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The Lafayette College Calculus Laboratories--Second 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 required for these notebooks can be found in the file Packages.zip under the entry for the first semester of this course (Resource Library Database item 4304).
Description

These laboratory materials represent the second 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.

The second semester has evolved considerably from the form presented here. People interested in more recent versions of these labs should contact the author.

Topics:
  • The Natural Logarithm Function
  • Exponential Growth
  • Logistic Growth
  • Direction Fields
  • Hyperbolic Trigonometric Functions and Their Inverses
  • Limits and Indeterminate Forms
  • Infinite Sequences and Series
  • A Model for an Epidemic
  • Approximating Functions with Polynomials
  • Power Series Representations of Functions
  • Parametric Equations
  • The Length of a Curve
  • Polar Coordinates
  • Area in Polar Coordinates
  • Subject

    *Mathematics > Calculus and Analysis > Calculus
    Related items

    *The Lafayette College Calculus Laboratories--First 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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    README.txt (2.2 KB) - Author notes
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    Lab-01.nb (32 KB) - The Natural Logarithm Function
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    Lab-02.nb (43.6 KB) - Exponential Growth
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    Lab-03.nb (45 KB) - Logistic Growth
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    Lab-04-HW.nb (38.9 KB) - Laboratory 4 Homework
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    Lab-04.nb (22.7 KB) - Direction Fields
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    Lab-05.nb (27.7 KB) - Hyperbolic Trigonometric Functions and Their Inverses
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    Lab-06.nb (133.2 KB) - Limits and Indeterminate Forms
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    Lab-07.nb (110 KB) - Infinite Sequences and Series
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    Lab-08.nb (38.9 KB) - A Model for an Epidemic
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    Lab-09.nb (46.6 KB) - Approximating Functions with Polynomials
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    Lab-10.nb (93.2 KB) - Power Series Representations of Functions
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    Lab-11.nb (88 KB) - Parametric Equations
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    Lab-12.nb (46.2 KB) - The Length of a Curve
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    Lab-13.nb (28.2 KB) - Polar Coordinates
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    Lab-14.nb (104.4 KB) - Area in Polar Coordinates
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    dataset1.dat (125 B) - US Census population data used in Lab-02.nb and Lab-03.nb
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    dataset2.dat (248 B) - US Census population data used in Lab-02.nb and Lab-03.nb

    Files specific to Mathematica 2.2 version:
    Download
    Lab-01.ma (14.5 KB) - The Natural Logarithm Function
    Download
    Lab-02.ma (19.3 KB) - Exponential Growth
    Download
    Lab-03.ma (24.1 KB) - Logistic Growth
    Download
    Lab-04-HW.ma (15.7 KB) - Laboratory 4 Homework
    Download
    Lab-04.ma (9.7 KB) - Direction Fields
    Download
    Lab-05.ma (13.5 KB) - Hyperbolic Trigonometric Functions and Their Inverses
    Download
    Lab-06.ma (74.6 KB) - Limits and Indeterminate Forms
    Download
    Lab-07.ma (53.6 KB) - Infinite Sequences and Series
    Download
    Lab-08.ma (15 KB) - A Model for an Epidemic
    Download
    Lab-09.ma (18.7 KB) - Approximating Functions with Polynomials
    Download
    Lab-10.ma (46.3 KB) - Power Series Representations of Functions
    Download
    Lab-11.ma (41.3 KB) - Parametric Equations
    Download
    Lab-12.ma (18.4 KB) - The Length of a Curve
    Download
    Lab-13.ma (15.4 KB) - Polar Coordinates
    Download
    Lab-14.ma (44.9 KB) - Area in Polar Coordinates