12/14/2020 at 5:16pm-6:49pm

Dear my past self,

Anthony, it has been almost 4 months since I have learned tons of calculus, focusing on integrals and series. My Calculus 2 journey has been rough, especially at the beginning. You know, when I began Calculus 2, I was disorientated for the first few weeks. I thought everything was new especially the format of the homework, how much participation credit I needed, and the heavy truckload of (450?!) questions I was assigned for homework. Especially with the integration part of the class, I felt like these integration techniques were forced upon me! Due to so much work I have to do, I felt confused about the new integration techniques and didn’t make progress like I hoped to. I didn’t even begin my official HOT Topic presentations until the start of Week 3, where I presented integration by parts, and I managed to get my first H there.

Starting Week 3, the WeBWorK workload was slightly more manageable, but still tedious. Especially when working with trigonometric substitution, I was very confused about this topic especially I had little to no background knowledge about trigonometric integrals and identities. However, I took the advantage to watch videos on the course hub to understand the procedure for certain problem formats. Because of these videos, I was able to get my second H, and solve the group trigonometric substitution problem presented in Week 4.

In Week 4, I am relieved by partial fraction decomposition, but not too much. Partial fraction decomposition is an algebraic technique, but it can be complex at times. I was able to do simple problems involving splitting fractions into A and B, however, I remain confused when there are more complex problems involving this topic. But again, I was also to successfully get my third H.

In Week 5, I am starting to jump for joy as we are learning improper integrals. Since we are learning about improper integrals, they somewhat remind me of basic u-substitution problems. U-substitution was an easy topic, but couldn’t understand it until we learned improper integrals. But, because this topic was easy, I have blasted through most of the problems in this topic. This is also the first time that my HOT topics are up to par.

After Week 5, I have learned to manage my time and learn these topics early enough. The Series topics were harder, but I was able to progressively understand it over time. Even though that we have to learn a handful of convergent tests, it is going to be manageable as long as we look carefully at the problem and read the instructions. (By the way, I love the topic sequences, because they remind me of Frames-and-Arrows problems back in 1^st grade).

I am now going to give you advice:

1) Manage your time to do the assignments in this class. For instance, if you usually squeeze some time for Friday to do the WeBWorK sets and during the class time to watch videos and do assignments, try to keep that regular schedule unless plans change. Avoid doing homework spontaneously, because chances are, you may somehow fall behind. I also have been hearing some students doing homework in the last minute, so I ask you not to do it.

2) Watch videos (and take notes) before doing any math work yourself. As you watch the videos, it is important that you take notes of the entire procedure of math problems. If you don’t understand anything from the video, it is best to ask questions during your COLD session. I know that during in-person classes a while ago, videos do help, but they aren’t a replacement for attending class and taking notes. However, now with online class, it is important that you watch videos in order to understand the material (especially with asynchronous classes!).

3) Have your integration and trig identity tables ready. I have seen some integration tables appear on the Web. These tables are very helpful, but you must choose the appropriate table(s) you will use during your time on Calculus 2. One thing I have found integration tables helpful is when I have to find the integrals resulting in inverse trigonometric functions. I believe that trigonometric substitution is one of the hardest integration techniques to apply, but the use of trig identity tables will make this topic more bearable.

4) I will admit that fact that study groups in this class didn’t work like the way I wanted. Therefore, I rarely join study group sessions. However, I will say this: Try to do weekly study groups. I really want you to join study groups for few reasons. You may think that you can do all the studying alone, however, study groups allow you to check each other’s progress, teach others what you know, and to ask other questions. To some degree, study groups may enhance your social skills.

5) Since you will be taking this class for the first time, make sure you orientate yourself and familiarize yourself will all of the topic you will learn this semester. Practice the WeBWorK problems before trying to solve HOT Topic problems. These HOT Topic problems will demonstrate your understanding of that particular topic. Make sure you prepare your HOT Topic solution ahead of time and write down the numbered steps to help you walk through your solution. If your ever get an O in your HOT Topic presentation, don’t panic! Analyze what you have done wrong in your solution and fix them. You can always try again. And, I know that you can get 10 H’s this semester. You can do it, Anthony!

Have a great semester! One more thing, don’t cause a time paradox!

Best,

My present self (Anthony John Regner)