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Integration Review
We reviewed basic integration rules such as u subsitition and the power rule. We used example problems to review these techniques. -
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Calc Review
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Differential Equations, Slope Fields, and Euler's Method
Today we reviewed the golden rule of separating variables when solving differential equations. We also reviewed the concepts of sketching particular solutions on slope fields and matching differential equations to slope fields. Next, we reviewed the growth and decay differential equations and the different forms of the logistics growth model. Today was the first day I fully understood why the differential equation and its solution can be written in two different forms. -
Sequences and Series
Today we reviewed the ideas of convergence and divergence in sequences and series. For sequences, we look at the boundedness of the function and check that it is monotonic (non-increasing or non-decreasing) to test for convergence. Sequences, unlike series, can converge to a number other than zero. The nth term test for series proves that if the limit of the function does not approach 0, then it diverges. We also reviewed a few of the more simple series tests for convergence. -
Taylor Series, Power Series
Today we reviewed how to write a taylor series in order to approximate functions at certain values. We also reviewed how to write these series as power functions. I finally understood that the LaGrange form of the remainder is really just the next term in the series, just like the alternating series remainder. -
More Series Convergence
We worked together with partners in class to do practice problems about series convergence. We also reviewed how to find the radius of convergence and in the interval of convergence. I had forgotten that derivates of functions have the same radii of convergence, but that the endpoint of the interval can be different (included or not included). -
Advanced Integration Techniques
Today we reviewed integration by parts and partial fractions. I feel very comfortable with these two methods of integration. We also reviwed L'Hopital's rule and improper integrals. I need to review the indeterminate forms and do some more practice with improper integrals, but I feel like I have a fair understanding of those two topics as well. -
Integration Applications
Today we reviewed integration applications involving area and volume. We also talked about finding volume of solids created when the base of the cross section is something we can easily find the area of. I feel comfortable with this technique and others such as the shell method, the disk method, and the washer method. -
Applications
Today we reviewed the different applications of integration. We practiced the different methods of surface revolutions, such as the Disk method (to be used when the radius is perpendicular to the axis of revolution), the Washer method (when there is a hole in the middle), and the Shell method (to be used when the axis of revolution is parallel to the radius). -
Polar Test
Today we took our last unit test, the Polar test. I felt fairly confident in the subject; I knew the formulas and the ways to convert functions from rectangular to polar and vice versa. I struggled with a few problems on the test, especially on the calculator part. I think I probably scored a low to mid B on the test. -
Practice Problems
In class today we completed practice multiple choice and free response problems involving a variety of topics. I found the free response questions pretty easy, but I struggled with a couple multiple choice questions. I need to review how to write summations and the theoretical ideas about functions and continuity versus differentiability and the concepts that follow. -
Review of Free Response
In class we completed a few practice free response questions. I felt comfortable with the concepts. I still may need to review series convergence and recognizing common Taylor series, but for the most part I feel like I have mastered most of the material. -
Last Review Day
Today was our final review day. We went over some of Hyman's Helpful Hints, which are good reminders for good test-taking. We took a walk to relax before the exam. I feel pretty prepared for the test. -
The Big Game
I thought that for the most part the test was manageable. I felt confident on the multiple choice, especially on the calculator section. I was also confident with the calculator part of the free response, but I struggled with the final free response question (a Taylor series question). I had to reread the questions multiple times to understand what I was even being asked to do, and I felt like I had never seen a question asked that way before. I think I probably scored in the 4-5 range.
