WEEK04: The Great Theorems MAT225 SII 2022
Dear Students,
Congratulations! You did it! You made it through your fourth week of MAT225 Multivariate Calculus! We finished all our lectures on Chapters 13-16 Multivariable Calculus and Chapter 17 Vector Calculus. So, this will be our last post as next week is devoted to review and testing.
This week, we finished our coverage of chapter 17 on Vector Calculus.
On Monday, we learned how to use Green's Theorem For Work In The Plane (2D) to calculate line integrals measuring work done in a Vector Field. We then learned about Flux and Green's Theorem Normal Form.
Tuesday was devoted to Triple Integration and Surface Integrals.
So, on Wednesday we had all the building blocks to extend Green's Theorem Normal Form to measure Flux in Space (3D) with the Divergence Theorem. Here's a Divergence Theorem example.
Thursday was all about extending Green's Theorem For Work in the Plane to work with 3D Vector Fields using Stokes' Theorem. Here's an example of Stokes' Theorem.
We also talked about Maxwell's Equations!
When studying for next week's exams, please remember that our syllabus skips 16.7 in Briggs 3rd edition Change Of Variables For Multiple Integrals (Jacobian Discriminant). We also skipped Parametrically Defined Surfaces in Space. We only used Parametrically Defined Curves in the Plane.
Please see our BlackBoard site for screencasts, sample code and handwritten notes: 401-405.
This Week's Tom Lehrer FILKs & DOX:
Be well,
A. Jorge Garcia
Applied Math & CS
Nassau Community College
Well, that's all folks!
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