This week was a good in AP Calculus. I got my test back for Chapter five and I did very well. I felt confident going in to it and felt like I understood the content very well. The concept of definite integrals was easy for me to pick up and I learned all the cool tips and tricks that went a long with it.
The start of chapter started as a huge review. At first I forgot how to substitute u in for an equation so I had to relearn that. Basically you take part of an equation and substitute in u. Then you need to find out what du = relative to dx. We substitute that into the equation and then we have successfully done u substitution. If the integral we are substituting into has bounds, you have to plug in he bounds to the equation you have =u. You update the bounds and then you are done. The nifty thing is the area is under the curve is the same for the original definite integral so long as you didn't screw up along the way. Most times it makes things a lot easier and is often easier to see.
Then we moved on to slope fields. I have yet to see a real use for this both realistic or calculus related. I have no idea how making a slope field will help me do anything. A slope field is a 5x5 grid that shows the slope of the dy/dx at any given point. Some of the patterns are pretty cool. I do see how these could be used in a different field. Also, the 3D slope fields look real cool. There are still things about slope fields I don't understand, so I'm going to do the worksheet now.
The start of chapter started as a huge review. At first I forgot how to substitute u in for an equation so I had to relearn that. Basically you take part of an equation and substitute in u. Then you need to find out what du = relative to dx. We substitute that into the equation and then we have successfully done u substitution. If the integral we are substituting into has bounds, you have to plug in he bounds to the equation you have =u. You update the bounds and then you are done. The nifty thing is the area is under the curve is the same for the original definite integral so long as you didn't screw up along the way. Most times it makes things a lot easier and is often easier to see.
Then we moved on to slope fields. I have yet to see a real use for this both realistic or calculus related. I have no idea how making a slope field will help me do anything. A slope field is a 5x5 grid that shows the slope of the dy/dx at any given point. Some of the patterns are pretty cool. I do see how these could be used in a different field. Also, the 3D slope fields look real cool. There are still things about slope fields I don't understand, so I'm going to do the worksheet now.