Skip to main content
\(\newcommand{\Z}{\mathbb{Z}} \newcommand{\reals}{\mathbb{R}} \newcommand{\real}[1]{\mathbb{R}^{#1}} \newcommand{\fe}[2]{#1\mathopen{}\left(#2\right)\mathclose{}} \newcommand{\cinterval}[2]{\left[#1,#2\right]} \newcommand{\ointerval}[2]{\left(#1,#2\right)} \newcommand{\cointerval}[2]{\left[\left.#1,#2\right)\right.} \newcommand{\ocinterval}[2]{\left(\left.#1,#2\right]\right.} \newcommand{\point}[2]{\left(#1,#2\right)} \newcommand{\fd}[1]{#1'} \newcommand{\sd}[1]{#1''} \newcommand{\td}[1]{#1'''} \newcommand{\lz}[2]{\frac{d#1}{d#2}} \newcommand{\lzn}[3]{\frac{d^{#1}#2}{d#3^{#1}}} \newcommand{\lzo}[1]{\frac{d}{d#1}} \newcommand{\lzoo}[2]{{\frac{d}{d#1}}{\left(#2\right)}} \newcommand{\lzon}[2]{\frac{d^{#1}}{d#2^{#1}}} \newcommand{\lzoa}[3]{\left.{\frac{d#1}{d#2}}\right|_{#3}} \newcommand{\abs}[1]{\left|#1\right|} \newcommand{\sech}{\operatorname{sech}} \newcommand{\csch}{\operatorname{csch}} \newcommand{\lt}{ < } \newcommand{\gt}{ > } \newcommand{\amp}{ & } \)

PrefaceTo the Instructor

This version of the calculus lab manual is significantly different from versions prior to 2012. The topics have been arranged in a developmental order. Because of this, students who work each activity in the order they appear may not get to all of the topics covered in a particular week.

Additionally, a few changes have been introduced with the release of the MathBook XML version. The most notable changes are:

  • The numbering scheme does not match the earlier numbering scheme. This was a necessary consequence of converting to MathBook XML.

  • The related rates lab has been mostly rewritten using the DREDS approach.

  • In the implicit differentiation lab, a section on logarithmic differentiation has been added.

  • The printed version only contains short answers to the supplemental questions rather than complete walk-through solutions. However, complete solutions may still be found in the HTML version.

It is strongly recommended that you pick and choose what you consider to be the most vital activities for a given week, and that you have your students work those activities first. For some activities you might also want to have the students only work selected problems in the activity. Students who complete the high priority activities and problems can then go back and work the activities that they initially skipped. There are also fully keyed problems in the supplementary exercises that the students could work on both during lab time and outside of class. (The full solutions are only in the HTML version.)

A suggested schedule for the labs is shown in the table below. Again, you should choose what you feel to be the most relevant activities and problems for a given week, and have the students work those activities and problems first.

(Students should consult their syllabus for their schedule.)

Week Labs (Lab Activities) Supplementary
Exercises
1 Velocity through
Limits
Supplement 1.4
2 Limits Laws through
Piecewise-Defined Functions
Supplement 2.14
3 Instantaneous Velocity through
Derivative Units
Supplement 3.5
4 Graph Features through
Nondifferentiability
Supplement 4.7
5 Higher Order Derivatives through
Graphical Features from Derivatives
Supplement 4.7
6 Leibniz Notation through
Derivative Formulas and Function Behavior
Supplement 5.12
7 Introduction to the Chain Rule through
Chain Rule with Leibniz Notation
Supplement 6.5
8 General Implicit Differentiation through
Logarithmic Differentiation
Supplement 7.4
9, 10 Introduction to Related Rates\(\dagger\) through
Making Graphs
Supplement 8.3,
Supplement 9.8

\(\dagger\) Students should read the related rates examples before coming to lab.