1. MAT 1236 Calculus III Section 14.3 Partial Derivatives http://myhome.spu.edu/lauw

2. HW.. WebAssign 14.3 Quiz 14.2, 14.3 Exam 1….

3. Preview Discuss the definitions of derivatives of functions with 2 variables Discuss how the concept is the extension of the 1 variable case

4. 1 variable Vs 2 variables

5. Quotient Difference

7. Derivatives

8. Partial Derivatives

10. y is kept constant Partial Derivatives x is kept constant

11. For, we hold y constant For, we hold x constant How to find partial derivatives?

12. Example 1 Find

13. Example 1(a), (b)

14. Example 1(c), (d)

15. Example 2 Find

16. Example 2 (a)

17. Example 2 (b)

18. Example 3 (Implicit Diff.) Find z as a function in x and y

19. Higher Derivatives

20. 1 variable Vs 2 variables: Higher Derivatives

21. Second Order Derivatives

24. Clairaut’s Theorem

25. Example 4 Find all the second order derivatives

26. Geometric Meanings

28. Example 5 Show that is a solution of Laplace’s Equation

29. Expectations Always start with one side and show that it equals to the other side. Normally, it is easier to start with the side with more complicated terms.

30. Quiz Take a look at the solutions Think about the grader’s comments Do not (get emotional and blame the grader) Talk to me in my office when you are NOT emotional