Mathematica 9 is now available

Wolfram Library Archive


All Collections Articles Books Conference Proceedings
Courseware Demos MathSource Technical Notes
Title Downloads

The Lafayette College Calculus Laboratories--Third 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 third 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 third semester truly exploits the capabilities of Mathematica for great 3D graphics. See the linear programming Lab for a powerful example.

Topics:
  • Introduction to Second Order Differential Equations
  • Applications of Second Order Differential Equations
  • Geometric Linear Programming
  • Scalar Fields and Singularities
  • Critical Points for Scalar Fields
  • The Gradient
  • The Lagrange Multiplier Method
  • Multiple Integration
  • Storage Tank Design
  • 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--Second Semester   [in Courseware and Class Materials]
    Downloads Download Wolfram CDF Player

    Download
    README.txt (2.2 KB) - Author notes
    Download
    Lab-01.nb (40.2 KB) - Introduction to Second Order Differential Equations
    Download
    Lab-02.nb (54.5 KB) - Applications of Second Order Differential Equations
    Download
    Lab-03.nb (36 KB) - Geometric Linear Programming
    Download
    Lab-04.nb (27.8 KB) - Scalar Fields and Singularities
    Download
    Lab-05.nb (55.3 KB) - Critical Points for Scalar Fields
    Download
    Lab-06.nb (54.5 KB) - The Gradient
    Download
    Lab-07.nb (41.9 KB) - The Lagrange Multiplier Method
    Download
    Lab-08.nb (88.7 KB) - Multiple Integration
    Download
    Lab-09.nb (118.3 KB) - Storage Tank Design

    Files specific to Mathematica 2.2 version:
    Download
    Lab-01.ma (15.4 KB) - Introduction to Second Order Differential Equations
    Download
    Lab-02.ma (21.2 KB) - Applications of Second Order Differential Equations
    Download
    Lab-03.ma (18.7 KB) - Geometric Linear Programming
    Download
    Lab-04.ma (16.4 KB) - Scalar Fields and Singularities
    Download
    Lab-05.ma (29.2 KB) - Critical Points for Scalar Fields
    Download
    Lab-06.ma (20.1 KB) - The Gradient
    Download
    Lab-07.ma (16.8 KB) - The Lagrange Multiplier Method
    Download
    Lab-08.ma (40 KB) - Multiple Integration
    Download
    Lab-09.ma (59.6 KB) - Storage Tank Design