Thursday, July 27, 2023

WEEK04: The Great Theorems MAT225 SII 2023

   

(My AP Classroom running Linux from 1994-2018)

WEEK04: The Great Theorems MAT225 SII 2023

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 D2L site for screencasts, sample code and handwritten notes: 401-404.


This Week's Tom Lehrer FILKs & DOX:








Be well,

A. Jorge Garcia

Applied Math & CS

Nassau Community College


Well, that's all folks,

A. Jorge Garcia

Applied Math, Physics & CS

Nassau Community College

A. Jorge García

Applied Math, Physics, CS

Nassau Community College

http://shadowfaxrant.blogspot.com

http://www.youtube.com/calcpage2009


Computing Independent Study Facilitator (Baldwin High Retired)

Continental Mathematics League Advisor (Baldwin High Retired)

Baldwin High Chess Club & Chess Team Founder (US Chess Federation Club Baldwin High Retired)

National Computer Science Honor Society Advisor (Grace Hopper NY Chapter Baldwin High Retired)

2017 PAEMST NYS Mathematics Secondary Nominee https://www.paemst.org (Baldwin High Retired)


HTH & stay safe,

A. Jorge Garcia

Teaching With Technology:
Coding since 1975,
HS Math & Physics since 1984,
College Math & CompSci since 1993,
 Linux Clusters since 2002,
CAS since 2011,
Retirement since 2020?
 
AP Computer Science: 1988-2019
AP Calculus BC: 1993-2018 
Applied Math, Physics and CS

Please support my classroom:
www.patreon.com/calcpage2020

https://www.udemy.com/user/alvar-garcia-fernandez

calcpage.redbubble.com

society6.com/calcpage

https://www.ebay.com/usr/sffbclub  



2017 NYS Secondary Math PAEMST Nominee


pastebin youtube slideshare

(IDEs & Code)
MATH 4H, AP CALC, CSH: SAGECELL
APCSA: code.cs50.io
APCSA: replit.com
Jupyter: CoLab

(Curriculae)
CSH: CodeHS
CSH: Code.org
APCSA: Big Java
APCSA: CSAwesome
APCSA: AP Central

RECOMMENDED AP COMPSCI REVIEW:
CRIB SHEET (given during exam)
FREE TEXTBOOKS
REVIEW BARRONS ONLINE 
REVIEW APCENTRAL (past FRQs)
REVIEW EDX REVIEW MOOC01 
REVIEW UDEMY REVIEW MOOC02 
REVIEW CODING_BAT 
REVIEW PRACTICE_IT 
REVIEW RUNESTONE 
AUDIT CS50

RECOMMENDED AP CALCULUS REVIEW:
CRIB SHEET (not given during exam) 
FREE TEXTBOOKS
REVIEW BARRONS ONLINE 
REVIEW APCENTRAL (latest AB FRQs)
REVIEW APCENTRAL (latest BC FRQs)
REVIEW APCENTRAL (older AB FRQs)
REVIEW APCENTRAL (older BC FRQs)
REVIEW EDX MOOC01 
REVIEW COURSERA MOOC02

XTRA CREDIT FILKS RUBRIC 
(1 video = up to 5 bonus points):
1) Use a recognizable tune.
2) Karaoke entire song changing up the words (about STEAM).
3) You are Singing, Dancing or Playing an instrument.
4) You upload your video to YouTube and provide the url.
5) YouTube Description includes the lyrics.

XTRA CREDIT ARTICLES RUBRIC
(up to 5 articles = 1 bonus point each):
1) Cover Sheet is a Summary of the article.
2) FullPage, 12 pt, DoubleSpaced, 1" Margin.
3) Article has to be STEAM related
4) Article has to be a current event.
5) Copy of entire article is attached.

NOTE TO READER:
In recent years our independent study class has been about the care and feeding of Linux Clusters: How to Build A Cluster, How To Program A Cluster and What Can We Do With A Cluster? 

BTW, Shadowfax is the name of the cluster we build! FYI, we offer 4 computing courses: 

CSH: Computer Science Honors with an introduction to coding in Python using SAGE, IDLE, VIDLE and Trinket

CSA: AP Computer Science A using CS50, this IDE and this IDE and OpenProcessing

CSI: Computing Science Independent Study using OpenMPI and 

CSL: Computing Science Lab which is a co-requisite for Calculus students using Computer Algebra Systems such as SAGE.

====================
CIS(theta) aka CSI
Membership Hall Of Fame!

CIS(theta)* 2020-2021: 
DiegoM(12), GeordiP(12), MattB(12), MattO(12), MelanyeCG(12), NickE(12), WilliamF(12)
*Honorable Mention: I retired before we got to start our project this year...

CIS(theta) 2019-2020:
AaronH(12), AidanSB(12), JordanH(12), PeytonM(12)

CIS(theta) 2018-2019:
GaiusO(11), GiovanniA(12), JulianP(12), TosinA(12)

CIS(theta) 2017-2018:
BrandonB(12), FabbyF(12), JoehanA(12), RusselK(12)

CIS(theta) 2016-2017: 
DanielD(12), JevanyI(12), JuliaL(12), MichaelS(12), YaminiN(12)

CIS(theta) 2015-2016: 
BenR(11), BrandonL(12), DavidZ(12), GabeT(12), HarrisonD(11), HunterS(12), JacksonC(11), SafirT(12), TimL(12)

CIS(theta) 2014-2015: 
BryceB(12), CheyenneC(12), CliffordD(12), DanielP(12), DavidZ(12), GabeT(11), KeyhanV(11), NoelS(12), SafirT(11)

CIS(theta) 2013-2014: 
BryanS(12), CheyenneC(11), DanielG(12), HarineeN(12), RichardH(12), RyanW(12), TatianaR(12), TylerK(12)

CIS(theta) 2012-2013: 
Kyle Seipp(12)

CIS(theta) 2011-2012: 
Graham Smith(12), George Abreu(12), Kenny Krug(12), Lucas Eager-Leavitt(12)

CIS(theta) 2010-2011: 
David Gonzalez(12), Herbert Kwok(12), Jay Wong(12), Josh Granoff(12), Ryan Hothan(12)

CIS(theta) 2009-2010: 
Arthur Dysart(12), Devin Bramble(12), Jeremy Agostino(12), Steve Beller(12)

CIS(theta) 2008-2009: 
Marc Aldorasi(12), Mitchel Wong(12)

CIS(theta) 2007-2008: 
Chris Rai(12), Frank Kotarski(12), Nathaniel Roman(12)

CIS(theta) 1988-2007: 
A. Jorge Garcia, Gabriel Garcia, James McLurkin, Joe Bernstein, ... too many to mention here!
====================

Thursday, July 20, 2023

WEEK03: Iterated Integrals MAT225 SII 2023

  

(My AP Classroom running Linux from 1994-2018)

WEEK03: Iterated Integrals MAT225 SII 2023

Dear Students,

Congratulations! You did it! You made it through your third week of MAT225 Multivariate Calculus! 

We covered chapter 16 on Iterated Integrals and part of Chapter 17 on Line Integrals. We learned how to set up area, volume and mass problems as double integrals. We practiced working with different regions on the XY-plane using these area elements: dydx, dxdy and rdrd𝜭. We also worked with line integrals for calculating mass and work. Last, but not least, we played with conservative fields and the Fundamental Theorem of Line Integrals.

Oh, don't forget Fubini's Theorem!

Please see our D2L site for screencasts, sample code and handwritten notes: 301-303.

Today we are taking TEST3B. Please note there is no test next week (see syllabus). We will spend the whole week finishing up Chapter 17 dealing with line integrals in the plane and surface integrals in space as well as triple integration. We will learn: 

The 4 Great Theorems

Green's Theorem for Work

Green's Theorem for Flux

The Divergence Theorem

Stokes' Theorem

 

Elementary Calculus Review FILKs:




Be well,

A. Jorge Garcia

Applied Math & CS

Nassau Community College


Well, that's all folks,

A. Jorge Garcia

Applied Math, Physics & CS

Nassau Community College

A. Jorge García

Applied Math, Physics, CS

Nassau Community College

http://shadowfaxrant.blogspot.com

http://www.youtube.com/calcpage2009


Computing Independent Study Facilitator (Baldwin High Retired)

Continental Mathematics League Advisor (Baldwin High Retired)

Baldwin High Chess Club & Chess Team Founder (US Chess Federation Club Baldwin High Retired)

National Computer Science Honor Society Advisor (Grace Hopper NY Chapter Baldwin High Retired)

2017 PAEMST NYS Mathematics Secondary Nominee https://www.paemst.org (Baldwin High Retired)


HTH & stay safe,

A. Jorge Garcia

Teaching With Technology:
Coding since 1975,
HS Math & Physics since 1984,
College Math & CompSci since 1993,
 Linux Clusters since 2002,
CAS since 2011,
Retirement since 2020?
 
AP Computer Science: 1988-2019
AP Calculus BC: 1993-2018 
Applied Math, Physics and CS

Please support my classroom:
www.patreon.com/calcpage2020

https://www.udemy.com/user/alvar-garcia-fernandez

calcpage.redbubble.com

society6.com/calcpage

https://www.ebay.com/usr/sffbclub  



2017 NYS Secondary Math PAEMST Nominee


pastebin youtube slideshare

(IDEs & Code)
MATH 4H, AP CALC, CSH: SAGECELL
APCSA: code.cs50.io
APCSA: replit.com
Jupyter: CoLab

(Curriculae)
CSH: CodeHS
CSH: Code.org
APCSA: Big Java
APCSA: CSAwesome
APCSA: AP Central

RECOMMENDED AP COMPSCI REVIEW:
CRIB SHEET (given during exam)
FREE TEXTBOOKS
REVIEW BARRONS ONLINE 
REVIEW APCENTRAL (past FRQs)
REVIEW EDX REVIEW MOOC01 
REVIEW UDEMY REVIEW MOOC02 
REVIEW CODING_BAT 
REVIEW PRACTICE_IT 
REVIEW RUNESTONE 
AUDIT CS50

RECOMMENDED AP CALCULUS REVIEW:
CRIB SHEET (not given during exam) 
FREE TEXTBOOKS
REVIEW BARRONS ONLINE 
REVIEW APCENTRAL (latest AB FRQs)
REVIEW APCENTRAL (latest BC FRQs)
REVIEW APCENTRAL (older AB FRQs)
REVIEW APCENTRAL (older BC FRQs)
REVIEW EDX MOOC01 
REVIEW COURSERA MOOC02

XTRA CREDIT FILKS RUBRIC 
(1 video = up to 5 bonus points):
1) Use a recognizable tune.
2) Karaoke entire song changing up the words (about STEAM).
3) You are Singing, Dancing or Playing an instrument.
4) You upload your video to YouTube and provide the url.
5) YouTube Description includes the lyrics.

XTRA CREDIT ARTICLES RUBRIC
(up to 5 articles = 1 bonus point each):
1) Cover Sheet is a Summary of the article.
2) FullPage, 12 pt, DoubleSpaced, 1" Margin.
3) Article has to be STEAM related
4) Article has to be a current event.
5) Copy of entire article is attached.

NOTE TO READER:
In recent years our independent study class has been about the care and feeding of Linux Clusters: How to Build A Cluster, How To Program A Cluster and What Can We Do With A Cluster? 

BTW, Shadowfax is the name of the cluster we build! FYI, we offer 4 computing courses: 

CSH: Computer Science Honors with an introduction to coding in Python using SAGE, IDLE, VIDLE and Trinket

CSA: AP Computer Science A using CS50, this IDE and this IDE and OpenProcessing

CSI: Computing Science Independent Study using OpenMPI and 

CSL: Computing Science Lab which is a co-requisite for Calculus students using Computer Algebra Systems such as SAGE.

====================
CIS(theta) aka CSI
Membership Hall Of Fame!

CIS(theta)* 2020-2021: 
DiegoM(12), GeordiP(12), MattB(12), MattO(12), MelanyeCG(12), NickE(12), WilliamF(12)
*Honorable Mention: I retired before we got to start our project this year...

CIS(theta) 2019-2020:
AaronH(12), AidanSB(12), JordanH(12), PeytonM(12)

CIS(theta) 2018-2019:
GaiusO(11), GiovanniA(12), JulianP(12), TosinA(12)

CIS(theta) 2017-2018:
BrandonB(12), FabbyF(12), JoehanA(12), RusselK(12)

CIS(theta) 2016-2017: 
DanielD(12), JevanyI(12), JuliaL(12), MichaelS(12), YaminiN(12)

CIS(theta) 2015-2016: 
BenR(11), BrandonL(12), DavidZ(12), GabeT(12), HarrisonD(11), HunterS(12), JacksonC(11), SafirT(12), TimL(12)

CIS(theta) 2014-2015: 
BryceB(12), CheyenneC(12), CliffordD(12), DanielP(12), DavidZ(12), GabeT(11), KeyhanV(11), NoelS(12), SafirT(11)

CIS(theta) 2013-2014: 
BryanS(12), CheyenneC(11), DanielG(12), HarineeN(12), RichardH(12), RyanW(12), TatianaR(12), TylerK(12)

CIS(theta) 2012-2013: 
Kyle Seipp(12)

CIS(theta) 2011-2012: 
Graham Smith(12), George Abreu(12), Kenny Krug(12), Lucas Eager-Leavitt(12)

CIS(theta) 2010-2011: 
David Gonzalez(12), Herbert Kwok(12), Jay Wong(12), Josh Granoff(12), Ryan Hothan(12)

CIS(theta) 2009-2010: 
Arthur Dysart(12), Devin Bramble(12), Jeremy Agostino(12), Steve Beller(12)

CIS(theta) 2008-2009: 
Marc Aldorasi(12), Mitchel Wong(12)

CIS(theta) 2007-2008: 
Chris Rai(12), Frank Kotarski(12), Nathaniel Roman(12)

CIS(theta) 1988-2007: 
A. Jorge Garcia, Gabriel Garcia, James McLurkin, Joe Bernstein, ... too many to mention here!
====================