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Private In-Home and Online Calculus Tutoring in New Rochelle, NY

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Session Summaries by Calculus Tutors

New Rochelle, NY Calculus tutoring
Today we went over questions that the student had marked down in her pre-calculus/calculus packet and reading. She had questions regarding complex problems, like trying to find the quotient of the division of two polynomials when one is missing a particular degree term, or finding the oblique asymptote of a function. We also reviewed the inverse of trigonometric functions and terminal angles. Once we finished that, we went on to some integration of basic functions, like polynomials and trigonometric functions. She did well with that and only ever needed to be reminded to add +C to the end of her indefinite integrals. Other than that, it was simple learning moments like writing out the full differentiation of csc(x) to understand the integration of the former.
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New Rochelle, NY Calculus tutoring
We went through her homework regarding double derivatives in terms of xx, yy, and xy/yx. Lots of work with finding the critical points of a multivariable function and determining whether that point was a saddle point, min, max or none of the above. Her final is on Friday so review will start on Tuesday.
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New Rochelle, NY Calculus tutoring
The student had just taken a test over some prerequisites for calculus, so he didn't have any new homework, but he did have some questions over the concepts he wanted to go over with that were on the test, so I addressed those for him. We also previewed the upcoming unit introducing derivatives.
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New Rochelle, NY Calculus tutoring
The student and I had a great session this morning--we worked through problems designed to treat a derivative as a function unto itself. Graphing an original function and its derivative on the same axes really cemented that for the student. We started to review some material from the second unit and will do a little more before moving on to a more comprehensive view of derivatives.
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New Rochelle, NY Calculus tutoring
I met with the student for the first time today. We went over her review sheet for her test on Friday. Topics covered included composite function and their domains, plotting a function over a specific domain and its inverse, transformations of functions, and finding the equation of a best fit line. The student was very comfortable with function transformations. She had just a little bit of trouble finding the best fit equation for some data she had plotted, so I showed her how to use the slope formula and the point-slope formula to do that. We also reviewed the concepts of domain and range.
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New Rochelle, NY Calculus tutoring
We covered conic section transformations: rotations and translations. We solved some specific problems by transforming the coordinate system into the canonical form without the mixed xy term. We considered the formula for the angle of rotation to get the canonical form. We drew a few examples of ellipses and hyperbolae, as well as parabolas in the rotated frame. We also covered coordinate system change into the polar coordinate system. We considered significance of r-intercepts, and the Theta-angle. The student's attitude towards the materials presented is very positive and creative. The student is able to find the most interesting parts in the subjects covered, and use his computer to generate unusual images based on simple formulas. I could see the level of overall understanding of the subject improve. To be ready for the exam on Thursday fully, some more drills will be welcome. The take home strategies from this lesson are a few: when trying to determine the type of the conic section from a general formula, first determine the coefficients of the quadratic terms. Then calculate the angle of rotation, then insert the new coordinates into the equation and determine the simplified formula of the conic section in the new coordinates. Another takeaway could be to memorize and use the discriminant to quickly determine the type of the conic section.
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