## Tuesday, July 31, 2018

### MAT225 Multivariable Calculus The Great Theorems! (SSII 2018 - WEEK04)

MAT225 Multivariable Calculus
The Great Theorems!
(SSII 2018 - WEEK04)

Week04 started with Line Integrals in the plane to calculate Work and Flux. We practiced Double and Triple Integrals as well as Surface Integrals and Flux Integrals in Space.

We reviewed the Fundamental Theorem for Line Integrals then we discovered Green's Theorem for Work in the Plane, Stokes' Theorem for Work in Space and the Diveregence Theorem for Flux in Space.

Actually, we saw both forms of Green's Theorem. The other regards Flux Integrals in the Plane aka Green's Theorem in Normal Form.

We talked about the Divergence Theorem as an experimental result when Gauss was studying Electric Fields so this theorem is also called the Gauss-Green Theorem and leads to Gauss' Law. We finished with a discussion of Maxwell's Equations and how they relate to Gradient Fields as well as the Divergence and Curl of a Vector Field.

We finished the course this week by not testing on Thursday. So, this is our last blog post for the class.

Week05 is all about review and testing. I hope you learned a lot! Have a great rest of the summer!

SageCells (401) Week04 Day01
Green's Theorem for Work
More Green's Theorem
Green's Applications
Green's & Flux

SageCells (402) Week04 Day02
Triple Integrals
More Triple Integrals
Cylindrical Coordinates
Flux in Space

SageCells (403) Week04 Day03
Surface Integrals
Divergence Theorem
More Divergence Theorem
Diffussion & LaPlace
Line Integrals in Space

Filks: Science!

Documentaries!

RECOMMENDED AP CALCULUS REVIEW:
CRIB SHEET (not given during exam)
REVIEW BARRONS BOOK
REVIEW BARRONS ONLINE
REVIEW DELTAMATH AB CALC FLASH CARDS
REVIEW APCENTRAL (lastest BC FRQs)
REVIEW APCENTRAL (older AB FRQs)
REVIEW APCENTRAL (older BC FRQs)
REVIEW EDX MOOC01
REVIEW EDX MOOC02
REVIEW COURSERA MOOC03

XTRA CREDIT FILKS RUBRIC:
1) Use a recognizable tune.
2) Karaoke the whole song,
2) changing up the words (STEM).
3) You are in the whole video,
3) Singing, Dancing or Playing an instrument.
4) providing me with the url.
5) YouTube Description includes the lyrics.

XTRA CREDIT UP T0 5 ARTICLES RUBRIC:
1) Cover Sheet is a Summary of the article.
2) Full Page, 12 pt Font,
2) Double Spaced, 1" Margins.
3) Article has to be STEM related
4) Article has to be a current event.
5) Copy of entire article is attached.

Well, that's all folks!
Teaching with Technology,
AJG
A. Jorge Garcia

Applied Math, Physics & CompSci