To the Incoming Math Analysis Students...

Dear Incoming Math Analysis Students,

My name is Josefina and I took Math Analysis during my senior year.

First of all, I want to wish you all luck on the upcoming year! I hope you are all prepared and excited for Mrs. Kirch's class! My experience with Math Analysis was difficult but it was also fun. The most difficult part of Math Analysis was getting used to watching videos instead of having an in-class lecture. The best advice I can give you is to not slack off on your homework, especially the summer assignment! It was hard for me to keep up with the homework for this class because I had other classes and AP's to worry about, but I had to make time for this class so that my grade wouldn't go down. It is also important to do the summer assignment because if you don't do it you will fall behind the rest of your class. I also want you guys to go into Mrs. Kirch's class with a positive attitude and an open mind. The most important thing in this class is to be able to accept change and the different rules that Mrs. Kirch has set up.

The best way to adjust to the flipped classroom is to keep an open mind. At first, you guys will feel overwhelmed with all the new things that are you are exposed to, but pretty soon you will get used to it. In the flipped classroom, Mrs. Kirch required us to make our own videos as assignments. The first video that I recorded  was in Mrs. Kirch's class and it was difficult for me the first time. It was difficult because I had never recorded a video before but by the end of the year, we had recorded a lot of videos and I felt that I got better at it. The most difficult part about recording videos was getting the right equipment to record the videos, but if this this a problem for you, Mrs. Kirch has the supplies for you to record your video. I would also advise you to keep up with your work in class! This is important because you will regret it if you slack off. Mrs. Kirch sets up recommended deadlines for work and it is a good idea to follow them.

The flipped classroom is very different from a normal classroom.The biggest change is the video lessons. In Math Analysis, we need to watch videos at home to learn the material and in class, we do practice problems that would normally be assigned homework. Another difference in the flipped classroom is that we do not use our textbook at all. Mrs. Kirch creates her own packets (the SSS) that we used instead of the textbook, so don't expect to be using your Math Analysis book frequently. As you can see, Mrs. Kirch had us set up our own blog and we used this blog to do a majority of our homework assignments. This blog was hard to keep up with because some of the assignments we had were difficult.  The biggest difference between a flipped classroom and a normal classroom was the homework we were assigned because we don't have the usual textbook assignment, we have videos and blog posts for homework.

Please keep an open mind towards the flipped classroom, it well help a lot!
Have fun in Math Analysis next year, Mrs. Kirch is an awesome teacher!

Unit V Big Question

The difference quotient is used to find derivatives. A derivative is the slope of a line that is tangent to a graph. A derivative is written as f '(x). The difference quotient finds the slope of a secant line. A secant line crosses through two points on a graph. The tangent line only touches the graph once. With the difference quotient we can find the derivative and the slope of the tangent line at a specific point by simply plugging in an x-value after we find the derivative. We can also find the equation of the tangent line by using the ordered pair we are given. First we find the derivative and plug in the x-value, then we use y=mx+b and use the ordered pair to solve. There are many things we can find with the derivative.

Sources:
http://www.coolmath.com/precalculus-review-calculus-intro/precalculus-algebra/24-the-difference-quotient-01.htm