alembert’s Formula
Show that it satisfy the wave equation (2.12) and the initial conditions (2.13)