Recent Tutoring Session Reviews
"Today I went over more examples of Riemann sums with the student. We also looked at the use of integrals to find areas under curves. He has done well, getting 80's or better on his tests (except the first one, which will be dropped) and doing very well with his homework. This is his last week."
"The student and I covered fxn properties (inc/ dec/ concave up/ down) but taking the 1st and 2nd derivs of functions. We spent a lot of time reviewed trig and inverse trig functions and how to find all roots. Lastly, we drew functions based on qualitative criteria given by the book."
"We spent the beginning of the session finishing up problems from last week involving finding the slope of a line tangent to a curve at a specific point using the difference of the function. Following that, we moved on to the topic of maxima and minima. After learning the basics of this topic, we were able to move on to applied uses for maxima and minima such as maximizing area or minimizing cost. We will probably spend a large part of the next section working on this topic as it can be complicated when modeling real life situations."
"We covered the product rule and quotient rule, which are essentially two formulas to help us in integrating products and quotients of functions. These are intricate formulas to memorize, but the nice thing is that once you plug your function in, you can just rely on the rules we've already been using to differentiate. You seemed very adept at using the formulas and taking the derivatives, but keeping proper notation can be easy to forget. Remember to be disciplined about writing out each step and using proper notation so you don't get mixed up as the derivatives get more complex! For homework see the worksheets I emailed you. Also review solving equations. I'm really pleased with the progress we've made over the last couple of sessions. Everything is coming together with differentiation, and we're finally ready to apply what we've learned!"
"This was our first session and we started talking about a little bit of pre-calculus review with differences of squares, plotting, and trig functions. Then we moved into the calculus portion which at this point is mainly limits. We talked about when limits are undefined, infinite, and finite. We talked about different methods to simplify limits to get the appropriate answer. The student seemed to be paying great attention in class and reading the book. She was quick to pick up on methods and definitions. She was probably struggling the most with complicated limits which is a topic that many people struggle with at first but I believe she will improve greatly after she has had more practice."
"The first question I had for the student today was how he was feeling with implicit differentiation. We spent our last two sessions on it, and he just had his lecture session on it as well. He is still not rock solid on it yet, but more comfortable than he was, and he was ready to forge ahead into new material: sign charts, extrema, critical points, etc. There are lots of pieces and parts to each problem, and the combination of all of them can be tricky. He admitted that it isn't the calculus that makes it troublesome, but all the different algebra rules and things that are required to solve some problems. He did well today, and I believe, with some more practice, he will feel very comfortable with the material soon."