Recent Tutoring Session Reviews
"Today I helped the student go over some new topics she was learning in calculus. We took what she knew from describing the area between curves and applied it to describing volumes of rotation. We went over the two most basic methods, first the disc method, and from there I showed how you could derive the second method, the disc method. We went over rotations around both horizontal and vertical axis, the y-axis and x-axis. Then we went over how if you understand all of this, you can also easily generalize to rotations around any vertical line or any horizontal line."
"He has started learning some applications of integrals. He had a homework set on using integrals to find the areas between curves. I think he understands this material better than most of the other topics in the course. He could use some more practice with graphing functions, but he'll have his graphing calculator to help with that -- it just takes a little more time. But once he can see the region, he's good to go. He knows how to draw the slices (horizontal or vertical), how to set up the integral, and how to evaluate it. I had to help him a little with finding intersection points, but he knows how to use his calculator for that, too. Near the end of the assignment, I showed him how to use his calculator to evaluate the integral. He still has to set it up first, and that's where he'll earn most of the points on his test anyway."
"During this session we covered integral calculus based on real-world problems. Each problem was a "word"-type problem that related to business, physics, census reports, etc. The student had a good grasp on this subject, and it took little help from me to guide him through the process of setting up and solving the problems. I left my notes with him for his review. He will continue to study the material to prepare for his exam next week. Tuesday we will meet again to review the material he has covered since his last exam. I do not have any major concerns regarding this session."
"The student is starting calculus, and currently learning about limits. He seemed to understand how to find limits by plugging in numbers close to the target value. We went over common methods such as simplifying fractions and using conjugates. We went over a few examples to make sure he knew which method to use in different situations."
"Infinite sums of series. We went over the students homework which requires you to know the material very well to properly finish it, and the student had a good idea of what to do for most problems. We went over power series, geometric series, alternating series, and combinations of those. We practiced using some test to see if the series is convergent or divergent."
"In yesterday's session, the student and I covered exponential growth and decay. We talked about the standard form of each and used it to model a city experiencing an epidemic, and then to model its growth once a cure has been discovered. We reviewed implicit differentiation again, discussing the role of independent variables. Since we had additional time, we covered some physics concepts. This included an overview of vectors, moments, and gravity, applying them to seesaw problems and astronomy."