Scientific Computing
Science, Technology, Engineering, Arts & Math
Teaching & Learning Math & Science with Technology
Graphing Calculators, Numerical Methods, Computer Algebra Systems & Linux Clusters
Why Shadowfax? Our cluster is so fast that we named it after the Lord Of The Rings character!
Website once known as CalcPage.tripod.com (1988 – 2008)
Wow, we covered a lot this week, didn't we? We introduced the concept of finding area bounded by a curve and the X-Axis, as well as bounded by 2 curves, using a Definite Integral using the Fundamental Theorem of Calculus.
First we approximated these areas by sketching Left & Right Riemann Rectangles by hand. Then we found the average of LSUM and RUM equaled TRAPSUM. So, we wrote a TI-BASIC program called LRTE.BAS on our TI-84s to approximate these areas for large n, the number of rectangles. This is a Limiting Process, just as the numerical derivative was. As n approaches Infinity, the error in our estimates aproaches Zero!
LRTE is short for the program's output: LSUM, RSUM, TRAPSUM, TRAPERROR where TRAPSUM=(RSUM+LSUM)/2 and an overestimate to the TRAPERROR=(RSUM-LSUM)/2. We found that, when the limit exists, LSUM, RSUM and TRAPSUM will all converge to the correct area, but TRAPSUM did so quickest. Our program had inputs for a & b, the limits of integration, as well as n, the number of rectangles. LRTE had a precondition to: set y1=f(x), the integrand.
We also talked about the Indefinte Integral as an Anti-Derivative Function. We figured out several anti-derivatives by just thinking about the derivatives we know already going backwards. We worked with the Fundamental Theorem of Calculus, Definite and Indefinite Integrals. We found the basic anti-derivatives (see NUMA NUMA below) based on all the derivatives we knew plus we worked with U-Substitution when the integrand was based on a Chain Rule. We even found anti-derivatives for f(x)=cos(x)^2 and g(x)=sin(x)^2.
Thanx for a great summer, I think we had a great experience! You are taking the final as I type. So, good luck on the final and all your future endeavors! Bye, Bye!
Please see WEEK05 notes on our Google Drive and our Screencasts on BrightSpace & YouTube!
Last, but not least, here's this week's Filks! We start each class with a fun Filk or short Documentary related to a specific topic we're learning in class or something related to STEAM.
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,
