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Friday, January 28, 2011
Thursday, January 27, 2011
Monday, January 24, 2011
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Tuesday, January 11, 2011
Monday, January 10, 2011
Scribe Post 1/10/11
So, Firefox just crashed and deleted my whole scribe post when I had one word left. Fun night. We started off class with a brief discussion of the midterm and how it is going to work. Basically, it will include non-calc and calc free-response questions so be prepared for both. Also, homework is due Friday, except for today's assignment which is due Wednesday, which is also the day we have a quiz on Diffy Qs.
In class today, we began by talking about #6 on the slope fields packet. We also talked about the hot tub word problem. Here are a few helpful hints to keep in mind when working on Diffy Q problems:
-If you have a hard time with slope fields, make a table of values!
-You only need to add "C" to one side of your anti-derivative equation, as if you add c to both sides then subtract from one side, you still have a constant.
-Just because you are taking the anti-derivative of a fraction doesn't mean the anti-derivative is necessarily the natural log function
We then talked about Julia moving around the room. This taught us about position, displacement, and distance. We learned that position was Julia's location at a particular moment (e.g. position was -8 when Julia was at -8). Displacement was how far Julia traveled from her start location to her ending location, or final position minus initial position (e.g. Julia started at -8 and ended at -1 so her displacement was 7). We then decided that distance is how far Julia traveled total, and it must always be positive, as you can't un-travel. Julia's distance was 13, as it was the total of the absolute value of each leg of her trip (she started at -8, went to 2, then went back to -1). We then had a little discussion about how her velocity related to her movements. For example, as Julia went from -8 to 2, her velocity was positive, and was increasing then decreasing. As Julia traveled from 2 to -1, her velocity was negative, and was decreasing then increasing. The homework packet has a nice fill-in-the-blank section that explains this a little better, and Mr. O'Brien says that the concept of velocity in relation to displacement and distance can be a little hard to grasp at first. Overall, it was a productive class!
Here are a few links to help with today's lesson:
http://www.schooltube.com/video/4eae3449edc2899b3d00/Calculating-the-distance-between-two-points-on-a-number-line-by-Camille-Morton She makes understanding distances easy enough for a five-year-old to understand. It's cheesy, so be warned.
http://www.intmath.com/Differential-equations/1_Solving-DEs.php This breaks down differential equations into a manageable form, which I found helpful before the quiz Wednesday.
Homework: Packet Mr. O'Brien handed out, quiz on differential equations Wednesday, extra credit to anyone who can find a good visual representation of #6 in the slope fields packet.
UPDATE:
While looking for some practice problems for the midterm, I came across this link:
http://www.analyzemath.com/calculus.html
It has a bunch of problems for quite a few of the topics we've done so far and applets to help explain them!
In class today, we began by talking about #6 on the slope fields packet. We also talked about the hot tub word problem. Here are a few helpful hints to keep in mind when working on Diffy Q problems:
-If you have a hard time with slope fields, make a table of values!
-You only need to add "C" to one side of your anti-derivative equation, as if you add c to both sides then subtract from one side, you still have a constant.
-Just because you are taking the anti-derivative of a fraction doesn't mean the anti-derivative is necessarily the natural log function
We then talked about Julia moving around the room. This taught us about position, displacement, and distance. We learned that position was Julia's location at a particular moment (e.g. position was -8 when Julia was at -8). Displacement was how far Julia traveled from her start location to her ending location, or final position minus initial position (e.g. Julia started at -8 and ended at -1 so her displacement was 7). We then decided that distance is how far Julia traveled total, and it must always be positive, as you can't un-travel. Julia's distance was 13, as it was the total of the absolute value of each leg of her trip (she started at -8, went to 2, then went back to -1). We then had a little discussion about how her velocity related to her movements. For example, as Julia went from -8 to 2, her velocity was positive, and was increasing then decreasing. As Julia traveled from 2 to -1, her velocity was negative, and was decreasing then increasing. The homework packet has a nice fill-in-the-blank section that explains this a little better, and Mr. O'Brien says that the concept of velocity in relation to displacement and distance can be a little hard to grasp at first. Overall, it was a productive class!
Here are a few links to help with today's lesson:
http://www.schooltube.com/video/4eae3449edc2899b3d00/Calculating-the-distance-between-two-points-on-a-number-line-by-Camille-Morton She makes understanding distances easy enough for a five-year-old to understand. It's cheesy, so be warned.
http://www.intmath.com/Differential-equations/1_Solving-DEs.php This breaks down differential equations into a manageable form, which I found helpful before the quiz Wednesday.
Homework: Packet Mr. O'Brien handed out, quiz on differential equations Wednesday, extra credit to anyone who can find a good visual representation of #6 in the slope fields packet.
UPDATE:
While looking for some practice problems for the midterm, I came across this link:
http://www.analyzemath.com/calculus.html
It has a bunch of problems for quite a few of the topics we've done so far and applets to help explain them!
Thursday, January 6, 2011
Scribe Post 01/06/2011
Today, to start off class, we got our Unit 3 Supercorrection Follow-up Tests back and went over the problems in class. Apparently, everyone did fairly well on it, but we went through each problem anyway for review.
Then we went to the blog, to do the two problem sets for the day that took up the whole class period.
The first one, 7-3, we went through and Mr. O'Brien explained step-by-step. The second one, 7-2, was mostly for practice.
Here are the notes/solutions to the problem sets, which you can find a copy of in the previous blog post as 'in class problems'.
(By the way, on the first page of solutions, the cut off note on the left hand side is supposed to read 'not all given in the original word problem'.)
And here is link about differential equations just in case you need a quick refresher. Example 1 is probably the best thing to go over if necessary.
Finally, our homework for tonight was a handout packet about Slope Fields. See Mr. O'Brien if you need a copy. And we were also assigned several word problems which you can find linked in the previous post or here.
The next scribe will be Caitlin Throne.
Then we went to the blog, to do the two problem sets for the day that took up the whole class period.
The first one, 7-3, we went through and Mr. O'Brien explained step-by-step. The second one, 7-2, was mostly for practice.
Here are the notes/solutions to the problem sets, which you can find a copy of in the previous blog post as 'in class problems'.
(By the way, on the first page of solutions, the cut off note on the left hand side is supposed to read 'not all given in the original word problem'.)
And here is link about differential equations just in case you need a quick refresher. Example 1 is probably the best thing to go over if necessary.
Finally, our homework for tonight was a handout packet about Slope Fields. See Mr. O'Brien if you need a copy. And we were also assigned several word problems which you can find linked in the previous post or here.
The next scribe will be Caitlin Throne.
Tuesday, January 4, 2011
Scribe Post 1/4/2011
We started off class with the Supercorrection Follow-Up Test. There were seven problems, and we were allowed to use calculators on problems 1 + 2. This took us up to 10:10, at which point we began a game centered around slope fields. We had to match pictures of slope fields with their respective differential equations and a general description of their solution curves.
If after this game, anyone is still a little confused, this link offers some practice problems and solutions http://www.education.com/reference/article/slope-fields/
Additionally, check out this link -- you can generate your own slope fields, set display range / number of tick marks, set initial conditions, etc. http://www.math.lsa.umich.edu/courses/116/slopefields.html
Tonight’s homework is on matching differential equations and slope fields. Apologies for the abnormally short scribe post, but this was pretty much all that went on today.
UPDATE: Turns out that slope fields pertain to the more difficult differential equations we've been working on of late rather well, and have done a good job introducing us to the concept of using initial values provided in the wording of the problem to generate our own solution curves. This site encapsulates that fairly well, and also talks a little bit about Euler's Method, the simplest way of obtaining a numerical solution of a differential equation.
If after this game, anyone is still a little confused, this link offers some practice problems and solutions http://www.education.com/reference/article/slope-fields/
Additionally, check out this link -- you can generate your own slope fields, set display range / number of tick marks, set initial conditions, etc. http://www.math.lsa.umich.edu/courses/116/slopefields.html
Tonight’s homework is on matching differential equations and slope fields. Apologies for the abnormally short scribe post, but this was pretty much all that went on today.
UPDATE: Turns out that slope fields pertain to the more difficult differential equations we've been working on of late rather well, and have done a good job introducing us to the concept of using initial values provided in the wording of the problem to generate our own solution curves. This site encapsulates that fairly well, and also talks a little bit about Euler's Method, the simplest way of obtaining a numerical solution of a differential equation.
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