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The Lafayette College Calculus Laboratories--First Semester
Author

Robert Root
Organization: Lafayette College
Department: Mathematics
Education level

College
Objectives

The course differs from other Computer Algebra System-based Calculus sequences in several ways. The CAS is not in daily use by the students, they still must do most of their computations and algebra by hand. The CAS is included in a weekly laboratory only. This more conservative approach allows our laboratory with only 28 machines to serve a population of 250-300 calculus students a semester, with availability for occasional use by students in upper level courses as well. The laboratory is typically used to introduce students heuristically to a new topic before they encounter it in lecture or homework. We attempt to use the CAS to expose students to the concepts and techniques of calculus in (the now platitudinous) three ways: graphically, numerically, and symbolically.

Another goal of some labs is to introduce our students to applications that were previously too complex for beginning calculus students computational skills. Our sizable contingent of engineers are effectively motivated by this exposure, and increasingly are returning to Mathematica to solve their computational problems in courses beyond the calculus sequence.
Materials

Calculus, 5th edition by Swokowski (PWS)
Calculus, 4th edition by Stewart (Brooks Cole)

See below for the Mathematica notebook files for each of the laboratories. The packages in Packages.zip are required for all three semesters of this course.
Description

These laboratory materials represent the first semester in a three semester scientific and engineering calculus sequence developed at Lafayette College in Easton, Pennsylvania. These materials were assembled from a sequence of courses taught from Swokowski's Calculus, 5th edition, but they have been adapted and modified to fit the course taught from Stewart's text in its third and now its fourth edition. Throughout the changes in text the course has met three times per week in a conventional classroom setting and a fourth time in a Mathematica lab.

This course is meant to be only an incremental change from a traditional calculus course, introducing a CAS rather than a graphing calculator. While many of the labs could be implemented on a calculator, the graphics available on the computer screen are much better, and there are certain labs that use Mathematica's sophisticated graphical tools. For an example, see the rational functions lab or the Newton's method lab.

Topics:
  • Some Basics of Mathematics and Mathematica
  • Comparing Graphs of Functions
  • Estimating Limits
  • Secant Lines & Difference Quotients
  • Properties of Derivatives
  • Newton's Method of finding Roots
  • Extreme Values of Functions
  • Concavity & Derivatives
  • Rational Functions
  • Optimization
  • Area of a Region with Curved Boundary
  • Integrals, Areas and Average Temperatures
  • How Far to Harvard Square?
  • Subjects

    *Applied Mathematics > Optimization
    *Mathematics > Calculus and Analysis > Calculus
    Related items

    *The Lafayette College Calculus Laboratories--Second Semester   [in Courseware and Class Materials]
    *The Lafayette College Calculus Laboratories--Third Semester   [in Courseware and Class Materials]
    Downloads Download Wolfram CDF Player

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    LabReportSuggestions.txt (3.3 KB) - Plain-text file
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    PackagesREADME.txt (957 B) - Text file
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    README.txt (2.2 KB) - Author notes
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    Lab-01.nb (35.4 KB) - Some Basics of Mathematics and Mathematica
    Download
    Lab-02.nb (66.6 KB) - Comparing Graphs of Functions
    Download
    Lab-03.nb (37.6 KB) - Estimating Limits
    Download
    Lab-04.nb (24 KB) - Secant Lines and Difference Quotients
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    Lab-05.nb (29.4 KB) - Properties of Derivatives
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    Lab-06.nb (35.9 KB) - Newton's Method for Finding Roots
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    Lab-07.nb (31 KB) - Extreme Values of Functions
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    Lab-08.nb (36.4 KB) - Concavity and Derivatives
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    Lab-09.nb (31 KB) - Rational Functions
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    Lab-10.nb (231.7 KB) - Optimization
    Download
    Lab-11.nb (34.7 KB) - Area of a Region with Curved Boundary
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    Lab-12.nb (39.1 KB) - Integrals, Areas and Average Temperatures
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    Lab-13.nb (24.2 KB) - How Far to Harvard Square?
    Download
    LabReportSuggestions.hqx (8.9 KB) - Macintosh format Word document
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    Mystery.m (1.2 KB) - For use with Lab-07.ma
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    Packages.zip (8.2 KB) - ZIP archive
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    RationalGraphics.m (18 KB) - For use with Lab-09.ma includes a command for putting rational functions in proper form.

    Files specific to Mathematica 2.2 version:
    Download
    Lab-01.ma (17.4 KB) - Some Basics of Mathematics and Mathematica
    Download
    Lab-02.ma (29.5 KB) - Comparing Graphs of Functions
    Download
    Lab-03.ma (22 KB) - Estimating Limits
    Download
    Lab-04.ma (14.1 KB) - Secant Lines and Difference Quotients
    Download
    Lab-05.ma (12.8 KB) - Properties of Derivatives
    Download
    Lab-06.ma (17.4 KB) - Newton's Method for Finding Roots
    Download
    Lab-07.ma (15.3 KB) - Extreme Values of Functions
    Download
    Lab-08.ma (18.4 KB) - Concavity and Derivatives
    Download
    Lab-09.ma (16.1 KB) - Rational Functions
    Download
    Lab-10.ma (194.7 KB) - Optimization
    Download
    Lab-11.ma (19 KB) - Area of a Region with Curved Boundary
    Download
    Lab-12.ma (22.1 KB) - Integrals, Areas and Average Temperatures
    Download
    Lab-13.ma (18.1 KB) - How Far to Harvard Square?