1. Chapter 8 Partial Differential Equation

2. 8.1 Introduction Independent variables Formulation Boundary conditions Compounding & Method of Image Separation of variable Laplace transform

3. 8.3 Formulation Transport phenomena

4. 8.4 Boundary Conditions First type function specified Second type derivative specified IV,259 Third type Mixed Condition

5. 8.4 Boundary Conditions Integro-differential B.C.

6. 8.5 Particular Solution Skip

7. 8.5.2 Superposition Second order linear partial differential equation Is the solutions Is also the solution Infinite number of particular solutions can be added together to give a further solution

8. 8.6 Orthogonal functions The method of separation of variables gives the solution as sum of an infinite function. Are said to be orthogonal with respect to Over the interval from to if

9. Example 1

10. Sturm-Liouville Equation

11. Integrate over a b

12. If orthogonal

13. i ii iii

14. 8.7 Method of Separation of Variables

16. Eigen Super position Initial Condition

17. Orthogonal

20. Heat conduction in cylinder

23. Super position Eigen