Recent Tutoring Session Reviews
"During our session, we went over some of the student's calculus homework assignments. Last time we had just started working on the chapter dedicated to integration, and his course is now further into the chapter, dealing with more complicated applications of integration. The first couple of problems we worked on covered the use of rectangles to estimate the area under a curve, as well as using geometric formulas to find the area under the curve of neatly shaped functions. After completing the first set of problems, he told me that they had just started u substitution and integration by parts in class, two difficult concepts that he didn't fully understand yet, so we spent the rest of the session going over the formulas for these two techniques of integration, and doing examples to show him how they work."
"Today we discussed differential equations: slope fields (interpreting them, drawing them, finding graphically a particular solution) and separable differential equations - find the general solution and a particular solution)."
"Today's focus was on converting from polar to parametric equations for the purpose of computing the derivative. We also worked on sketching polar coordinates and how to figure out what kind of limacon it is. We also went back and reviewed a bit of arc length and we covered the derivation of the formula, which she had never been shown. It seemed to clear a lot of things up for her, knowing where the formula had come from."
"We started a new section on the Mean Value Theorem. The student said she understood my explanation and we were able to use it to look at the definitions of increasing and decreasing functions. Using our new definitions and theorems, the student was able to solve the problems. We also reviewed logs and solving inequalities."
"The student is studying for her next calculus exam, which will be Friday. During this session we started reviewing a practice test that she has for her upcoming exam. We discussed the first half of the practice test, which included problems asking for analysis of the concavity of functions and whether they are increasing or decreasing. We reviewed first and second derivatives, and how to calculate if a function is increasing or decreasing and concave up or down. We also went over how to check answers using a calculator. I am hopeful that this in particular will help her on her next exam, as timing is not an issue for her and she should have time to check all of her answers. With this method, on the problem that she solved incorrectly, she discovered her error on her own and was successfully able to redo the problem and find the correct solution."
"The student and I discussed concepts in calculus, and in his Engineering Science classes. Specifically we focused on the first derivative test and matrix algebra used to solve nodal circuit analyses. He is sharp and capable, and I enjoy working with him as he is a great student."