## MATH 142: Elements of Calculus II Half Page Summaries

Hopefully, most of the students taking this class will be successful enough to hire someone to do calculus for them should the need arise. In this case the most important outcome of this class may be to recognize what calculus can do and what problems it is applicable to. To help realize this goal you will be asked to briefly summarize a week of lectures in your own words.

Summaries should be approximately one handwritten page (assuming wide ruled paper) or half a page typed. They should describe the key ideas presented in lecture but need not include calculations. They will be graded out of 10 points according to the following grading scheme:

• -1 point for missing a key idea (e.g. the product rule)
• -1 point for each extra half page (handwritten)
• -1 point for each sentence fragment
• -1 point for every 3 spelling or grammatical errors
• -5 points for copying a classmate's work
• -9 points for turning in copies of lecture notes, printed out web pages, or other things that aren't summaries

A sample half page summary for a Calculus I course (sections 2.6-3.2) is given below:

This week we learned about the derivative and how to calculate it. We found the instantaneous rate of change of a function by taking the limit of average rates of change. We saw from the graph that this equals the slope of the tangent line to the graph of the function. We practiced calculating this limit for different functions. This is called differentiation or finding the derivative of a function.

For some functions we can calculate derivatives without finding limits of slopes. We learned rules for derivatives of a constant, a constant multiple, x to a power, and a sum. We practiced these, then learned rules for derivatives of products and quotients.

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