- WS1
- Graphical techniques for approximating the derivative as a function. Series of ``which is the function and which is the derivative'' problems. Intuitive peek at maximum/minimum problems. New technique: plotting two functions on one graph.
- WS2
- The book does a ``ball'' problem with initial velocity 96 (example 4). After extensive calculations, it turns out that the final velocity is -96. The authors make no comment about this remarkable coincidence. We return to the theme of using parameters to prove that v0 always equals vf and use this more general form of the answers to check that their dimensions are correct. To reinforce a more scientific attitude to such problems, an additional problem discusses the inverse square law effect. Other, simpler, word problems reinforce the use of parameters and/or the scientific approach towards assessing the reasonableness of proposed models. Finally, there is a problem involving a function defined by data instead of by formula.
- WS3
- Problem on inverse square law—this material will be referred to repeatedly throughout the year and is not treated at all in the text. New material:
D, Simplify, f'[x]. The theme is to use these tools to check calculations done by hand—not to use to replace drilling these fundamental tools (power rule, product rule, quotient rule).
- WS4
- Applied problems that call for using several equations. New material: Expand, Factor. Again, the theme is to use these tools to check calculations done by hand—not to use to replace drilling the fundamental chain rule (but the last problem is one that would be abysmal to do by hand).
- WS5
- Problem to check that the role of inverse functions in calculus is understood. New material: Together. Problem to make sure scope of the generalized power is understood. Problem that asks students to generalize from specific cases.
- WS6
- Optional worksheet testing whether the maximum value property and its application to the closed interval extremum problem is well understood by asking students to produce examples of various situations.
- WS7
- Word problem techniques including the text's ``5 step process'', ``plausibility'', and ``dimensional'' checks. Extra information on how to do the latter. Careful selection of max/min problems with usual emphasis on using parameters to get general solutions.
- WS8
- An important illustration of doing the general problem—here, a final question is posed that simply can't be tackled without keeping the parameters in the answer. More word problems and some trig differentiations with ``shape''.
- WS9
- Distinguish differentiating identities from differentiating equations. Use to compute implicit derivatives—first use of Solve (non-numeric context). Use of in graphing implicit functions. Students ask to generalize word problems and make use of their generalized solutions.
- WS10
- Note: this worksheet is superceded at Mines by a lab project. Manipulation of algebraic equations. Newton's method using . Introduction to Solve, NSolve and FindRoot. Application to the ``asteroid problem''.