I teach an engineering class entitles Engineering, Design and Development. My students are really excited about this project and need justification for their current problem. if you could take a minute out of your day to fill out their survey I would be very greatful. The link is here -> [link removed]
I used the integration method to calculate the following equation to find out the area between 1 and 4 was 51. The equation is 0.6666x^3 - x^2 + 8x + c.
However, when I use Trapezoidal rule and simpsons rule, the results are 82.
Th...See MoreOn 2/26/15, Tom wrote: > I used the integration method to calculate the following > equation to find out the area between 1 and 4 was 51. > The equation is 0.6666x^3 - x^2 + 8x + c. > > However, when I use Trapezoidal rule and simpsons rule, > the results are 82. > > Why there are such difference in result? >
Those numerical integration tools are approximations, and their accuracy is heavily influenced by the length of the intervals.
To get a sense of just how off these methods are when you try to apply them with such a large interval, as you have, you should draw the curve of the original function, f(x) = 2x^2-2x+8, which between x=1 and x=4 is a steeply increasing parabola. Now draw the trapezoid. Now look at the huge difference between the area of the actual curve and the area of the trapezoid that approximates that area.
These rules can be very accurate ways of doing numerical integration but you always have to look at the error analysis part of it to see how good the approximations are. To improve the accuracy you have to split the domain into smaller pieces and apply the trapezoid rule to each piece and then add up the little pieces of area you get. The smaller you make the intervals, the greater the accuracy.
If you do not have a good way of graphing the function so you can look at and compare the curve and trapezoid visually you might have a look at this program - it is free and it does a great job of graphing functions.
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I have used this program for years with my students to help them "see" what is really going on, in questions like this.
I am wondering how people are implementing this model in their Mathematics program and what you are doing to help those students on whom you are focusing?
What is it?On 2/17/15, Erin wrote: > I am wondering how people are implementing this model in > their Mathematics program and what you are doing to help > those students on whom you are focusing?
A google search comes up empty on "Focus on Five". Do you have a link to something that explains what that model is?
Hello .. We are looking to adopt new math textbooks for our K-8 school. I haven't seen a lot of rave reviews on any of the common core aligned texts out there. Anyone already using a new "common core" aligned series. Do you love it? Hate it? Just in between? I'd love to hear some real world experiences.
We are currently beginning the process of researching and then will be deciding what to pilot. I am finding that many of the texts are similar, and most have an on-line piece which allows students to access the text on line and assessments which can be created and given on- line. One series I really like is Everyday Math from McGraw Hill. The materials are set up to allow the standards to drive the teaching, and give teachers differentiation information for classroom teaching and materials to supplement, but there is no "text" that is driving the instruction. This is a new way of teaching for most of us, but the CCSSM are asking us to learn to teach in a new way, and I believe with solid support this is one of the best resources I have seen yet. I am not finished previewing what is out there at this time.