Recent Tutoring Session Reviews
"Today we covered more on sequences and series. We used the alternating series test and comparison test to see whether a series converged or diverged. We also did more ratio and root tests. We used substitution convert functions such as sin x, cos x, and ln (1+x) to infinite series. We learned that for a p series, if the exponent was greater than one, the series converged. Otherwise, the series diverged. The student was eager to learn the material. His scores are certainly improving. We also approximated the sum of an alternating series, like we did in the last session. Overall, the student is grasping the material well."
"In our first session, the student and I got a feeling for her comfort level in math. We reviewed what mathematical functions are and how to represent them algebraically (equations) and geometrically (graphs). We explored the idea of limits and how they allow us to investigate behavior in regions of functions that aren't well defined. This is an abstract and--thus far in our calculus course--ungrounded concept, but she proved to be a quick learner. Great work! I also briefly introduced the concept of derivatives, which we will cover in depth in our sessions to come. For homework, I assigned problems in her textbook and exercises on the website. MOST IMPORTANTLY: review our notes from the session and from an external source. The goal before the next session is to be very comfortable with the CONCEPT of limits--we don't need to do much rigorous math yet."
"Specifically, we went over rotating graphs. At first, the student seemed a bit unsure but once she realized how easy it was to work with the formula and working with her calculator, it came very natural to her."
"In today's session, we touched on the derivatives for trig functions and walked through the properties of the sine and cosine derivatives. We also looked at how to find the general graph of a derivative of a function based on the graph of the base function. The majority of the session was spent on implicit derivation, which is the next big topic for calculus. We spent some time going through practice problems for finding the implicit derivative and will continue to practice this in tomorrow's session."
"Today, we started the anti-derivative chapter. For the first section, we started doing Riemann sums - seeing how as the interval of delta x becomes smaller and smaller, we get a better approximation of the area under the function. The problems are easy, but time consuming. I showed him how to use Excel to cut down on tedious computation."
"Today we reviewed all the material covered in the course in order to prepare for the final. He did a great job asking questions and working with me to understand difficult concepts. Overall it was a great review and he did a great job staying focus throughout the session."