Recent Tutoring Session Reviews
"We discussed the first and second derivative tests in finding extrema, as well as the closed interval method. He did not, at first, understand the relationship between all three but began to in application. He is concerned about the pace of the course but is beginning to see how he can adapt. He is doing well now."
"This session we talked about related rates, which is the main application of implicit differentiation. These problems mainly deal with one of two scenarios: Volume or the Pythagorean Theorem. Instead of taking the derivative of y with respect to x, however, we are taking the derivative of a length with respect to time to find the relationships between length, and velocity for multiple dimensions. We spent most of our time talking about this topic today."
"Last session with this student before his final exam (covering integration). Started off with a top-to-bottom review of the integration concept. Talked about the problem of finding the area under the curve, approximation via finite Riemann sums, exact values as a limit of Riemann sums and examples in which the limit of a Riemann sum can be calculated exactly. From there we discussed the Fundamental Theorem of Calculus (evaluation theorem) and went over examples involving anti-differentiation. Finally, we had an in-depth discussion of substitution methods (i.e., anti-differentiation of the chain rule) for both indefinite and definite integrals. After this session he has at least seen and understood the key concepts that will be on his final although he'll need plenty of practice to execute well on the final exam. He'll be studying tonight and meeting with his study group tomorrow so I have high hopes of a passing grade in the course. Also, if he has any questions I've asked him to send an email for help."
"We checked and solved exercises related to antiderivatives and their uses for definite integrals, and solving differential equations. Both graphical and analytical solutions were presented. The student is well skilled in these subjects and confident in her abilities. She did really well on her recent tests in calculus."
"We solved two hard problems. The second involved trigonometric functions. The student has some gaps on them, but he was able to understand the solution. He needs a lot of practice, which will be our focus next session. The first involved position, velocity and acceleration functions. He also needs more practice on this topic, in order to train himself at noticing relationships between functions, their first, and their second derivatives."
"Tonight we went over the student's final review packet that was given to her by her professor. She was understanding the majority of the packet, so we just went over the problems that she wasn't fully understanding. After going over these problems, she was able to reason her way through these problems."