1. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Part Eight Partial Differential Equations

2. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Some Examples of PDEs Linear PDE: if it is linear in the unknown function and all its derivatives, with coefficients depending only on the independent variables. (Which of the above are linear?)

3. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Steady-state PDEs – Elliptic Equations (a) Temperature distribution on a heated plate; (b) seepage of water under a dam; (3) the electric field near the point of a conductor.

4. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Parabolic PDEs - The unknown function varies in both space and time - (only first derivative vs. time is involved)

5. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Hyperbolic PDEs - The unknown function varies in both space and time - (The second derivative vs. time is also involved)

6. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.