1. MAT 3724 Applied Analysis I 1.0 Review http://myhome.spu.edu/lauw

2. Teams AinsleyHiegel 1.3 AdamHanson 1.6+2.3 AloraBourbonnie EllenKimLisaGoodhewNathanaelSleight TaraWalkerRachelMurphyKristianRubesh 1.5 HannahJudd 1.8 KathrynYancey 1.9 RobertRendleTaylorElzinga SalvadorEng DengShelbieDavis PaulSchale1.7EveranChaffee 1.4 JoshTjelleJameyFrykholm PatrickMaguireRyanSalgado

3. HW Download HW 1.0

4. Preview Integrating Factor (Linear First Order ODE) Multivariable Chain Rule Be sure to pay attention to expected presentation.

5. ODE, PDE Ordinary Differential Equations Partial Differential Equations

6. Linear (First Order) D.E. Technique: Multiply both side by the integrating factor

7. Example 1

8. Verify is the general solutions Verify…

9. Expectations When there are two groups of related calculations, do not mix them up.

10. Two-Column Format Integration by parts, substitutions, partial fractions, …

11. Example 2 **Reminder: Tell Wai to specify the interval at the end. He usually does not remember. You can take one point off from him. Ha, ha!

12. Remarks

13. The Chain Rule

14. The Chain Rule: Case 1

15. Example 3 Find

16. The Chain Rule: Case 2

17. Example 4 Find

18. Other Cases Similar

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

20. 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.

21. Example 6 Find all the u(x,t) such that