Final Exam Blog Post

The post is a letter to a Math Analysis Honors student in my class next year.  
1. What do you want to say to them to help them have the most successful year possible?  
Math analysis is very rigorous course in terms that you have to stay on top of things. This class requires you to stay organized, manage your time, and work hard in order to succeed. I know it may seem quite overwhelming in the beginning of the year but honestly it is a very great class to take in order to challenge your management. To have the most successful year I believe that you just must stay on top of your things and get things done on time. If not then you will catch yourself falling behind and not being able to catch back up. It is important that all of you taking this class are prepare for the work load and for the many requirements entailed to pass this class such as the Internet. This class requires you to use your resources like the computer a lot and just everything given to you by Mrs. Kirch herself. It is important mainly as I said before that you remain organized and up to date. Also, and important factor for success is to work hard. You need to be able to put in the work in this class in order to succeed. It won't come to you unless you put in the effort. This is necessary for the entire year, even towards the end when you start getting lazy. Working had and staying on top of things are two of the most important factors that you need to possess for success. 

2. How can they best adjust to the flipped classroom and learn to work with all the technology I require of them?  (do you have any specific tips for them or experiences you could share?)
Adjusting to the flipped classroom the first few weeks are pretty challenging and difficult but as soon as the year progresses you forget about it. At first I had trouble adjusting to the whole learning at home part but after a while you start to notice how much it actually benefits you because in class you get to ask questions. To adjust to the use of technology and flipped classroom just get used to learning at home and getting a quiet place at home where you can study and complete your online lessons. Also you need to come in knowing how to work the computer and have technology such as the graphing calculator. 

3. What can they expect to be different from their previous math classes?
The flipped classroom is nothing like what you may expect from your normal math classes. This is a class where you are challenged by your knowledge in technology, and also your capability of staying focused. This classroom requires you to stay on top of things and not fall behind as you can in other math classes. The work load is also different and the responsibility you take on in this course is also much greater. Responsibility I feel is a factor that is much more entailed for this course because you need to be able manage your time and stay focused, even with all the technology that may distract you. 

Unit V BlG Question Blog Post

Unit V BlG Question Blog Post
1. Explain in detail where the difference quotient comes from. 
The difference quotient is derived from a graph in which we are trying to figure out the slope of the tangent line. This slope that we are trying to find of this tangent line is also known as the derivative which is usually shown as f' (x). The difference quotient comes from the point on the graph in which the slope of the tangent line is crossing at. This point is referred to as (x, f(x)). The change of x where another tangent line crosses the graph is known as the change of x (delta x+ x) plus x. The secant line is the place where the line crosses at two points which also helps explain this difference quotient where the second ordered pair is known as (x+deltax, f(x+delta x). After getting these two points you use the slope formula of y2-y1/x2-x1 in order to solve further. When plugging in the values of the ordered pairs you are able to cancel some values and are then left with the difference quotient. 

Citation: http://upload.wikimedia.org/wikipedia/commons/8/8c/Derivative.png