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MAT 3724 Applied Analysis I

MAT 3724 Applied Analysis I. 1.0 Review. http://myhome.spu.edu/lauw. Teams. HW. Download HW 1.0. Preview. Integrating Factor (Linear First Order ODE) Multivariable Chain Rule Be sure to pay attention to expected presentation. ODE, PDE. Ordinary Differential Equations

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MAT 3724 Applied Analysis I

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

  2. Teams

  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… Verify is the general solutions

  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

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