MAT 3724 Applied Analysis I 1.0 Review

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Presentation transcript:

MAT 3724 Applied Analysis I 1.0 Review

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

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 Partial Differential Equations

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

Example 1

Verify is the general solutions Verify…

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

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

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!

Remarks

The Chain Rule

The Chain Rule: Case 1

Example 3 Find

The Chain Rule: Case 2

Example 4 Find

Other Cases Similar

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

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.

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